Hierarchical Integration of Planning and Scheduling for Industrial

Article pubs.acs.org/IECR

Hierarchical Integration of Planning and Scheduling for Industrial Waste Incineration Matteo L. Abaecherli,† Elisabet Capón-García,*,† Philipp Steinleitner,‡ Oliver Weder,† Andrej Szijjarto,§ and Konrad Hungerbühler† †

Institute of Chemical and Bioengineering, ETH Zürich, Vladimir-Prelog-Weg 1, 8093 Zürich, Switzerland Department of Chemistry, TU München, Lichtenbergstraße 4, 85748 Garching, Germany § Energy & Waste Management, Lonza AG, Rottenstr. 6, 3930 Visp, Switzerland ‡

S Supporting Information *

ABSTRACT: This works aims to demonstrate that hierarchical integration of planning and scheduling of industrial waste incineration improves the energy efficiency of the process, compared to available scheduling approaches. Through the integration with planning models, scheduling models can rely on more far-sighted information; therefore, energy deficits and excesses can be better compensated in the long run. Subsequently, the auxiliary fuel consumption of the incineration process can be further reduced, which leads to an overall increase of the energy efficiency. Planning and scheduling models are formulated as mixed-integer linear programming (MILP) problems with discrete time representation, based on single, uniform grids. The considered waste incineration system consists of storage tanks, a complex piping network, tank wagons for waste transport, unloading stations, and firing lances of incineration units. The conducted industrial case studies reveal substantial improvement potential of daily empirically based waste incineration routines and show that systematic integration of planning and scheduling outperforms consecutive stand-alone scheduling of industrial waste incineration both economically and environmentally by reducing auxiliary fuel usage and CO2 emissions per ton of waste treated, by 16% and 1%, respectively.

1. INTRODUCTION Hazardous waste incineration is an established waste-to-energy (WtE) technology encountered all over the process industry.1 Its advantages include (i) the significant reduction of waste volume, (ii) the elimination of hazardous substances, (iii) the thermal valorization of waste, and (iv) the possibility to treat waste close to its generation sites, thus reducing transport distances.2,3 Consequently, hazardous waste incineration is especially suited for energy-intensive sectors of the process industry with high waste production, such as the chemical one. In fact, major chemical sites often have their own in-house treatment units. Even though waste management has been identified to offer large opportunities for systematic optimization and process improvements,4 there have been only limited efforts to systematically support decision makers in industrial waste incineration management so far. Therefore, decision makers nowadays still rely on empirical approaches to define waste treatment strategies based on different and often conflicting criteria and targets. This is especially challenging in view of the problem complexity, as well as the limited time frame to make decisions and execute tasks, such as waste transfer from the production to the incineration sites, the allocation of waste to temporary storage and/or treatment units, the mixing of compatible waste streams, and the © XXXX American Chemical Society

operation of the incineration ovens. Moreover, these tasks must be sequenced and organized such that holdups in the production are avoided, technical and legal constraints are always respected, and resources are deployed as efficiently as possible in the long run.4,5 Specifically, decision makers are responsible to derive waste generation forecasts, from a midterm production plan, which are further translated into incineration goals with corresponding inventory requirements. Based on these goals, they then assign and arrange tasks and resources to specific units and operations in detail for a shortertime frame. Similar courses of action can be found all over the process industry, where tactical planning is required to generate overall production, inventory, distribution or sales plans based on customer or market information and short-term planning, also known as scheduling, is carried out to allocate resources and tasks to different units at the production level according to imposed plans.6−9 Research efforts in process system engineering, focusing mainly on supply chain management as well as Received: Revised: Accepted: Published: A

March 27, 2017 May 24, 2017 June 9, 2017 June 11, 2017 DOI: 10.1021/acs.iecr.7b01250 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

Article

Industrial & Engineering Chemistry Research process and product planning,6,9−11 have shown that the combination of short-term scheduling with more far-sighted and aggregated planning allows one to (i) allocate resources more efficiently,12 (ii) increase production flexibility,9 (iii) provide detailed scheduling information for relative long planning horizons to decision makers,10 and (iv) substantially increase economic benefits.13 Still, because of different objective functions and resolutions, the integration of both planning and scheduling models remains often a challenging task10 and can lead to a significant increase in model size and, thus, excessive solution times.14 This is especially true in the case of large problems with strongly fluctuating demand and high equipment utility, such as waste incineration, as they require to find feasible solutions close to system limits.6 To our knowledge, industrial waste incineration scheduling and planning has been only attempted as an independent nonintegrated entities so far. Heretofore, Wassick4 introduced a long-term scheduling model to systematically support decision-making in industry. The process scheduling problem was formulated as a discrete time resource-task-network and consisted of (i) resources, such as treatment units, pipes, storage tanks, waste streams, and (ii) tasks, such as material transfers from one unit to another and the operations of units. Tests in industry revealed potential economic benefits when using systematic modeling and optimization to schedule waste treatment. Furthermore, the importance of efficient waste treatment in order to avoid holdups in the production processes was emphasized. More recently, Abächerli et al.15 introduced a novel mathematical methodology able to optimize short-term waste incineration schedules in industry. The optimization model was formulated as a mixed-integer linear programming (MILP) model and had the objective of reducing the usage of auxiliary fuel, while respecting all technical and regulatory constraints imposed. The incineration was driven by rewarding waste treatment and penalizing excessive storage. The underlying system represented a typical industrial incineration site including a piping network as well as different incineration furnaces, firing lances, storage tanks, tank wagons for waste transport, and unloading pumps. Results in collaboration with an industrial partner indicated potential process cost reduction due to reduced usage of the auxiliary fuel, which lead further to (i) a reduction of the workload and thus to an increase of the flexibility of the incineration units; (ii) a reduction of fume production per ton of waste treated and, thus, to a workload reduction of the fumes cleaning units, as well as reduced CO2 emissions. In view of the complex nature of industrial waste incineration problems, where logistics and inventory management, in addition to operational optimization, are key challenges that must be sequenced based on medium or long-term goals, while respecting all technical and legal constraints, and the lack of farsighted and high-resolution optimization tools in the field, this work aims to introduce and integration strategy for planning and scheduling able to support decision maker in industrial routines. In the literature, different methods of integrating scheduling and planning problems have been proposed, such as (i) full-space methods, (ii) hierarchical methods, or (ii) iterative methods.6,11 Full-space problems have the main disadvantage that they have a limited applicability for real-world problems if solved rigorously, as they scale poorly with model size. Although there are different techniques that allow one to cope with large-scale problems9,12,16 and such problems could also be solved unrigorously, the application of full-space

methods on smaller problems with tight formulations remains the rule.11 For this reason, the full-space integration method is unsuitable for industrial waste incineration, which is a very complex and large problem, as seen in previously introduced scheduling approaches.15 Alternatively, the hierarchical problem decomposition, performed in hierarchical and iterative integration methods, has proven to be a more suitable technique to tackle integrated planning and scheduling tasks in real-world problems.14 Thereby, the problems are decomposed in upper and lower subproblems, where targets or high-level decision are passed top-down. The difference between these two integration methods resides in the possibility to transfer information bottom-up during the solution process. In iterative methods, planning models obtain scheduling performance information during the solution process, thus allowing them to adapt their high-level decisions, based on scheduling performance information, and eventually obtain optimal solutions.6,11 Because of the feedback loop between planning and scheduling, iterative integration methods are considered to be quite promising; still, their application remains formulation-specific and, therefore, difficult to adapt to other problems.6 In contrast, in hierarchical methods, no bottom-up information transfer occurs during the solution process. The top-down information flow bears the risk that no feasible solution is found. To overcome this problematic, different techniques have been introduced to determine nearby feasible solutions, e.g., heuristics rules can be applied to derive feasible schedules from unfeasible solutions or approximated scheduling models can be applied in the upper level, thus providing more-realistic plans.6,11 Alternatively, a bilevel hierarchical decomposition algorithm, known as the rolling horizon approach, can be applied. In the rolling horizon approach, short-term schedules for all subhorizons of a finite or infinite planning horizon can be obtained iteratively, following an optimized long-term planning strategy, which is updated after each iteration.14 In every iteration step, only the most recent subhorizons are solved rigorously, while the remaining ones are kept in aggregate form. Consequently the problems can be solved with reasonable computational effort.14,17 Despite the iterative nature of the approach, the rolling horizon methodology cannot be classified as iterative integration methods, because there is no bottom-up information transfer during the solution process.6 Still, the twoway interplay between planning and scheduling in this approach allows one to implement detailed solutions of already-solved subhorizons in the planning level directly, thus influencing the definition of high-level decisions and targets for future subhorizons. Not surprisingly, various application of the rolling horizon in the process industry can be found in the literature, especially dealing with problems concerning transportation and logistics, supply chain, inventory management, energy supply as well as production, process and strategic planning.6,9−11,17−21 Contrary to iterative methods, hierarchical approaches are not strictly formulation-specific.6 Consequently, established rolling horizon strategies could be adopt in the industrial waste incineration problem, especially those dealing with operation planning and logistics and storage management, as these are key issues of the waste incineration problem.15 In view of the above-mentioned benefits of the rolling horizon approach, which is an established integration method constituting good compromises between modeling accuracy and computational effort, as well as allowing for partial bottomup information flow, in this work, we hierarchically integrate B

DOI: 10.1021/acs.iecr.7b01250 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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Industrial & Engineering Chemistry Research

Figure 1. Simplified overview of waste incineration systems. The left side of the figure shows the system overview of the scheduling level; the right side of the figure shows the system overview of the planning level, in which unloading pumps are disregarded.

planning and scheduling of industrial waste incineration, according to the rolling horizon approach. In doing so, we intend to provide systematic support to decision makers in industrial waste incineration routines in order to increase the process efficiency, which has been proven to increase the process profitability and sustainability.15 The subsequent sections are structured as follows: First, a brief overview of the considered waste incineration system is provided and the problem is defined. Then, the rolling horizon framework is introduced and the planning and scheduling models are described. Next, an illustrative example and an industrial case study are assessed to demonstrate benefits and applicability of the introduced methodology. Finally, the obtained results are discussed and conclusions are drawn.

emissions to the atmosphere per ton of treated waste are reduced.15 The objective of this work is to hierarchically integrate planning and scheduling of liquid industrial waste incineration in order to improve the energy efficiency, which consequently reduces the costs and the environmental impact of the process. This is achieved by systematically minimizing the overall auxiliary fuel consumption, through smart management of logistics, mixing, and treatment policies of waste streams with different energy content. Given the following: • a finite planning and scheduling horizons with discrete time representation; • a set of fully characterized waste streams including the elemental analysis, pollutant loads and key physicochemical characteristics, such as density, pH, and heat of combustion; • waste production forecasts for both the scheduling and planning horizon; • an incineration system including tank wagons for waste transfer and storage tanks with given material composition and capacity, a piping network with given pumping rates as well as unloading pumps and incineration lances with given volumetric throughputs; • a set of compatibility constraints on waste mixing and storage; • a set of connectivity constraints between all processing, storage, and transfer equipment; • a set operational and technical constraints of the incineration units, including the size of the combustion chamber, the required temperature range as well as the maximal fume production rate and auxiliary fuel supply rate; • a set of legal emissions constraints; and • a set of economic data describing waste specific treatment as well as storage and auxiliary fuel consumption costs; The objective is to provide (i) a plan, containing • expected storage occupancy and incineration performance; • short-term incineration targets; • estimations on the economic performance; where the consumption of auxiliary fuel is minimized through efficient mixing, storage and treatment of waste streams with different energy content and the incineration is triggered by

2. PROBLEM STATEMENT The general liquid waste incineration system considered in this work has been described earlier by Abaecherli et al.15,22 It consists of waste storage tanks, a complex piping network, tank wagons for waste transport, unloading stations, and firing lances of the incineration units. The waste management and incineration problem considered in this work includes all tasks related to waste transfer, storage, mixing, and treatment, which occur after waste is generated and directly stored in tanks at different production facilities. Figure 1 provides a schematic overview of the waste incineration system considered in the scheduling and planning models. As it can be seen, unloading pumps are disregarded in the planning level. Therefore, the reason is that planning is sought to provide long-term strategictargets and not detailed, high-resolution schedules; therefore, waste transfer logistics in the planning model can be simplified, compared to the scheduling model. Auxiliary fuel, such as natural gas, is used in case of energy deficits to reach and maintain the minimum required incineration temperature, which guarantees a continuous and complete combustion of the waste. Appropriate mixing and scheduling of waste with different energy content can prevent energy deficits or excesses during the incineration process, leading to reduced auxiliary fuels consumption. As a direct consequence, (i) the operating costs of the incineration process decrease, (ii) the workload of the incineration units decrease (and, thus, the flexibility of the operation and the treatment capacity increase), (iii) the amount of fumes to the cleaning units per ton of waste treated decreases (thereby reducing the use of water, electricity, and chemicals), and finally (iv) the C


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Figure 2. Basic concept of a rolling-horizon approach with finite planning horizon. The active subhorizon is shown in gray, aggregated subhorizons are shown in white, and fixed subhorizons are cross-hatched. Black arrows indicate waste treatment targets that are obtained from the planning models and are imposed to scheduling models; white arrows represent the transfer of the final waste stocks in the different storage tanks to the planning models.

obtained, which can vary from run to run. Finally, fixed subhorizons are former active subhorizons for which a detailed schedule is already available. Thus, no new schedule or plan needs to be calculated for them.14 Figure 2 illustrates the rolling horizon concept, based on an example of a finite planning horizon split into four subhorizons, where, in each iteration step, both planning and scheduling problems are solved sequentially and information is shared between the two temporal levels. It can be seen that active subhorizons shift in time with every iteration and the number of aggregate subhorizons decrease with every iteration step, while the number of fixed ones increases. 3.1. Hierarchical Integration of Planning and Scheduling. Planning and scheduling are integrated according to the rolling horizon approach described above. The long-term goal consists in minimizing the use of auxiliary fuel over the finite planning horizon, thus improving cost efficiency and sustainability of the incineration process and delivering detailed short-term schedules to support decision-making in daily routines. The detailed schedules are obtained consecutively, based on waste treatment targets imposed by the planning level, and by trying to minimize auxiliary fuel consumption. Throughout the introduced rolling horizon approach, the targets are adapted in every iteration step, according to the resulting schedules. The iteration scheme of the rolling horizon approach is shown in Figure 3. At the beginning of every iteration step j, the jth subhorizon (SHj) is set as active subhorizon SHact. All remaining subhorizons [SHj+1...SHjend] are set as aggregate subhorizons SHagg. Next, the planning model is solved for the horizon comprising the active subhorizon SHact and all aggregated ones SHagg with the objective being to minimize the auxiliary fuel consumption. As a result, incineration targets for the active subhorizon SHact are obtained, which, in a next step, are set as objectives for the scheduling of the active subhorizon SHact. Then, trying to fulfill the imposed targets and minimizing auxiliary fuel consumption, the scheduling model is solved for the active subhorizon SHact only. The obtained shortterm schedule is used to calculate the initial waste stock at the production facilities V0w and the initial amount of waste stored in intermediate storage tanks VI0 w for the upcoming subhorizon.

rewarding waste treatment and penalizing excessive storage. AS an additional objective, we want to provide (ii) detailed shortterm schedules for waste incineration, containing • high-resolution incineration plans and expected incineration performance data, including temperature, auxiliary fuel consumption, fumes production, and pollution load; • high-resolution waste transfer information including transfer type, source, destination, quantity, starting time, and duration; • a detailed storage inventory; • mixing recipes including involved waste streams, location, quantity, starting time, and duration; and • a detailed overview over the short-term economic performance; These efforts are pursued so that the imposed treatment targets are met as closely as possible and the consumption of auxiliary fuel is minimized.

3. METHODOLOGY In this work, planning and scheduling are integrated according to a bilevel hierarchical decomposition algorithm known as rolling horizon. However, since it has no bottom-up feedback in the solution process, the iterative nature of this approach allows only part of the planning horizon (a subhorizon) to be solved rigorously in each iteration step, while the rest is represented in an aggregated form. Furthermore, the iterative two-way interplay between planning and scheduling allows unaccomplished tasks to be carried over from a subhorizon to the next, thus allowing one to obtain planning and scheduling solutions, with reduced computational effort.14,17 In the rolling horizon, short-term schedules for all subhorizons of a finite or infinite planning horizon are obtained iteratively, following an optimized long-term planning strategy, which is updated after each iteration. Thereby, the planning horizon can be divided into active, aggregated, and fixed subhorizons. Active subhorizons are subhorizons for which a detailed schedule is obtained in a given iteration step. With each iteration, they shift forward in time. Aggregated subhorizons are those subhorizons that follow the active ones. For them, in each iteration, only a less-detailed plan is D


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to support decision-making in industry in the long run systematically. The production facilities are modeled as waste inventories that provide the amount of waste stored locally at the end of each time period mPF,plan of the planning horizon (eq 3). Vin,plan w,τ w,τ indicates the waste inflow for each period of the planning horizon τ, and V0w gives the initial waste stock. From the production facilities, waste can either be sent to intermediate storage tanks msto,plan or directly to the incineration units w,i,τ mdir,plan . The amount of waste that can be stored at the w,1,τ production facilities is limited by VPF w (see eq 4). in,plan mwPF,plan = V w0·ρw |τ = 1 + mwPF,plan ,τ , τ − 1 |τ > 1 + Vw , τ · ρw −

∑ (mwsto,plan ,i,τ ) i

−

∑

(mwdir,plan ,l ,τ )

∀ w, τ

≤ VwPF

∀ w, τ

(3)

l

mwPF,plan ,τ ρw

(4)

In eq 5, the amount of waste that can be transferred from the production facilities to intermediate storage tanks msto,plan is w,i,τ limited by the tank volumes VIi . Furthermore, waste that must be incinerated directly cannot be stored intermediately. Thus, msto,plan is zero for all waste streams (w ∈ wdirect ) . The binary w,i,τ w variables bsto,plan indicates whether or not waste stream w is w,i,τ being transferred to storage tank i in period τ. Every storage tank can receive up to Nsto1,plan different waste streams (eq 6) and each waste stream can be sent to maximally Nsto2,plan different intermediate storage tanks in any period (see eq 7).

Figure 3. Iteration scheme of the rolling horizon approach. The dark gray box includes operations and outputs linked to planning, while the light gray box includes operations and outputs linked to scheduling. j is the iteration variable and jend is the final iteration and correspond to the total number of subhorizons considered. SHj represents the jth subhorizons, while SHact, SHagg, and SHfix represent the active, aggregate, and fixed subhorizons, respectively.

mwsto,plan ,i,τ

comp I ≤ bwsto,plan ∪ w ∉ wwdirect) , i , τ · Vi ∀ w , i , τ |((w , i) ∈ wiw , i

ρw

mwsto,plan =0 ,i,τ

is derived from the final stock level at the production act facilities mPF and the density of w,t of the active subhorizon SH I0 waste streams ρw (eq 1), while Vw is derived from the final amount of waste stored in intermediate storage tanks mIw,i,t of the active subhorizon SHact and ρw (eq 2).

∀ w , i , τ |((w , i) ∉ wiwcomp ∪ w ∈ wwdirect) ,i

V0w

V w0|iter j + 1 =

VwI0|iter j + 1 =

mwPF, t ρw

⎞ ⎟⎟ ⎝ ρw ⎠ w,i,t

∀ i , τ |i ∈ wiwcomp ,i (6)

≤ N sto2,plan ∑ bwsto,plan ,i,τ

∀ w , τ|(w ∈ wiwcomp ∪ w ∉ wwdirect) ,i

i

(7)

In eq 8, the amount of waste that can be transferred directly from the production facilities to incineration lances mdir,plan is w,1,τ limited by maximum lance throughput for every period Vmax,plan . l The binary variables bdir,plan indicate whether or not waste w,1,τ stream w is being transferred to incineration lance l in period τ. Every incineration lance can receive up to Ndir1,plan different waste streams (eq 9) and each waste stream can be sent to maximally Ndir2,plan different incineration lances in any period (eq 10).

∀ w , t |t = t end iter j

bwsto,plan ≤ N sto1,plan ,i,τ

w ∉ wwdirect

(1)

⎛ mI

i

∑

∀ w , t |t = t end iter j

∑ ⎜⎜

(5)

(2)

Finally, the obtained short-term schedule is then fixed for the remaining iterations and the active subhorizon SHact is attributed to the fixed subhorizons SHfix. These steps are repeated until all subhorizons are fixed and thus detailed schedules are available for all of them. If necessary, the waste production forecast can be updated between iterations. 3.2. Planning Model. The objective of the planning model is to determine the most efficient incineration solution in the long run and derive short-term treatment targets, which are then imposed on the scheduling models. The planning model is derived from the scheduling model introduced by Abächerli et al.,15 especially the link of logistical and operational aspects and the objective function were partially adopted. The general structure of the planning model coincides further with the waste treatment enveloped introduced by Wassick4 that is used

mwdir,plan ,l ,τ ρw

max,plan ≤ bwdir,plan ∀ w , l , τ |(w , l) ∈ wlwpipe , l , τ · Vl ,l

mwdir,plan =0 ,l ,τ

≤ N dir1,plan ∑ bwdir,plan ,l ,τ

∀ w , l , τ |(w , l) ∉ wlwpipe ,l

∀ l , τ |l ∈ wlwpipe ,l

w

≤ N dir2,plan ∑ bwdir,plan ,l ,τ l

E

∀ w , τ |w ∈ wlwpipe ,l

(8)

(9)

(10)


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L,plan mw,l,τ is limited by the minimum and maximum lance throughput per time period (Vmin,plan , Vmax,plan ) . The binary l l inc,plan variable bl,τ indicates whether or not a waste stream w an incineration lance l is used to incinerate waste in period τ. Furthermore, the pollution charge of the incinerated waste, obtained from mL,plan w,l,τ and the waste-specific pollution load Pw,x should not exceed given thresholds Pmax,plan (see eq 22). k,x

Similar to waste inventories at the production facilities described in eq 3, the waste inventories for intermediate storage I0 tanks mI,plan w,i,τ can be derived (eq 11), where Vw,i gives the initial IL,plan waste stock and mw,i,1,τ indicates the amount of waste being sent to incineration in each period. I0 I,plan sto,plan mwI,plan − , i , τ = Vw , i· ρw |τ = 1 + mw , i , τ − 1|τ > 1 + mw , i , τ

∑ mwIL,plan ,i,l ,τ l

∀ w, i, τ

dir,plan mwL,plan, + , l , τ = mw , l , τ

(11)

⎛ m I,plan ⎞ w,i,τ ⎟ ≤ ViI ⎟ ⎝ ρw ⎠

w

mwI,plan ,i,τ ρw

blinc,plan ·Vlmin,plan ≤ ,τ

w

(12)

∑ bFI,plan f ,i,τ ≤ 1

∀ w , f , i , τ |(w , f ) ∈ wfw , f

∑

bfWI,plan ≤1 ,i,τ

(14)

mkF,plan ,y ,τ =

y

∑ i ∈ ilipipe ,l

(17)

∀ i , τ |i ∈ ilipipe ,l (18)

IL2,plan bwIL,plan ,i,l ,τ ≤ N

∀ k, y, τ

l ∈ lkl , k

⎛ m F,plan ⎞ k ,y,τ ⎟ ≤ VkF,plan Tkmax ⎟ ρ ⎝ k ,y ⎠

∀ k, τ (25)

The energy released through combustion in an incinerator at any time period qcomb,plan is obtained in eq 26 from the amount k,τ G,plan of waste and auxiliary fuel incinerated (mL,plan w,l,τ , mk,τ ) as well as from the higher heating values of the different waste streams and the auxiliary fuel (Hw, HG) . In eq 27, qcomb,plan is limited by k,τ lower and upper energy limits (qmin,plan , qmax,plan ), which are k,τ k,τ derived from the energy released by cooling the produced fumes and the maximal and minimal allowed temperatures max (Tmin k , Tk ) of each incineration unit as well as the specific heat capacities of the various compounds produced in the incineration reaction (see eqs 28 and 29). By introducing the inequality in eq 27, nonlinearities that arise in the energy balance can be avoided. A more-detailed description regarding how nonlinearities can be avoided when modeling the energy balance can be found in the work of Abaecherli et al.15

w

IL1,plan bwIL,plan ,i,l ,τ ≤ N

G,plan G (mwL,plan ·Y y , l , τ · Yw , y) + mk , τ

∑ ⎜⎜

∀ i , l , τ |(i , l) ∈ ilipipe ,l

l ∈ ilipipe ,l

∀ k, τ

(24)

The binary variable indicates whether or not a waste stream w is being transferred from a tank i to an incineration lance l in period τ (see eq 17). This is only possible if there is a pipe connection between tank i and lance l ((i,l) ∈ ilpipe i,l ). If this is not the case, mIL,plan w,i,l,τ = 0 at all times. In any period τ, every lance can only receive up to NIL1,plan different waste streams (eq 18) and each waste stream can be sent maximally to NIL2,plan different lances (eq 19).

∑

∑ ∑ w

(16)

∀ i , l , τ |(i , l) ∉ ilipipe ,l

(22)

(23)

IL,plan bi,l,τ

mwIL,plan ,i,l ,τ = 0

∀ k, x, τ

l ∈ lkl , k

From the amount of waste and auxiliary fuel combusted at a G,plan given time period (mL,plan w,l,τ , mk,τ ), as well as from the waste- or fuel-specific fumes production (Yw,y, YGy ), the amount of fume components produced in an incineration unit during a given F,plan time period mk,y,τ is obtained using eq 24. A detailed description on deriving Yw,y and YGy can be found in the work of Abaecherli et al.15 The total amount of fumes produced in any time period is limited by VF,plan . k

∀ i, τ

IL,plan ∑ mwIL,plan , i , l , τ ≤ bi , l , τ · M

≤

Pkmax,plan ,x

bkG,plan ·MkGmin,plan ≤ mkG,plan ≤ bkG,plan ·MkGmax,plan ,τ ,τ ,τ

(13)

(15)

w ∉ wwmix

∀ l, τ

The amount of auxiliary fuel used to overcome energy deficits in each incineration unit mG,plan is constrained by k,τ minimum and maximum lances throughput per time period (MGmin,plan , MGmax,plan ). k k

∀ i, τ

f

(mwL,plan , l , τ · Pw , x)

∑ ∑

Equation 14 determines the binary variable bFI,plan f,i,τ , which indicates whether or not a waste family f is stored in tank i in period τ. Only one waste family f can be attributed to any intermediate storage tank in any period (eq 15). Nonmiscible waste streams (w ∉ wmix w ) cannot be stored with other waste streams in any period (eq 16). bwWI,plan ≤ bFI,plan ,i,τ f ,i,τ

⎛ m L,plan ⎞ w,l ,τ ⎟ inc,plan max,plan · Vl ⎟ ≤ bl , τ ρ ⎝ w ⎠

(21)

∀ i, τ

∀ w , i , τ |(w , i) ∉ wiwcomp ,i

(20)

∑ ⎜⎜ w

I comp ≤ bwWI,plan , i , τ · Vi ∀ w , i , τ |(w , i) ∈ wiw , i

mwI,plan ,i,τ = 0

∀ w, l, τ

i

The total amount of waste stored in a tank is limited by the tank volume VIi (eq 12). Equation 13 is used to derive the binary variable mWI,plan w,i,τ , which indicates whether or not waste stream w is stored in tank i in any period τ. If waste stream w is I,plan not compatible with tank i ((w,i) ∉ wicomp w,i ), mw,i,τ = 0.

∑ ⎜⎜

∑ (mwIL,plan ,i,l ,τ )

∀ l , τ |l ∈ ilipipe ,l (19)

qkcomb,plan = ,τ

∑ ∑ w

The total amount of waste incinerated through a specific lance in any time period mL,plan is constituted by waste w,l,τ originating directly from the production facilities mdir,plan and w,l,τ IL,plan from intermediate storage tanks mw,i,l,τ (eq 20). In eq 21,

G,plan (mwL,plan ·H G , l , τ · Hw) + mk , τ

∀ k, τ

l ∈ lkl , k

(26)

qkmin,plan ,τ

F

≤

qkcomb,plan ,τ

≤

qkmax,plan ,τ

∀ k, τ

(27)


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qkmin,plan ,τ

⎛ ⎞ ⎛ Tkmin T0 ⎞ ⎜ F,plan ⎜ Cpk , y + Cpy ⎟ min 0 ⎟ = ∑ ⎜mk , y , τ ·⎜ ⎟⎟ ·(Tk − T )⎟⎟ ⎜ 2 y = H 2O ⎜ ⎝ ⎠ ⎝ ⎠

⎛ ⎛⎛ Tkmin ⎞⎞ T cond ⎞ ⎜ F,plan ⎜⎜ Cpk , y + Cpy ⎟ min cond H 2O cond 0 vap⎟⎟ + ∑ ⎜mk , y , τ ·⎜⎜ − T ) + ΔH ⎟⎟ ⎟⎟ ·(Tk − T ) + Cp ·(T 2 ⎜⎜ ⎟⎟ y = H 2O ⎜ ⎝ ⎠ ⎝ ⎠⎠ ⎝

qkmax,plan ,τ

The main objective of the planning model is to reduce the overall auxiliary fuel consumption over time, thus improving the energy efficiency and reducing the environmental impact of the incineration process. In addiiton, analogous to the work of Abaecherli et al.,15 the incineration must be triggered by penalizing excessive storage at the production facilities and by rewarding waste treatment. All these elements can be included in one single objective function weighted by their financial impact, in order to have a common basis for comparison (see eq 30). z plan = costG,plan + costS,plan − rev plan

(30)

The total cost of auxiliary fuel consumption (cost ) can be derived by the amount of auxiliary fuel consumed in each period of the planning horizon mG,plan and by considering the k,τ unit price of auxiliary fuel (CG) (see eq 31). G ∑ ∑ (mkG,plan , τ )·C

(31)

τ

z=

S,plan

The costs for additional storage (cost ) are dependent on the waste-specific charges CS,plan that occur in all periods of the w planning horizon, depending on the amount of excess waste storage σ−,plan (see eq 32). Excess waste storage σ−,plan and the w,τ w,τ remaining free storage capacity σ+,plan is obtained by evaluating w,τ the amount of waste stored at the production facilities mPF,plan w,τ exceeding the available free storage capacity Vfree w (see eq 33). costS,plan =

∑ ∑ (CwS·σw−,,plan τ )

Vwfree −

mwPF,plan ,τ ρw

= σw+,,plan − σw−,,plan τ τ

∑ Cwinc·(λw+ + λw−) + C G·λG,− λ+w

∀ w, τ

mwgoal −

(33)

w

l

τ

∑ ∑ mwL,l ,t = λw+ − λw− t

The overall treatment revenues (rev ) are derived from the waste-specific treatment prices (Cinc w ) and the amount of waste treated over any incineration lance in any period of the planning horizon (see eq 34). inc ∑ ∑ ∑ (mwL,plan , l , τ · Cw )

(35)

λ−w

The deviations and are obtained in eq 36, where the scheduled amount of waste treated (mLw,l,t) is subtracted from the waste-specific treatment target imposed by the planning model mgoal w , which equals the total planned amount of waste act treated mL,plan w,l,τ over all periods of the active subhorizon ττ (see G+ G− eq 37). In a similar way, the deviations λw and λw are obtained in eq 38 from the difference between the amount of auxiliary fuel used (mGk,t) and the target imposed by the planning model on auxiliary fuel consumption (mGgoal), which equals the planned amount of auxiliary fuel used (mG,plan k,τ ) (see eq 39).

plan

rev plan =

(29)

w

(32)

w

τ

∀ k, τ

3.3. Scheduling Model. The scheduling model is adopted from the work of Abaecherli et al.,15 except for the objective function, which is changed in order to integrate it with the planning model introduced above. In this work, the objective is to achieve the treatment targets imposed by the planning model for the active subhorizon as precisely as possible. Similar to that observed in the work of Li and Ierapetritou,17 where, in the scheduling model, the objective is to minimize the difference between the results generated in the planning and the obtained feasible schedule, this is achieved by minimizing the positive and negative deviation from the imposed waste treatment target (λ+w, λ−w ) and by penalizing excessive natural gas usage compared to the imposed plan λG− (see eq 35). The prioritization criterion is obtained by weighting the deviations according to the waste specific incineration costs (Cinc w ) or the auxiliary fuel costs (CG), respectively.

G,plan

k

(28)

⎛ ⎞ ⎛ Tkmax T0 ⎞ ⎜ F,plan ⎜ Cpk , y + Cpy ⎟ max 0 ⎟ = ∑ ⎜mk , y , τ ·⎜ ⎟⎟ ·(Tk − T )⎟⎟ ⎜ 2 y = H 2O ⎜ ⎝ ⎠ ⎝ ⎠

⎛ ⎛⎛ Tkmax ⎞⎞ T cond ⎞ ⎜ F,plan ⎜⎜ Cpk , y + Cpy ⎟ max cond H 2O cond 0 vap⎟⎟ + ∑ ⎜mk , y , τ ·⎜⎜ − T ) + ΔH ⎟⎟ ⎟⎟ ·(Tk − T ) + Cp ·(T 2 ⎜⎜ ⎟⎟ y = H 2O ⎜ ⎝ ⎠ ⎝ ⎠⎠ ⎝

costG,plan =

∀ k, τ

mwgoal =

∑ ∑ mwL,plan ,l ,τ τ ∈ ττact

mGgoal − (34) G

(36)

∀w (37)

l

∑ ∑ mkG,t = λwG+ − λwG− t

∀w

l

k

∀w (38)


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Figure 4. Horizon length and resolution of planning and scheduling level. At the planning level, an operation plan at a resolution of 1 day is obtained for all nonfixed subhorizons of the 4-weeks planning horizon. At the scheduling level, a 7-day schedule at a resolution of 4 h is obtained only for the active subhorizon. The active subhorizon is shown in gray, the aggregated subhorizons are shown in white, and the fixed subhorizons are crosshatched.

mGgoal =

∑ ∑ mk,G,plan τ τ ∈ ττact

k

operations, which last 4 h, on average, in the case of the industrial partner. The scheduling horizon length was set to 7 days, since, at the industrial partner, waste production forecasts are updated weekly and short-term treatment strategies are set accordingly. At the industrial partner, production plans with a 1 day resolution are updated on a monthly basis. From them, a first waste production forecast can be derived. Therefore, in this work, the planning horizon was set to 4 weeks and the resolution was set to 1 day. Figure 4 provides an overview of the horizon length and resolution of both planning and scheduling level considered in this work. 4.3. Illustrative Example. The purpose of the current illustrative example is to show the advantages of integrated planning and scheduling, compared to a stand-alone scheduling approach. For this purpose, a scenario of four consecutive operation weeks with alternate high and low average energy loads of waste supply has been set up, based on historic waste production data from the industrial partner (see Figure 5). The

∀w (39)

4. RESULTS An illustrative example and a case study in industrial waste incineration management have been conducted in collaboration with an industrial partner to show the advantages of integrating planning and scheduling of industrial waste incineration, compared to stand-alone scheduling, in terms of energy efficiency and environmental impact of the process. Both the illustrative example and the case study were implemented in GAMS and solved using CPLEX 12.5 for MILP problems on a Dell Optiplex 9020 computer with an Intel Core i7−4790 processor (3.60 GHz CPU, 16 GB RAM). In view of (i) the size and nature of industrial waste incineration problems, where logistics and inventory management, but also operational optimization, are key challenges; (ii) the lack of far-sighted and high-resolution optimization tools in the field of industrial waste incineration; and, (iii) the aforementioned potential benefits of hierarchical model integration; this works aims to integrate planning and scheduling of industrial waste incineration in order to systematically improve the energy efficiency and the environmental impact of the process. 4.1. System Description. The case study and the illustrative example of the work are based on a chemical plant located in Switzerland. The plant has 30 different production facilities, which generate ∼65 000 tons of combustible waste each year; this waste is treated in an in-house incineration facility, using two ovens. The incineration facility has been described in detail in the work by Abächerli et al.15 and consists of (i) two incineration units with 10 and 9 incineration lances, respectively, (ii) 17 intermediate storage tanks, (iii) 12 unloading pumps, (iv) a piping network, and (v) tank wagons for transferring waste from the different production facilities to the incineration site. Over 2000 different combustible waste streams have been fully characterized and can be attributed to one of 37 different waste families. On average, over 100 different waste streams are produced every week and must be disposed of using incineration. 4.2. Representation of Time. In this work, for both the planning and the scheduling models, time is discretized in periods of uniform duration, thus providing reference time grids for all tasks and operations to be planned or scheduled.23 Abaecherli et al.15 identified the unloading of tank wagons as the key reference task in industrial waste incineration

Figure 5. Average energy supply through waste. The daily average energy supply through waste for case study 1 is shown. The dotted lines show the weekly average, while the data points show daily average heating values. A clear difference in terms of weekly average energy supply can be seen.

optimality gap was set to 0.01% for the planning and 0.50% for the scheduling models. As additional stopping criteria, the solving time for both scheduling and planning model was limited to 15 000 CPU s. In a first step, the problem was solved for each of the 4 weeks consecutively, using the scheduling model introduced by Abaecherli et al., which comprises the same objective function as the planning model in this work.15 Equation 40 provides a general formulation of such an objective function, where the goal is to minimize the overall auxiliary fuel costs, while H


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energy input through waste in Weeks 2 and 4 drive the scheduling model to deliver a minimum temperature schedule, thus minimizing the use of natural gas. Still, according to the scheduling model, there is no way to avoid using natural gas to complete the process within the operational constraints. For Weeks 1 and 3, the temperatures had a tendency to be higher, sometimes even at the maximum allowed temperature, indicating that the energy supply is sufficient to treat the waste without the use of natural gas. Apparently, the given conditions pose no major problems to determine schedules, which avoid natural gas usage completely. This fact is also reflected in the running times given in Table 1. For Weeks 1 and 3, the solving time is much lower than in the case of the other two weeks, where apparently finding the schedule that minimizes natural gas consumption is more involved and requires much longer CPU processing times. In the case of integrated planning and scheduling, in Weeks 2 and 4, the average temperatures are lower than in Weeks 1 and 3; however, contrary of the previous case, they often deviate from the minimum temperature, showing a more dispersed pattern. Furthermore, as already mentioned, no natural gas is required in any week in order to be able to treat the occurring waste. This implies that, in the case of integrated planning and scheduling, the energy shortages, which are forecasted ahead of the scheduling horizon, are taken into consideration on the planning level and waste treatment in Week 1 is targeted in such a way that energy-rich waste is held back for upcoming periods with low energy availability. In terms of running time, it can be observed that, with every week, the solving time increases (see Table 1). This is due to the fact that the solutionfinding flexibility for the scheduling model is decreased with each iteration round. In the last week, it is no longer possible to postpone the incineration of some waste further back in time; as a result, it is more difficult to find a schedule that satisfies the targets imposed by the planning level, thereby making the task of finding an optimal solution more complex and, therefore, more time-intensive. To better understand how the integration of planning and scheduling is able to outperform consecutive scheduling, Figure 7 provides insights on the amount and the average energy content of waste stored at the end of each subhorizon, and thus is transferred from one week to the next one. It can be seen that, in the case of integrated planning and scheduling, after the first week, less waste with higher energy content is saved for later, compared to the case of consecutive scheduling. Thereby, the energy deficits of the second week can be partially

triggering waste incineration by penalizing excessive storage and by providing incentives for waste treatment. objective function = auxiliary fuel costs + storage costs (40)

− incineration revenues

The amounts of waste stored at the production facilities and in intermediate storage at the end of each scheduling period were used as initial wastestocks for the subsequent week, similar to the case of integrated planning and scheduling (eqs 1 and 2). In a second step, the integrated planning and scheduling problem was solved, and in a third step, the performance of the two different approaches were compared. The waste forecast and the initial amount of waste stored (95 t of waste, with an average energy content of 4.5 MWh/t) were identical for both approaches. Table 1 shows that, in the first case, with consecutive scheduling, no natural gas is required in weeks 1 and 3, which Table 1. Comparison of Consecutive Scheduling and Integrated Planning and Scheduling According to the Introduced Rolling Horizon Approach Consecutive Scheduling

Week Week Week Week

1 2 3 4

Rolling Horizon

natural gas usage [t]

running time [CPU s]

natural gas usage [t]

running time [CPU s]

0 28 0 12

62 15 473 373 15 053

0 0 0 0

268 501 5361 10 246

are the weeks with a high average energy supply through waste (see Figure 5). However, in both weeks with a low average energy supply through waste, the optimal solution of the scheduling problem requires the utilization of natural gas in order to overcome energy deficits in the incineration process and therefore to be able to properly incinerate the occurring waste. In contrast, when integrating planning and scheduling, no natural gas requirements are scheduled in any of the four weeks. The average temperature profile of one of the incineration ovens (Figure 6) reveals that, in the case of consecutive scheduling, in Weeks 2 and 4, the temperatures is always at the lower limit, except in a few instances. These deviations are probably due to the stopping criteria imposed to the scheduling model, which allows one to terminate the optimization prematurely, leaving a certain optimality gap. Overall, the low

Figure 6. Oven temperatures for incinerator 1. The two plots show the average incineration temperature for each period of the four weeks considered in Case Study 1. The plot on the left side shows the case of consecutive scheduling, and the plot on the right reflects the integration of planning and scheduling, according to the introduced rolling horizon approach. The lines indicate the limits of the allowed temperature range. I


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Figure 7. Amount and average energy content of stored waste at the end of each scheduling subhorizon. On the left side, the quantities of waste remaining at the end of each week in the case of consecutive scheduling are shown in light gray and their average energy content is shown in dark gray. On the right side, the same information is provided for the integration of planning and scheduling, according to the introduced rolling horizon approach. The initial conditions in both approaches were the same. The final wastestock shown includes both the wastestock at the production facility and the waste stored in the intermediate storage tanks at the end of each subhorizon.

difference in energy supplied to the incineration units between the integration of planning and scheduling and the sequential scheduling approach amounts to ∼75 MWh, which is equivalent to 5.2 tons of natural gas. However, in the case of consecutive scheduling, a total of 40 tons of natural gas were needed in order to guarantee proper combustion over the four weeks (see Table 1), corresponding to an average natural gas consumption of 0.14 MWh per ton of waste treated (see Table 2). Despite the fact that, in the case of integrated planning and scheduling, less energy-rich waste is left for future at the end of the four-week period, the overall performance is still more energy-efficient than in the case of consecutive scheduling. This is due to the fact that the energy saved through the complete avoidance of natural gas through the integration of planning and scheduling exceeds the reduced energy content of the remaining waste at the end of the fourth week, compared to the consecutive scheduling approach. 4.4. Case Study. The case study was conducted to show the potential benefits of using systematic planning and scheduling, integrated according to the introduced rolling horizon approach, compared to consecutive scheduling over a long time period. Similar to the illustrative example, the problem was first solved for each of the 52 weeks consecutively using the scheduling model introduced by Abaecherli et al.,15 and in a second step, the methodology integrating planning and scheduling introduced above was applied to solve the waste incineration problem for the same year. Since the planning horizon spans four weeks, all results are presented as four-week averages. In a third step, the performance of the two

compensated. In the second week, less waste is treated in the case of integrated planning and scheduling; however, because of the higher average energy content of the treated waste, natural gas usage becomes dispensable. Similar trends can be observed for the last two weeks of the illustrative example. In Week 3, energy-rich waste is saved for Week 4 to compensate for the lack of energy content and finally, in Week 4 less waste with a higher energy content is treated when integrating planning and scheduling compared to consecutive scheduling. Over the four weeks, in both cases, similar amounts of waste were treated: at the end of the fourth week, in both cases, there were ∼60 tons of waste left. In the case of integrated planning and scheduling, however, the average energy content of the remaining waste is ∼25% lower than in the case of consecutive scheduling. The total amount of waste treated in both cases and the average energy content are shown in Table 2. The Table 2. Performance of Consecutive Scheduling and Integration of Planning and Scheduling According to the Introduced Rolling Horizon Approach

amount of waste treated [t] average energy content of treated waste [MWh/twaste] average natural gas usage [MWh/twaste]

consecutive scheduling

rolling horizon

4144 3.45

4145 3.47

0.14

0.00

Figure 8. Historic energy supply to the incineration units at the industrial site. The plot provides the four-week average energy supply per ton of waste treated from waste and natural gas for the year 2014. The dark gray part indicates the energy supply through natural gas, while the light gray part gives the average energy contained in the different waste streams that have been incinerated. J


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Figure 9. Modeled and historic cumulated amount of waste treated. The plot shows the historical performance (HP) of the industrial site, in terms of total quantity of waste treated accumulated over each four-week block of 2014, as well as the modeled performance in the case of consecutive scheduling (CS) and in the case of integrated planning and scheduling, following the introduced rolling horizon approach (RH).

Figure 10. Modeled and historic cumulative natural gas consumption. The plot shows the historical performance (HP) of the industrial incineration plant, in terms of natural gas consumption accumulated over each four-week block of 2014, as well as the modeled performance in the case of consecutive scheduling (CS) and in the case of integrated planning and scheduling, following the introduced rolling horizon approach (RH).

Figure 11. Modeled and historic amount of natural gas consumption per ton of waste treated. The plot shows the historical performance (HP) of the industrial incineration plant in terms of total quantity of natural gas consumption per ton of waste treated for each four-week block of 2014, as well as the modeled performance in the case of consecutive scheduling (CS) and in the case of integrated planning and scheduling, following the introduced rolling horizon approach (RH).

conditions in this case study are not equal to those at the incineration site in 2014; therefore, comparisons between historic and modeled performance should be studied with caution. Figure 9 shows the cumulated amount of waste treated in 2014 at the industrial partner as well as the modeled cumulated amounts for both the consecutive scheduling and the integration of planning and scheduling. The total annual modeled performance of both approaches deviate by 60%. In Figure 11, the average natural gas consumption per ton of waste treated is shown for every four-week block of 2014. It can be seen that the modeled performance, obtained either through consecutive scheduling or by the integration of planning and scheduling, is always better than the actual historical performance of the industrial partner. A theoretical reduction of natural gas of >50%, compared to the actual industrial performance, is possible for any of the two approaches compared in this case study, with the exception of the four-week blocks including Weeks 1−4, 33−36, and 37−40. In the first block including Weeks 1−4, the extensive modeled natural gas consumption is probably due to the low average energy content of waste of 3.216 MWh/twaste occurring in this four-week period, as seen in Figure 8. Hence, not many options are left to systematically optimize the exploitation of energy contained in the waste to overcome the energy deficits, because there is simply not enough energy supply through waste, making extensive use of natural gas unavoidable. For the remaining two four-week blocks (Weeks 33−36 and 37−40), it seems that the waste production and other operational constraints would not allow one to improve the waste incineration performance significantly, compared to the actual historic waste management, despite average energy supply through waste. When comparing the consecutive scheduling and the integration of planning and scheduling in terms of energy efficiency, the integration of planning and scheduling outperforms consecutive scheduling in most four-week blocks of 2014, in terms of natural gas consumption per ton of waste treated, as seen in Figure 11. The different four-week blocks can be divided in three groups: (i) blocks in which both approaches perform equally well, (ii) blocks in which the integration of planning and scheduling outperforms consecutive scheduling, L


Article

Industrial & Engineering Chemistry Research apparently worse performance of the integration of planning and scheduling, compared to competitive scheduling, is an artifact of the imposed stopping criteria of the optimization, the simulation was repeated for this four-week block, increasing the available solution time. The results of this additional run showed that, when solved to optimality, the integration of planning and scheduling was able to provide a better performance, compared to the consecutive scheduling, in terms of natural gas consumption per ton of waste treated. Hence, thes eobservations prove that the tight stopping criteria are responsible for the initial unfavorable result of the block containing Weeks 33−36 seen in Figure 11. The reduction of the average natural gas consumptions is not only economically relevant in the incineration process but it also has a positive environmental impact. As a direct consequence, the amount of fume production per ton of waste treated is reduced and, with it, the workload of the incineration units, which leads to increased operation flexibility and higher treatment capacities. Furthermore, the workload of fume cleaning units is reduced, resulting in lower water, electricity, and scrubbing chemicals consumption per ton of waste treated, which is economically as well as environmentally beneficial. Finally, the emissions to the atmosphere per ton of waste treated are also reduced. As an example, Figure 12 shows the modeled and historic cumulative amount of CO2 emitted to the atmosphere in 2014. The difference between the historical performance and the simulation results from the rolling horizon approach at the end of the year indicates a theoretical potential savings of 8.1% CO2 emissions, which could be achieved through optimal waste incineration management. Furthermore, integrated planning and scheduling outperforms consecutive stand-alone scheduling by 0.8%, in terms of total CO2 emissions in 2014, which correspond to ∼2600 t of CO2. As a consequence of the aforementioned difficulty to compare the systematic outcome of the rolling horizon approach to the actual performance, it could be difficult to reach a reduction of natural gas above 60% and a reduction of CO2 emission of 8% through systematic optimization of industrial waste incineration. Nevertheless, the results of the case study emphasize that there is a substantial improvement potential in current industrial waste incineration routines. Furthermore, it proves that far-sighted integration of planning and scheduling provides better (or at least equally good) results than stand-alone scheduling.

The integrating strategy adopted in this work follows a bilevel hierarchical decomposition method, following a socalled “rolling horizon” approach. Therefore, high-resolution schedules can be obtained according to imposed targets by the planning level, which also consider future events laying beyond typical scheduling horizon lengths. Feasible schedules are obtained iteratively for all subhorizons of a planning horizon, and in a subsequent step, these schedules are fed back to the planning horizon, which re-evaluates the targets for the remaining subhorizons, taking into account the results of the already-obtained feasible schedules. The process is terminated when a feasible schedule is obtained for all subhorizons of the planning horizon. Both planning and scheduling models are formulated as mixed-integer linear programming (MILP) problems with a discrete time representation, based on single uniform grids. Based on real industrial data, an illustrative example and a case study have been examined in order to show the benefits of using a rolling horizon approach, compared to consecutively solving stand-alone scheduling problems, and show the potential benefits of integrating planning and scheduling in industrial routines, compared to consecutive stand-alone scheduling. For this, a scenario of four consecutive operation weeks with alternating high and low average energy loads of waste supply has been set up. It could be shown that, in the case of integrated planning and scheduling, in the weeks with high-energy supply through waste, some energy-rich waste is saved for upcoming weeks with lower energy content, and thus auxiliary fuel usage can be reduced or even completely avoided. In contrast, in the case of consecutive scheduling, the system provides less far-sighted solutions, leading to the requirement of 0.14 MWh of auxiliary fuelin this case, natural gasper ton of waste treated, in order to overcome the energy shortages. The results suggest that, by applying more far-sighted approaches that integrate planning and scheduling, results that are better than (or, in the worst case, at least as good as) those observed in the case of consecutive scheduling can be obtained with similar computational effort. In addition, a case study was constituted to show the potential benefits of using systematic planning and scheduling, integrated according to the introduced rolling horizon approach, compared to consecutive scheduling over one year and to put the results in reference to the actual historical performance at the industrial incineration plant. Results indicate that integrating planning and scheduling, compared to consecutive stand-alone scheduling, leads to significant improvements, in terms of auxiliary fuel usage (∼16% savings) and CO2 emissions (∼1% reduction) per ton of waste treated. In addition, the findings of the illustrative example, indicating that integration of planning and scheduling leads to results that are better than, or at least as good as, the results observed in the case of consecutive scheduling, were confirmed. Furthermore, the results of the case study showed that there is a substantial improvement potential in the way waste is incinerated in the industry today, identifying potential auxiliary fuel savings of 60% and CO2 emission reduction of 8% per ton of waste treated through systematic optimization of industrial waste incineration. In the future, the methodology that has been introduced should be helpful for decision-makers, who must cope with nontrivial waste management, where empiric decision making is insufficient to optimally master the complex tasks, in terms of energy efficiency, e.g., in large chemical sites, with in-house

5. CONCLUSION Until now, waste incineration scheduling has been tackled as an independent entity, despite the fact that it has been repeatedly proven that the combination of both planning and scheduling can lead to more efficient solution with high resolution for a relatively long horizon. With this work, we introduce an integration approach for industrial waste incineration planning and scheduling with the objective of systematically supporting decision makers in daily routines by improving the energy efficiency of the incineration process, leading to a more economic and sustainable performance. The increase of the energy efficiency is achieved by finding optimized far-sighted and high-resolution storage, mixing and scheduling strategies of waste streams with different energy content, such that the auxiliary fuel consumption is minimized. Therefore, waste incineration is triggered by rewarding treatment and penalizing excessive storage. M


Article

Industrial & Engineering Chemistry Research f = set of waste families i = set of intermediate storage tanks j = set of subhorizons k = set of incinerator units l = set of lances s = set of fractions t = set of time periods of the scheduling model u = set of unloading pumps w = set of waste streams x = set of pollutants y = set of fume components τ = set of time periods of the planning model

waste incineration units and a large variety on liquid waste. Therefore, long-term testing of the introduced integration approach in industry would be desirable. By doing so, the performance of the approach, compared to empiric decisionmaking, could be better evaluated, thus providing deeper analysis on how decision making in daily routines is systematically supported. Moreover, the effect of uncertainty in waste production forecasts and waste composition on the integrated planning and scheduling system should be analyzed in depth and eventually included in the integration method introduced in this work. Nevertheless, at this stage of the project, the methodology introduced can help decision-makers to anticipate possible bottlenecks in waste incineration by providing valuable information on expected storage availability and incineration performance, thus allowing early precautionary measures to be taken, if needed. Moreover, the methodology that has been introduced can easily be used to evaluate different scenarios, such as new investments, or unforeseen events, such as unit breakdowns, or to sensitize people within a company on the importance of accurate waste generation forecasts.

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Subsets

ilpipe = subset of pipe connections between intermediate i,l storage tank i and incineration lance l lkl,k = subset of lances l belonging to incinerator k tdt,d = subset of time periods t belonging to day d wdirect = subset of waste streams w that must be directly w incinerated (no intermediate storage possible) wmix w = subset of mixable waste streams w wf w,f = subset of waste streams w belonging to waste family f wicomp = subset of compatible waste streams w and tanks i w,i wipipe = subset of pipe connections between production w,i facility of waste w and tank i τact τ = subset of periods τ belonging to the active subhorizon

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.iecr.7b01250. Optimization statistics for the planning model and scheduling model in the rolling horizon approach (PDF)

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Parameters

CG = cost of auxiliary fuel [MU/kg] Cwinc = charged prices to production facilities for the treatment of a specific waste stream w [MU/kg] CSw = cost of additional storage of waste w per period [MU/ kg] CpH2O = specific heat capacity at constant volume of water at temperature T0 [kJ (kg K)−1] 0 CpTk,y = specific heat capacity at constant volume of fume compound y at temperature T0 [kJ (kg K)−1] Tcond Cpk,y = specific heat capacity at constant volume of fume compound y at temperature Tcond [kJ (kg K)−1] CpTk,yk,max = specific heat capacity at constant volume of fume compound y at temperature Tmax [kJ (kg K)−1] k Tmin k Cpk,y = specific heat capacity at constant volume of fume compound y at Tmin [kJ (kg K)−1] k D = number of days of the scheduling horizon [days] Hw = higher heating value of waste stream w [kJ/kg] HG = higher heating value of auxiliary fuel [kJ/kg] M = large positive constant used in big M constraints MGk max,plan = maximum auxiliary fuel inlet in incinerator k per period in the planning model [kg] MGmin,plan = minimum auxiliary fuel inlet in incinerator k per k period in the planning model [kg] Ndir1,plan = maximum number of different waste streams w that can be received by an incineration lance l per period in the planning model [-] Ndir2,plan = maximum number of different incineration lances l that can receive a waste stream w per period in the planning model [-] NIL1,plan = maximum number of different intermediate storage tanks i that can send waste to an incineration lance l per period in the planning model [-] NIL2,plan = maximum number of different incineration lances l that can receive waste from intermediate storage tanks i per period in the planning model [-]

AUTHOR INFORMATION

Corresponding Author

*Tel.: +41 44 633 44 86. E-mail: [email protected]. ORCID

Elisabet Capón-García: 0000-0002-4469-7845 Funding

This work was supported by Lonza Group AG and the Swiss Commission for Technology and Innovation (CTI) [CTI-No. 15840.1 PFIW-IW]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Financial support received from the Swiss Commission for Technology and Innovation (CTI) and Lonza Group AG is appreciated. Special thanks go to the waste and energy management of Lonza AG Visp for the technical support and help received, as well as to Dr. Claudio Abächerli, Sara Badr, and Vasco Bolis for proofreading and contributions to the manuscript.

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ABBREVIATIONS EWO = enterprise-wide optimization MILP = mixed-integer linear programming MSW = municipal solid waste MU = monetary unit WtE = waste-to-energy

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NOMENCLATURE

Sets

d = set of days in a scheduling horizon N


Article


mGw goal = targeted amount of waste w to be treated in the scheduling model in the scheduling model [kg] mLw,l,t = mass of waste w incinerated over lance l in period t in the scheduling model [kg] mL,plan w,l,t = mass of waste w incinerated over lance l in period τ in the planning model [kg] mIw,i,t = mass of waste w stored in tank i at the end of period t in the scheduling model [kg] mI,plan w,i,τ = mass of waste w stored in tank i at the end of period τ in the planning model [kg] mIL,plan w,i,l,τ = mass of waste w transferred from intermediate storage tank i to incineration lance l in period τ in the planning model [kg] mPF w,t = mass of waste w stored at production facility at the end of period t in the scheduling model [kg] mPF,plan = mass of waste w stored at production facility at the w,τ end of period τ in the planning model [kg] msto,plan = mass of waste w transferred from the production w,i,τ facility to intermediate storage tank i in period τ in the planning model [kg] comb,plan qk,τ = energy released through combustion in incinerator k in period τ in the planning model [kJ] qmax,plan = maximum energy input of incinerator k in period τ k,τ in the planning model [kJ] qmin,plan = minimum energy input of incinerator k in period τ k,τ in the planning model [kJ] revplan = total revenue through waste incineration in the planning model [MU] σ+,plan = slack variable giving the amount of waste w stored at w,t the production facility free of charge in a period τ of the planning model [kg] σ−,plan = slack variable giving the amount of waste w w,t exceeding the free available storage capacity in a period τ of the planning model [kg] λ+w = slack variable giving the amount of waste w incinerated in the scheduling model below the imposed treatment target imposed by the planning model [kg] λ−w = slack variable giving the amount of waste w incinerated in the scheduling model exceeding the treatment target imposed by the planning model [kg] λG+ w = slack variable giving the amount of auxiliary fuel required in the scheduling model below the target imposed by the planning model [kg] λG− = slack variable giving the amount of auxiliary fuel w required in the scheduling model exceeding the target imposed by the planning model [kg]

Nstol,plan = maximum number of different waste streams w that can be received by an intermediate storage tank i per period in the planning model [-] Nsto2,plan = maximum number of different storage tanks i that can receive a waste stream w per period in the planning model [-] Pw,x = amount of pollutant x contained in waste stream w [kg/kg] Pmax k,x = maximum allowed load of pollutant x in incinerator k per period [kg] T0 = outside temperature [K] Tcond = condensing temperature of water [K] Pmax = maximal temperature allowed in incinerator k [K] k Tmin = minimal temperature required in incinerator k [K] k V0w = initial volume of waste stream w at production facility [m3] Vdir,plan = maximum allowed waste that can be transferred to an incineration lance l per period in the planning model [m3] VFk = maximum allowed fume volume for incinerator k per period in the planning model [m3] VIi = volume of storage tank i [m3] I0 Vw,i = start volume of waste stream w contained in intermediate storage tank i [kg] Vin,plan = forecasted volume of waste stream w produce in w,τ period τ in the planning model [m3] Vmax,plan = maximum volumetric throughput of an incinerl ation lance l per period τ in the planning model [m3] Vmin,plan = minimum volumetric throughput of an incinerl ation lance l per period in the planning model [m3] VP,plan = maximum volumetric throughput of a pipe per period of the planning model [m3] VPF w = maximum available storage volume for waste stream w at production facility [m3] Vsto,plan = maximum allowed waste that can be transferred to an intermediate storage tank per period in the planning model [m3] VTW = volume of tank wagons [m3] Yw,y = amount of fume component y occurring by the combustion of waste w [kg/kg] YGy = amount of fume component y occurring by the combustion of auxiliary fuel [kg/kg] ΔHvap = specific heat of vaporization of water [kJ/kg] ρwmax= density of waste stream w [kg/m3] ρTk,yk = density of incineration compound y at Tmax [kg/m3] k Variables ∈ R

zplan = objective function of the planning model [MU] z = objective function of the scheduling model [-]

Binary Variables

Variables ∈ R+0

bdir,plan = binary variable indicating whether waste w is being w,l,τ transferred to an incineration lance l in period τ in the planning model bFI,plan = binary variable indicating whether waste family f is f,i,τ stored in tank i in period τ bG,plan = binary variable indicating whether auxiliary fuel is k,τ used in incinerator k or not in period τ in the planning model IL,plan bi,l,τ = binary variable indicating whether waste from an intermediate storage tank i is transferred to an incineration lance l in period τ in the planning model inc,plan bl,τ = binary variable indicating whether or not incineration lance l is used to incinerate waste in period τ in the planning model

G,plan

cost = total cost of auxiliary fuel in the planning model [MU/kg] costS,plan = total cost of additional storage of waste w in the planning model [MU/kg] mdir,plan = mass of waste w transferred from the production w,l,τ facility to incineration lance l in period τ in the planning model [kg] F,plan mk,y,τ = mass of fumes components y produced in incinerator k in period τ in the planning model [kg] mGgoal = targeted amount of auxiliary fuel to be treated in the scheduling model in the scheduling model [kg] mG,plan = mass of auxiliary fuel combusted in incinerator k in k,τ period τ in the planning model [kg] O


Article

Industrial & Engineering Chemistry Research bsto,plan = binary variable indicating whether waste w is being w,i,τ transferred to an intermediate storage tank i in period τ in the planning model bWI,plan = binary variable indicating whether waste stream w is w,i,τ stored in tank i in period τ in the planning model

(18) Papadimitriou, D.; Fortz, B. A Rolling Horizon Heuristic for the Multiperiod Network Design and Routing Problem. Networks 2015, 66 (4), 364−379. (19) Cuiwen, C.; Xingsheng, G.; Zhong, X. A data-driven rollinghorizon online scheduling model for diesel production of a real-world refinery. AIChE J. 2013, 59 (4), 1160−1174. (20) Zamarripa, M.; Marchetti, P. A.; Grossmann, I. E.; Singh, T.; Lotero, I.; Gopalakrishnan, A.; Besancon, B.; André, J. Rolling Horizon Approach for Production−Distribution Coordination of Industrial Gases Supply Chains. Ind. Eng. Chem. Res. 2016, 55 (9), 2646−2660. (21) Marquant, J. F.; Evins, R.; Carmeliet, J. Reducing Computation Time with a Rolling Horizon Approach Applied to a MILP Formulation of Multiple Urban Energy Hub System. Procedia Comput. Sci. 2015, 51, 2137−2146. (22) Abaecherli, M. L.; González, D. S.; Capón-García, E.; Hungerbühlera, K. In Mathematical Optimization of Real-time Waste Incineration Scheduling in the Industry, 26th European Symposium on Computer Aided Process Engineering: Parts A and B; Elsevier: Amsterdam, 2016; p 13. (23) Floudas, C. A.; Lin, X. Continuous-time versus discrete-time approaches for scheduling of chemical processes: A review. Comput. Chem. Eng. 2004, 28 (11), 2109−2129.

Rolling Horizon Flowsheet

j = set of subhorizons, which is equivalent to the set of iterations in the rolling horizon approach SHj = subhorizon j SHact = active subhorizon SHagg = aggregate subhorizon SHfix = fixed subhorizon

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REFERENCES

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Hierarchical Integration of Planning and Scheduling for Industrial

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