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Process Systems Engineering
Production planning, scheduling and process control system in micro-algae and biogas supply chain YOHANES KRISTIANTO Nugroho, and Liandong Zhu Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.8b03960 • Publication Date (Web): 09 Jan 2019 Downloaded from http://pubs.acs.org on January 15, 2019
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Industrial & Engineering Chemistry Research
Production planning, scheduling and process control system in micro-algae and biogas supply chain Yohanes Kristiantoa,, Liandong Zhub,* a
b
Materials and Production, Aalborg University, Copenhagen, Denmark School of Resource and Environmental Sciences, Wuhan University, 129 Luoyu Road, Wuhan 430079, PR China *
Corresponding author E-mail:
[email protected];
[email protected] Tel: +8613517256480; Fax: +862768778893
Abstract
Biomass feedstock is a potential solution to future source of biofuels and fine chemicals. A major challenge of its availability to meet energy demands extend the scope of production planning from single to multi locations. However, multi-location production planning needs an integrated production scheduling to minimize idle times and over-stocks and process control to hedge against any change in production planning. This article models an integration of production planning, scheduling and process control system, and formulates the model as a bi-level generalized disjunctive programming (GDP). We use a reformulation technique that coverts bi-level into a single level programming. We solve the model by using Branch and Reduce method, and add outer approximation (OA) cutting plane at each lower bounding iteration. The computational result shows that the supply chain can mitigate stock out or over stock, and generate no delivery delay. In terms of computational results, we find that the algorithm is capable of minimizing optimality gaps within the range of allowable error. Keywords: production planning, scheduling, process control, branch and reduce, generalized disjunctive programming, mixed integer non-linear programming 1. INTRODUCTION The focus of this article is to model hierarchical planning of biogas and biodiesel production from micro-algae supply chain. The planning unifies production scheduling into the supply chain, production and distribution planning. We add process control into the model as a way to minimize delivery delay, due to process and supply flow variations. The reason to choose micro-algae as a substrate is that the species lives almost in any place, which contains water, from the sea to rivers, and from fresh to wastewater. Biomass from micro-algae is a raw material of biogas and biodiesel production. Biomass consists of sugar, lipid and protein. Through a series of biological reactions, those three elements are degraded to volatile fatty acids (VFA), and which finally are converted into methane. In addition to micro-algae biomass, we can extract oil from algae, which is one of 1 ACS Paragon Plus Environment
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the highest. Thus, unified supply chain and production planning, scheduling and control has an objective to maximize both biogas and algae oil extraction yields. While algae biomass is a raw material of biogas and algae oil, algae biomass production and distribution are two areas of interests of this article. Algae biomass production depends on temperature and light penetration into photo-bioreactor (PBR). The use of outdoor PBR minimizes reactor energy requirements, substrate contamination and quick water evaporation 1. However, outdoor bioreactor is susceptible against variations of temperature and light intensity. Process control of algae biomass, algae oil and substrate concentrations has to hedge against variations of temperature and light intensity. For instance, temperature and substrate dilution rate controls maintain the level of algae biomass concentration 2,3,4. Control of product distribution (ratio among algae oil, biogas and algae biomass) has an economic implication on the supply chain operations. The control of product distribution has to maximize the total supply chain profit concerning economic, process and operational constraints. The control of product distribution and biofuels process needs the integration of production scheduling and process control. Some contributions suggest the integration is to connect state variables of transient period and amount of outputs, and production lot size and slot lead times 5. Bhatia and Biegler 6 integrate production scheduling and control of multi-product batch plants. In a more general product setting, Mishra et al. 7 formulate production scheduling and control integration as a mixed integer dynamic programming (MIDO), which needs a certain algorithm, for instance, Benders decomposition 8 and two-stage stochastic programming 9. Both contributions set production scheduling as the master problem and process control as the sub-problem. The subproblems are mostly highly nonlinear and non-convex 10, and therefore the solution method needs to simplify the model, so that it has less nonlinearity and non-convexity. Both Mishra et al. 7, and Bhatia and Biegler 6 assume that the product demand is known and the raw materials supply is abundant. In addition, both contributions focus on short term scheduling of multiproduct batch plant by excluding the impact of ramp-up period during a changeover time from one production order to another. Our current contribution complements both contributions by generating a feasible production schedule just after the production scheduler knows the optimal ramp-up period from the production planner. Production planner sets the optimal ramp-up period after receiving a weekly production plan from production capacity planning. We also coordinate production capacity planning of the entire supply chain in order to minimize the entire supply chain costs and delivery lead times. Thus, our contribution coordinates factory operations from tactical to operational planning in order to be capable to promise supply chain customers about delivery lead times. Considering the biofuels supply chain, we identify several challenges. First, the variability of raw material flows comes from a photo-bioreactor (PBR) of algae biomass and Anaerobic Digester (AD) of biogas. Second, the integration of production planning and scheduling of biofuels has to be adapted to the specific needs and conditions arising at the shop floor. In biogas and algae oil production, the adaptation includes the addition of more time to hedge against micro-algae and algae-biomass flow variations. Third, the process control of the plant networks ensures that the 2 ACS Paragon Plus Environment
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production scheduling meets the lead times of biogas and algae oil demand. Raw material flows variability impacts on the biogas and diesel oil outputs. The integration of production planning and scheduling across the supply chain may dampen the impacts of those variability by coordinating materials inventory, production and delivery lot size. In each production plant, reactor process control improves process reliability and minimizes delivery delay by tuning of control parameters optimally. Thus, this article provides a model of an integrated production planning, scheduling, and control that optimum tuning control parameter based on optimal control of biogas and algae biomass kinetics. Addressing the challenges, we use reformulation of multi period Mixed Integer Nonlinear Programming (MINLP) model into disjunctive MINLP. The model contains several numbers of equality constraints. Therefore, we split the objective functions into an upper and lower level and reformulate the problem as bi-level programming 11. The upper level contains production and process control decision variables, while the lower level contains production-scheduling variables. Process control parameters connects the upper and lower level decision making, and adjusts the length of production schedule after receiving production capacity information from the upper level. Generalized Disjunctive Programming (GDP) 12 is capable of reducing the numbers of integer variables of process networks and job sequences. Afterwards, branch and reduce 13 sequentially finds the optimal solution after solving MINLP relaxation by using outer approximation (OA) 14. The organization of this paper is as follows. First, we present a brief introduction on production planning, scheduling and process control of biofuels production. Second, we model the biofuels supply chain. Third, we propose a bi-level MINLP algorithm to solve the model of biofuels supply chain networks, with emphasis on finding near global optimum solution at a shorter computational time. This article discusses computational results in the fourth section and make conclusion in the fifth section. 2.
BIOFUELS SUPPLY CHAIN DESIGN MODEL
This section provides a preliminary model of biofuels supply chain design. The model identifies control points in the production chains of microalgae and employs a control strategy to keep the plant running at an optimum level. The design integrates microalgae, bio-ethanol, and biogas production facilities. The objective is to generate a closed loop economy from algae biofuels by producing energy and consuming wastes circularly. 2.1 Supply chain process design To illustrate the application of the proposed model, we provide an illustrative example of biogasbiodiesel supply chain in Figure 1. We build the superstructure based on a work of Ward et al. 15, and extend the original process flow diagram to distributed algae oil and biomass, and biogas production facility. The supply chain consists of two main biofuels production processes that produce different types of fuels, bio-diesel and biogas. Algae bioreactor produces algae oil from biogas sludge of the 3 ACS Paragon Plus Environment
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biogas production facility, in this case, anaerobic digesters (AD). The AD produces biogas from municipal wastes, receives materials from bioreactor (biomass) and releases additional products, such as nutrients, CO2 and power back to bioreactor. AD releases methane and heat. The methane is the product, and the heat released during the digestion can provide hot water for a municipality. The current contribution includes biofuel process control into an integrated production planning and scheduling. Since the process is batch, process control objective is to maximize biogas, algae oil and algae biomass production yields during transient period. The efficiency of the process control affects production scheduling in terms of minimizing total production lead times. Algae oil CO2
Sunlight Nutrient
Anaerobic digester 1 Algae cultivation
Diesel
Fuels refinery 2
CH4
Fuels refinery 3
CH4
Fuels refinery 4
CH4
Fuels refinery 5
Diesel
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Filtrate digestate biomass Anaerobic digester 2
Algae biomass Sunlight Nutrient
Fuels refinery 1
Algae cultivation Anaerobic digester 3
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CO2 Algae oil
Figure 1. System boundary of closed loop biofuels supply chain There are three domains of decision variables in this contribution, production planning, process control and scheduling variables. Production planning parameters are reactor sizes, production and transportation capacity, and supply chain configuration. Process control parameters are state and control variable profiles of each fuel product and final state of each fuel production. Scheduling parameters are production sequence and lead times. This article categorizes the three decision domains into two different regions, upper and lower levels. The upper level contains design and control variables, while the lower level contains scheduling variables. In order to link both upper and lower levels, we use production lot size as a complicating variable to synchronize both levels.
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Industrial & Engineering Chemistry Research
This article uses a differential algebraic (DAE) system of equations of algae oil and biomass from a series of stoichiometry equations. This article manipulates the DAE in such a way that the model optimizes the product yield. The problem decomposition is shown as follows:
Figure 2. Hierarchical planning decision flows of biogas and biodiesel production from microalgae supply chain Figure 2 shows that the decision making process evaluates production and scheduling within twostage decision making scheme. Production lot size is a complicating variable between production and scheduling evaluation. The second stage decision-making determines production lead-time after considering transient time of biogas and algae oil production. The decision flows in Figure 2 is sequential. The first stage provides joint solutions for supply chain configuration and production and transportation planning, coupled with optimal transient process control of algae oil and biogas. The second stage solves production scheduling after receiving process control parameters from the first stage. Input parameters of the first stage decision making are unit production costs, inventory and transportation costs. Input parameters of the second stage decision making are processing time per unit of mass of products, production sequence, and process control parameters from the first stage. The first stage decision making has capacity constraint, process control constraint because of a differential algebraic (DAE) system of equations, and material flow constraint. The second stage decision making has only scheduling 5 ACS Paragon Plus Environment
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constraints. The scheduling decisions have to take into account about the transient time of biogas and algae oil synthesis. We formulate both first and second stages decision making as generalized disjunctive programming (GDP), in which each constraint of each production facility is satisfied whenever there is an activity in that such locations. GDP is beneficial for distributing DAE within each disjunction. The outputs are supply chain topology, inventory levels, production lot size and lead times, reactor sizes, process control parameters. In order to solve the hierarchical planning of biogas and biodiesel production from micro-algae supply chain. Scheme 1 is a pseudocode that shows the computational steps of building hierarchical planning of biogas and biodiesel production from micro-algae supply chain. After following Scheme 1, interested readers can go into more details about the formulation of hierarchical planning models by following explanations in Sections 2 and 3. 1. Stage 1: Biogas and algae oil process control parameters: Initialization: Lower bound LB := -∞ Upper bound UB := ∞ 1.1 Lower bounding Solve independently process control nonlinear optimization model (Eq.13) in order to maximize daily biogas production output 𝑞𝐶𝐻4 with regards to nonlinear dynamic constraints (Eqs.14-18), and Eqs.(24-30) in order to maximize algae biomass concentration [𝐵] and growth rate 𝜇𝐵 . Use interior point algorithm within B-B method and bounding the solution from above (UB), find optimum set of {𝐵, 𝑠, 𝑞, 𝐼𝑝 , 𝑓𝐵 , 𝐷} and {𝑠1, 𝑠2 , 𝑠3 , 𝑋1 , 𝑋2 , 𝑋3 , 𝐷 }, within their allowable interval. INPUT: Starting point, initial value for the barrier parameter. OUTPUT: an optimal solution 𝑞𝐶𝐻4 , 𝜇𝐵 of P if exists, else null. 𝐿 ∗ ∗ 𝑈 a. Split the interval of the relaxed problem R, 𝑞𝐶𝐻 , 𝑞𝐶𝐻 , 𝑞𝐶𝐻 , 𝑞𝐶𝐻 , 4 4 4 4 𝐿 ∗ ∗ 𝑈 𝜇𝐵 , 𝜇𝐵 , 𝜇𝐵 , 𝜇𝐵 into two and solve them separately b. Check convergence for the overall problem If the UB of node n is less than the UB of node n+1 then fathom Else c. Branch node n+1 into two new sub-problems and do the same step as parts a+b d. Repeat until the UB of node n
