Enhancement Methodology for Supply

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Ind. Eng. Chem. Res. 2008, 47, 748-759

Performance Assessment/Enhancement Methodology for Supply Chains T. Sundar Raj and S. Lakshminarayanan* Department of Chemical and Biomolecular Engineering, 4 Engineering DriVe 4, National UniVersity of Singapore, Singapore 117576

A well-coordinated supply chain is characterized by a harmonious balance between inbound logistics, production scheduling and product distribution. In multi-echelon decentralized supply chains, distribution logistics play a leading part in helping a supply chain gain advantage over competitors. Besides the uncertain consumer demand, the nonoptimal internal strategy practiced by the distribution nodes is a major problem that a supply chain must contend with. The performance of a supply-chain network that is controlled in a decentralized manner can be improved by reorganizing the operational aspects of the problematic nodes in the network. Our work is focused on (i) using time series obtained from an existing supply chain to determine the bottlenecks (poorly performing nodes) and (ii) suggesting performance improvement measures, such as retuning the reordering parameters or even changing the ordering policy itself. Simulation-based optimization of the supplychain network model is used to achieve these objectives and compute benchmark performance standards. The concepts presented are complemented by realistic simulation examples. 1. Introduction A supply-chain system is a well-balanced dynamics of material, information, and cash flows between raw material suppliers and market customers through the organizational barriers of inbound logistics, production plants, and multiechelon distribution network. Distribution logistics maintains inventory as a buffer at all distribution nodes to achieve the desired customer service level and handle sudden fluctuations in the market demand. It is rather well-known that entities at different levels in the supply chain (suppliers, manufacturers, retailers, and customers) often have an inaccurate understanding of the real demand. While each unit has control over only a part of the supply chain, each unit can impact the entire supply chain by ordering too much or too little. Therefore, each entity is influenced by decisions that others are making. The lack of coordination between different supply-chain levels, which is further accentuated by the ability to influence others (while being influenced by others), leads to the bullwhip effect. Poor demand forecasting, as well as delays in procurement, production, and communication, are some factors that can lead to the bullwhip effect. The bullwhip effect can also be attributed to the decentralized nature (separate ownership of different entities) of the supply chain. Each level of such a multilevel supply chain attempts to maximize its profitability at the expense of decreased overall profitability of the supply chain. Lee et al.1 outlined several measures to overcome or reduce the bullwhip effect. In addition to their recommendations, appropriate replenishment strategies and optimal values for the parameters in the replenishment policies must be used by each of the distribution nodes if the supply chain is to be free of inefficiencies such as stock outs, excess inventories and undesirable/excessive oscillations. Overly aggressive or cautious parameter values can affect the performance of the individual node, as well as undermine the performance of the entire supply-chain network. The influence of the replenishment rule parameters on the bullwhip has been demonstrated.2 This observation motivates the development of a methodology that can detect the rogue nodes in the network, rectify their performance, and * To whom correspondence should be addressed. Tel.: (65) 6516 8484. Fax: (65) 6779 1936. E-mail address: [email protected].

bring benefits to the entire supply chain. While several research articles address the issues of control and optimization of supply chains, works relating to the identification of the nuisance nodes, followed by amelioration of their performance, are relatively few. This work intends to provide one possible approach in this direction. Specifically, this work is aimed at the performance improvement of supply-chain systems that have decentralized operations. We contribute a methodology that first identifies poorly performing nodes and some system parameters (lead times) from the time series data generated by the supply-chain network. Then, a multistep heuristic procedure is used to improve the network performance in stages. The final improved performance is then compared with the benchmark performances offered by heuristic replenishment policies, namely, PI, SOP1, and SOP2. Both stationary and nonstationary demand patterns are considered to demonstrate the efficacy of the proposed approach. This paper is organized as follows. Section 2 provides the background information and a review of the literature related to control and optimization of supply chains. It also motivates the methodology developed in this paper. Section 3 introduces the supply-chain network considered in this paper. The supplychain configuration, model equations, mathematical expressions for the different replenishment policies, and performance indicators are also provided. Details of the proposed multistep performance improvement methodology are given in section 4. Two case studies are presented in section 5, and section 6 provides the conclusions arising from this work. 2. Literature Review 2.1. Bullwhip Effect and Disturbances. As mentioned previously, the bullwhip effect is a major problem in supply chains. Several researchers have analyzed the reasons for its occurrence and have suggested ways to minimize or remove it. Wikner et al.3 used a model of the three-echelon Forrester production-distribution system to show that the performance of the supply chain can be far from optimal due to bullwhip effect. They also proposed several approaches to improve the behavior of the system. Lee et al.4 developed a support model for the HP Company to describe the benefit of partially shared information flow over fully centralized and decentralized

10.1021/ie070256e CCC: $40.75 © 2008 American Chemical Society Published on Web 01/05/2008

Ind. Eng. Chem. Res., Vol. 47, No. 3, 2008 749

Figure 1. Decentralized distribution network.

systems to better manage material flow across the organizational barrier. Lee et al.1,5 identified demand forecasting, lead times, batch orders, supply shortages, and price variations to be the major causes for the bullwhip effect in supply-chain systems. Chen et al.6 observed that lead time and inaccurate demand forecasting causes demand variability at the upstream nodes in both centralized and decentralized systems. The sources for the bullwhip effect in a multi-echelon system have also been identified and quantified.7 Frequency-response techniques were utilized to prove that the order-up-to policy (replenishment rule) unavoidably results in the bullwhip effect, irrespective of the demand forecaster used. The bullwhip effect has also been shown to be possible with other replenishment policies, due to factors such as inaccurate demand forecasting, impact of lead time, and inappropriate replenishment rule parameters.7,8 Analytical expressions were developed to quantify the bullwhip effect and variance in inventory position.8 These expressions were used to identify the replenishment rule that results in a minimum bullwhip effect and a small inventory variance. A new replenishment rulescalled the smoothing order policys was also proposed to overcome the bullwhip effect.8 Hoberg et al.9 applied linear control theory concepts on a two-echelon supply-chain system to study the effect of inventory policy on the variability of the orders and inventories. They examined several inventory management policies and concluded that the use of inventory-on-hand for ordering leads to instability in the supply chain. In practice, the use of inventory position is recommended. In manufacturing-remanufacturing systems, factors such as product in-use time, return rate of used products,

and remanufacturing rate are shown to affect the inventory variance and the bullwhip effect.10 In supply chains, disturbances can arise due to exogenous (e.g., market demand) or endogenous (e.g., inappropriate internal strategies) reasons. Decision structures such as inventory control policies and production planning were found to cause cyclic disturbances in supply chains.11 Recent efforts have focused on data-based approaches to the detection of rogue oscillations in supply chains. Spectral principal components analysis (SPCA) has been used to identify the presence of oscillations in a supply chain that was comprised of four autonomous steel-making facilities.12 In addition, Naim et al.13 studied the robustness of the SPCA method to detect and diagnose the rogue oscillations using time-series data. The oscillation frequencies and the variables in which these appear can be used to identify problems in the supply chain. Identifying the root cause of the rogue disturbance from analysis of the power spectrum is a crucial step in diagnosis. The diagnosis aspect still remains an unresolved problem. Naim et al.14 proposed a systematic diagnostic approach (called the Quick Scan approach) to collect and synthesize the qualitative and quantitative information from the supply-chain system. The synthesized information is used to advise the supply-chain entities about the direction and magnitude of changes required in their operations so that performance improvement can be achieved. The application of this diagnostic methodology for 20 European automotive supply chains has shown that 10% of automotive supply chains are performing close to the supply-chain goal, 30% of the supply chain exhibits good practices, and the rest are struggling to

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Table 1. Internal Strategies of the Distribution Nodes Internal Strategy distributor node

case study 1

case study 2

replenishment policy

R1, R2, R3 R4, R5 R6, R7, R8 R9, R10 DC1 DC2 DC3 DC4

responsive nonresponsive nonresponsive responsive responsive responsive responsive responsive

responsive responsive responsive responsive responsive responsive responsive responsive

PI PI order-up-to policy order-up-to policy PI order-up-to policy SOP1 SOP2

implement lean production techniques. This indicates the importance of troubleshooting and reinforcement methods to revise the tactical decisions/strategies of the distribution nodes to improve the supply-chain network performance. These aspects are not addressed well in the current literature and, therefore, are the objective of the present work. Although exogenous disruptions are inevitable due to uncertain market behavior, substantial improvements in supply-chain performance can still be achieved by avoiding endogenous distortions that arise within the network. Of the several ways to reduce bullwhip and disturbance effects, retuning the replenishment rule parameters or adopting a better replenishment policy are significant and readily employable solutions. In the present work, the bullwhip effect will be used as a major beneficial constraint to improve network performance. 2.2. Control Laws for Supply Chains: Replenishment Strategies. The nodes in a supply-chain network can either practice batch replenishment strategy or continuous replenishment strategy. In batch replenishment strategy, the replenishment order is placed on the upstream node once every M sample intervals, irrespective of the demand faced at each sample interval. Alternatively, the replenishment order is postponed until the accumulated orders fulfill the minimum order quantity. In the continuous replenishment strategy, the replenishment order is placed on the upstream node at every sample interval. The bullwhip effect is shown to be inevitable under the batch replenishment strategy.15 Heuristic continuous replenishment rules, such as order-up-to policy, as well as proportionalintegral (PI) and cascade control strategy, were applied and their performance capability was analyzed in terms of excess inventory (inventory quantity that is in excess of the real demand), back order (customer orders that cannot be satisfied currently because the product is not currently in stock), and demand distortion.2 The order-up-to policy is shown to produce a stronger bullwhip effect, because of large lead times, irrespective of the demand forecaster. It was also demonstrated that the PI and cascade policies provide less back-order at the expense of holding higher excess inventory, whereas an order-up-to policy provides less excess inventory at the cost of high back-orders. For the distribution system facing a stochastic demand pattern, Lin et al.16 derived the minimum variance control (MVC) strategy for the distribution system by characterizing the demand pattern. The MVC strategy was obtained with the objective of minimizing the errors between the predicted in-hand and onroad inventories and the desired targets. By characterizing the downstream order as an ARIMA model, the future inventory level in-hand and on-road are predicted, along with the corresponding errors to minimize the objective function. For both stationary and nonstationary demand trends, the optimized performance of the MVC was determined to be superior to the optimized performance of the other existing schemes, such as order-up-to policy, PI control, and smoothing order policy with a bullwhip constraint. Although the MVC strategy performs

Figure 2. Schematic representation of distribution system.

better than other heuristic replenishment strategies, it is not readily extendable to all the nodes in the network, because of heavy interaction between the nodes, which causes difficulty in characterizing the right ARIMA demand model for all the nodes. Therefore, the present work has the objective of improving the performance of the supply-chain network by restricting the industrial heuristics to realistically implementable options. Perea-Lopez et al.17 considered a single manufacturing site, multi-product processing unit with the distribution network consisting of a warehouse, a distribution center, and a retailer with three different customers. Several ordering policies and the effect of the parameters were analyzed to understand the tradeoffs between the bullwhip effect, customer satisfaction, and cost. Although this work is strong on modeling and simulation aspects, it lacks a troubleshooting and performance improvement perspective. The centralized model predictive control (MPC) strategy of the entire supply-chain network has been shown to provide better performance than decentralized control of individual nodes in the supply-chain network.18 The MPC strategy applied to a three-echelon six-node system confirms the low safety stock requirement, compared to other heuristics.19 This is because the MPC strategy handles the uncertainty in plantmodel mismatch, and the constraints, in an effective manner. Better information sharing is also a key factor for the superiority displayed by MPC. The MPC strategy has been shown to perform well on a multi-product multi-echelon supply-chain system20 and compared somewhat unfavorably to a model reference control strategy.21 Despite the advantages offered by centralized control, decentralized operation is common in realworld supply chains that are characterized by strong and complex interactions. With there being relatively few attempts in addressing such issues in decentralized supply chains, we choose to consider only performance improvement in such decentralized systems. 2.3. Optimization in Supply Chains. There is a huge body of literature on the application of optimization methods to supply chains. Our intention here is not to provide an exhaustive overview of this area but to point to some relevant recent work. The optimization problem can be set up and solved (in general) as a mixed integer nonlinear programming (MINLP) problem or solved using simulation-based optimization strategies.22,23 Mele et al.23 optimized the parameters (review period and desired inventory setpoint) of a supply chain practicing orderup-to policy for a specific demand pattern. The drawback of their work is the non-inclusion of the bullwhip effect. Stochastic optimization approaches such as genetic algorithms have been very useful in solving the optimization problem.23,24 The supply chain may have multiple or prioritized objectives (see section 2.4); multiobjective optimization approaches are useful in these situations.25,26 To keep the presentation simple, only single objective optimization that minimizes supply-chain cost (expressed as a function of excess inventory and back order) is pursued in this work. Naim et al.27 presented a framework to design an efficient supply chain and analyze its dynamic behavior in two distinct phases. In the conceptual phase, the emphasis is on gaining


knowledge about the structure and operation of the supply chain. The technical phase is associated with the development and analysis of mathematical and simulation models; thus, it is more quantitative and computational in nature. The quantitative analysis includes tuning the supply-chain structure, decision rules, and lead-time parameters; structural redesign; and the examination of “what if” scenarios. While the framework is powerful, it is intended for the optimal design of new supply chains and does not address the issue of fortifying the existing supply chain to achieve better performance. There is no attempt to determine the inefficient nodes in the network with a view to improving their performance. Instead, the existing methods perform brute force optimization of the entire supply-chain system under specific demand patterns with full knowledge of the system characteristics and constraints. The present work aims to provide a performance improvement approach for an existing decentralized supply chain that is characterized by fixed architecture, connectivity, and location. 2.4. Performance Measures in Supply Chains. In modern supply-chain management, performance measurement and benchmarking are essential to synthesize business intelligence and to determine a range of possible action plans. From the management perspective, performance measures provide necessary information for decision makers to diagnose existing problems and for assisting the management in revising supply-chain goals, as well as re-engineering and tweaking business logistics. Beamon28 identified the performance measures of the manufacturing supply-chain system and listed various performance metrics to characterize the production, distribution, and inventory systems. Identifying the key performance metrics of the distribution system is tedious, owing to the complex nature of the distribution network. In general, performance metrics can be categorized into three groups, involving resources, output, and flexibility. Each group refers to different goals; therefore, an effective performance measure system should include at least one performance metric from each category to attain strategic goals. For the distribution network, the resources category represents the supply-chain costs (i.e., inventory cost, back-order cost, transportation cost); the output represents the revenue, customer service level, number of stock-outs, etc. The third category represents the flexibility in managing inventory level, order quantity, transportation capacity, and responsiveness of the inventory target set in accordance to the uncertain demand. The performance measures can also be categorized into qualitative and quantitative metrics, depending on their characteristics. Chan29 characterized new performance metrics such as visibility, trust, and innovativeness, and also quantified the existing metrics (such as resource utilization and flexibility) in several ways. Although qualitative measures are the important characteristics of a supply chain, it is more challenging to incorporate the qualitative measures (e.g., supplier performance and information flow) into quantitative models. Gunasekaran et al.30 developed a framework for measuring the strategic, tactical, and operational level of performance in a supply chain. Juran et al.31 organized the performance measures into customer-focused and companyfocused categories. Back-orders, fill rates, and customer satisfaction are metrics that are chosen to focus on customers. The lead-time variability, compliance with production schedules, and inventory levels are the metrics used to address companies. Different assessment techniques were identified for various levels of detail in which the supply chain can be represented. Once the performance of a supply chain is measured, it must be benchmarked against the performance of a theoretically best or practically optimal supply chain with the same connectivity

and demand pattern. This is best achieved in silico, using a mathematical model that adequately represents the supply chain. Various replenishment policies can be applied to the system and its parameters can be optimized to generate the benchmark performance. PI and smoothing-order policies (SOP1 and SOP2) are used as benchmarks to illustrate the effectiveness of our proposed approach. These benchmark performances will be obtained through simulation-based optimization that employ genetic algorithms. 3. Problem Description In this section, a decentralized supply-chain network with fixed architecture, connectivity, and location among the distribution nodes is considered for performance improvement. To be realistic, a multi-product multi-echelon decentralized supplychain network is considered. The system and its model are similar to that studied by Perea-Lopez et al.18 The distribution network (shown in Figure 1) consists of 10 retailers (labeled as R1-R10) and 4 distribution centers (identified as DC1-DC4), and it manages 9 different products, with a unique warehouse (W) and manufacturing facility (P) for each product. We seek to enhance the performance of this multi-product multi-echelon distribution network by analyzing the network data, followed by optimization that is implemented in stages. This demanddriven system is fully decentralized in which each distribution node belongs to (possibly) different companies. Each distribution unit prefers to adopt its own internal strategy to optimize local performance without considering the adverse bullwhip effects exerted on the other parts of the network or on the overall network performance. The internal strategy practiced by the distribution nodes of the existing network are given in Table 1. Explanations for the terms used under “Internal Strategy” and “Replenishment Policy” in Table 1 will be provided later. The internal strategy practiced by each distribution node is based on the decision made by its management to manage the inventory level. The inventory can be fixed at a constant target value or made responsive to the uncertain demand. The latter strategy (where the inventory target is changed in accordance with the uncertain demand pattern) is known to provide increased customer satisfaction with less back-order and minimal excess inventory.2,8 3.1. Material Balances and Information Flow. Lin et al.2 modeled the dynamic behavior of the distribution nodes using material and information flows (see Figure 2 for the schematic of a single product system). The discrete model proposed by them is adapted for the multi-product multi-echelon supply chain. The main objective of the distribution node (e.g., distributor) i is to organize the inventory position IPi,p(t) of the product p (where p ) A to I), at a discrete time t, at the desired target level. For node i, let Ygi,p denote the material flow from its supplier (e.g., warehouse) g and let Yij,p denote the material flow from node i to a downstream node (e.g., retailer) j. The inventory position at time t is dependent on the inventory position at time t - 1, the materials received, and the materials dispatched from node i (see eq 1). The inventory position (IPi,p(t)) is the sum of the inventory at hand (IHi,p(t)) and the inventory on road (IRi,p(t)) (see eq 2). IRi,p(t) is the sum of orders satisfied by the supplier but not received by the distributor node because of the lead time (transportation delay plus processing time) of Li,p samples. Based on the above description, we can write the following equations for distribution node i:

752


IPi,p(t) ) IPi,p(t - 1) + Ygi,p(t) -

∑j Yij,p(t)

SIPi,p(z-1) ) (Li,p + 2)

∀ g,i,j,p (1)

IPi,p(t) ) IHi,p(t) + IRi,p(t)

SIPi,p(z-1) ) Ki,p (constant)

(2)

U h ji,p(z-1) )

Equation 1 can be rewritten, using the z-transform, as

IPi,p(z-1) )

1 1-z

-1

(Ygi,p(z-1)) 1 1-z

-1

∑j Yij,p(z-1)

∀ g,i,j,p (3)

The dynamics of the inventory at hand is similar to that of the inventory position, with the only change being that the material dispatched by the supplier at time t - Li,p is used on the righthand side (RHS) of the material balance equation (eq 4).

IHi,p(t) ) IHi,p(t - 1) + Ygi,p(t - Li,p) -

∑j Yij,p(t)

(4)

Equation 4 can be expressed, using the z-transform, as

IHi,p(z-1) )

z-Li,p 1-z

(Ygi,p(z-1)) -

-1

1 1-z

-1

∑j Yij,p(z-1)

∀ g,i,j,p (5)

Equations 1, 2, and 4 may be used to express IRi,p(t), in terms of the z-transform, as

IRi,p(z-1) )

1 - z-Li,p (Ygi,p(z-1)) 1 - z-1

Ri,p 1 - (1 - Ri,p)z

(7) (8)

(Uji,p(z-1))

-1

(9)

In the above equations, Uji,p represents the actual downstream order and U h ji,p represents the “forecasted” downstream order. Equation 7 indicates that the optimum desired inventory target is equal to the responsiveness factor (i.e., Li,p + 2) multiplied by the forecasted demand (i.e., the forecasted demand for Li,p + 2 time periods). Li,p represents the lead time faced due to transportation time and the extra two discrete time periods signify the time taken by the supplier to process the order and for the distributor i to update the material p received. Thus, Li,p is dependent on the geographical location of the supplier and customer, modes of transportation available, and the product availability. With the accurate estimation of Li,p, it is possible to set appropriate setpoints that are responsive to the demand. The lead-time information can be obtained from the authorities of the distribution node or estimated from time-series data (using autocorrelation) gathered from the supply chain. Note that the proper estimation of the lead time is an important factor in improving supply-chain performance. The rate at which downstream orders are satisfied is dependent on the inventory level at hand. We consider two cases of downstream order processing methods. Case (1): Supplier maintains high inventory (IHi,p) and is capable of satisfying all downstream customer orders (Uji,p). This situation can be modeled by eq 10:

Yij,p ) z-1Uji,p when IHi,p >

(6a)

It must also be noted that the inventory on road at time t (IRi,p(t)) is the sum of the orders satisfied by the supplier during the past Li,p time periods (but not received at node i at time t due to the transportation delay):

∑j Uh ji,p(z-1)

∑j Uji,p

∀ i,j,p

(10)

Case (2): Supplier maintains limited inventory and has a policy of satisfying equal proportion of all downstream orders, with respect to the inventory at hand. This situation is modeled by eq 11.

t

IRi,p(t) )

∑ k)t-L

Ygi,p(k)

Yij,p ) z-1ki,pUji,p

(6b)

(11)

i,p

where Ygi,p(k) is the order shipped by supplier node g at time k versus an order placed by node i (i.e., Uig,p(k)). Generally, the decentralized node prefers to become more responsive to the market demand by maintaining flexible inventory position, to minimize inventory holding cost, excess inventory, and back-order cost. The flexibility in inventory position is achieved by setting the desired inventory position target SIPi,p(t) in response to the cumulative forecasted demand from all downstream nodes j’ for Li,p time periods (eq 7). Such a responsive strategy/policy is assumed to be practiced by several retailer nodes and distribution centers in our example. In contrast, retailers R4-R8 are assumed to adopt a constant inventory position (nonresponsive strategy) as the target (eq 8). The exponential forecaster with Ri,p ) 0.111 (eq 9) was used for all products in all distribution nodes that practice responsive strategy to forecast the downstream demand as suggested in the literature (by Lin et al.2).

where

ki,p )

IHi,p

∑j Uji,p

∈ [0,1]

when IHi,p
1, the

node is classified as aggressiVe. Nodes for which the back orders are significantly higher than excess inventory (for any product or products) are tagged as weak nodes. These nodes have BW , 1, because they replenish less merchandise than what is required by downstream customers. Distribution nodes practicing order-up-to policy and having BW > 1 (for any product or products) are considered to be conflict nodes. Conflict nodes are characterized by their rigid replenishment structure, which lacks tunable parameters. The aggressive nodes are first considered for performance improvement. The replenishment parameters of the aggressive nodes are retuned to dampen BW. This preference to improve aggressive nodes rather than the weak or conflict nodes is to eliminate the inventory variability caused by the nodes having

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Table 2. Existing Performance Measures of the Distribution Network Facing Stationary Demand nodes

AEI

ABO

BWmax

ABW

type

total active product nodes

R1, R2, R3 R4, R5 R6, R7, R8 R9, R10 DC1 DC2 DC3 DC4 sum

4.7601 3.9405 3.0808 6.3556 26.5851 14.0079 9.2474 15.583 83.56

4.8776 4.7315 4.414 6.2979 27.3918 14.354 9.7137 19.5495 91.33

2.2182 0.4385 1.0059 6.302 12.848 19.8547 4.5684 1.3014

2.0005 0.4065 1.0016 6.0597 10.1788 14.6134 3.5219 1.0701

A W C C A C A A

16 13 13 12 9 8 8 9

cost 771.016 563.68 487.162 759.21 340.054 158.827 106.182 221.335 3407.47

Table 3. Existing Performance Measures of the Distribution Network Facing Nonstationary Demand nodes

AEI

ABO

BWmax

ABW

type



45.8883 53.676 48.3745 64.7018 1942.5 1303.1 3967.5 5428.1 12853.84

4.911 4.5079 3.2772 5.8354 30.0442 13.2915 18.1288 104.4177 184.4137

122.9975 91.2343 1106.6 2382.8 3.8543 5.4827 3.0969 0.6024

47.4692 41.4681 424.1351 655.5763 2.37 3.3235 2.0498 0.4665

A A C C A C A W

16 13 13 12 9 8 8 9

large BW. This improvement is brought forth using the parameters of the aggressive nodes as decision variables and performing simulation-based optimization (details provided later). Let us assume that 5 nodes have been tagged as aggressive and each of them handles 3 products and implements PI replenishment policy (2 parameters). Here, the optimization problem solved will have 30 decision variables (5 × 3 × 2 ) 30). In the second stage, weak nodes are considered for improvement. The replenishment parameters of the weak nodes are retuned to enhance their performance. The benefit of improving weak nodes in the second stage (after dampening the aggressive nodes) is to have efficient improvement in them after the endogenous disruptions that are caused by other aggressive nodes have been removed. The optimization is effected in exactly the same way as was done for the aggressive nodes. In the first and second stages of performance improvement, the replenishment rule structure and internal strategy (e.g., demand forecasting) of the aggressive and weak nodes are retained; only the replenishment rule parameters are retuned. Finally, the conflict nodes are optimized by changing the replenishment rule and/or making the internal strategy responsive to the demand faced. Usually, in practice, a distribution node will not favor a revision in their internal strategy, in comparison to an adjustment in the parameter values of the replenishment rule. It also takes considerable effort to implement changes in the internal strategy. Hence, the choice of changing the internal strategies are delayed to the final stage of the performance improvement efforts and are also restricted only to the conflict nodes. The replenishment policy of the conflict nodes are changed to PI policy and the inventory setpoint is made responsive, as given by eq 7. The PI parameters are then optimized as in the earlier stages. The third stage of performance improvement is intended to handle distribution units that are insensitive to the first- and second-stage performance enhancement efforts. In all three performance improvement stages, the bullwhip constraint is sought to be satisfied. At the end of this multistep performance enhancement effort, the effectiveness of this approach is quantified through a comparison with benchmark performance (defined here as the optimum performance obtained using the similar type of replenishment rule in all the nodes of the network (PI/SOP1/SOP2) while respecting the bullwhip

cost 4063.944 3781.954 3388.652 4232.232 12427.03 7371.792 22319.52 34854.86 92440

constraint). The distribution network can be aligned to operate at an achievable performance benchmark if the third-party supply-chain consultants can implement suitable modifications to the ordering policies in any of the nodes. The model of the supply-chain system is implemented in Simulink.33 The dynamic behavior of the network is simulated for its response to the uncertain customer demand (represented by eqs 12 and 13) for the stationary and nonstationary demand scenarios, respectively. The decision variables (i.e., replenishment rule parameters) of the problematic nodes are changed by the optimizer through successive simulations, so that the network cost (eq 28) is minimized. Optimal parameters are obtained in this manner for the aggressive, weak, and conflict nodes at each stage of the proposed three-step approach. We use the Genetic Algorithm and Direct Search Toolbox in MATLAB34 and use its generalized pattern search (GPS) algorithm. The GPS algorithm is able to handle optimization problems with linear, nonlinear, and bound constraints, and it does not require functions to be differentiable or continuous. The bullwhip constraint is implemented into the optimization problem through the penalty function method. Related computer code (MATLAB and SIMULINK files) can be made available to interested readers upon request. 5. Results and Discussion Two scenarios are demonstrated here. Case study 1 considers the performance improvement framework when the supply chain is subject to a stationary demand pattern. The nonstationary demand case is considered in case study 2. Table 2 shows the existing (base) performance of the supply-chain network facing stationary demand. The average excess inventory (AEI), average back order (ABO), the maximum bullwhip effect (BWmax), and the average bullwhip effect (ABW), as computed from the timeseries data, are provided for each node and summarized in Table 2. The same information is provided in Table 3 for the supply chain facing nonstationary demand. In Tables 2 and 3, the nature of each node is identified as aggressive (A), weak (W) or conflicting (C), based on the criteria described in section 4. The number of products handled by the nodes in each group is given in the “Nodes” column. The lead information of all the nodes in the network is obtained using autocorrelation between


Figure 4. Performance of the distribution network under stationary demand. Table 4. Derived Lead Time Information from the Time-Series Data origin/destination DC1 DC2 DC3 DC4

R1 A-I

R2 A-I

R3 A-I

12

12

12

R4 A-I

R5 A-I

12

12

R6 A-I

R7 A-I

12

R8 A-I

R9 A-I

R10 A-I

PW1 A/B/C

PW2 D/E/F

PW3 G/H/I

12

24 24 36 36

36 24 24 36

36 36 24 24

12 12

12

Table 5. Performance Improvement by Retuning the Aggressive Nodes (Stage 1) nodes

replenishment

AEI

ABO

BWmax

ABW

type



PI PI order-up-to policy order-up-to policy PI order-up-to policy SOP1 SOP2

3.3899 3.9405 3.0808 6.3556 8.3074 14.0079 6.1667 14.4168 59.6656

5.299 4.7315 4.414 6.2979 11.1348 14.354 9.9434 19.7136 75.8882

0.5051 0.4385 1.0059 6.302 0.9676 19.8547 1 0.8736

0.2314 0.4065 1.0016 6.0597 0.8682 14.6134 1 0.6075

A W C C A C A A

16 13 13 12 9 8 8 9

appropriate time-series data (e.g., between an order placed by a node and the material received from the supplier). The estimated lead times for the inefficient nodes have been summarized in Table 4. 5.1. Results for Case Study 1: Stationary Demand. As shown in Table 2, the overall cost of the network is 3407.47. The average excess inventory is 83.56, and the average back order is 91.33. The performance enhancement framework is now implemented on this base-case performance. The benefits obtained by retuning the replenishment parameters of the aggressive nodes are shown in Table 5. The supply-chain cost is reduced to 3092 at this stage. This represents a significant improvement. The AEI and ABO are also reduced significantly (as expected) to 59.67 and 75.89, respectively. In the second stage, the parameters of weak nodes are optimized. A small reduction in the overall cost is obtained. The overall cost, AEI, and ABO are 3081, 59.61 and 75.91, respectively. Finally, more performance improvement is obtained by restructuring the internal strategy of the conflicting distribution nodes (as explained in section 4). At the end of stage 3, the overall cost

cost 695.112 563.68 487.162 759.21 122.486 158.827 90.2166 215.022 3091.71

is obtained. The overall cost, AEI, and ABO are 2905, 47, and 68, respectively. Elaborate details of the supply-chain performances at the end of stages 2 and 3 are not shown here, because of space constraints. The performance indicators (EI and BO) for all products in the retail and distribution center nodes are shown in Figure 4. In that figure, nodes 1-90 indicate the retailer nodes (10 retailer nodes × 9 products) and nodes 91126 indicate the distribution center (4 distribution centers × 9 products) nodes. The improvement through our performance improvement methodology is clearly visible in the EI and BO profiles across the nodes for all products. From Figure 4, it is easy to visualize the high EI and BO spikes in the base performance of the nodes R9, R10, and DC2. After the threestage performance improvement, their EI and BO are reduced considerably and are similar to the benchmark performance shown in Figure 4. Overall, an ∼15% improvement in performance was obtained (the supply-chain costs decrease from 3407.47 to 2904.8). The PI and smoothing order policies (SOP1 and SOP2) were used in all the distribution nodes to estimate the achievable

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performance of the distribution network for benchmarking purpose. The overall supply-chain cost for the PI, SOP1, and SOP2 policies turned out to be 3000.2, 2731.12, and 2766.65, respectively. It is observed that SOP2 outperforms PI strategy slightly and SOP1 provides the best performance. The result obtained from our three-stage performance enhancement procedure compares favorably with the performance obtained with the benchmarks. With reference to the performance benchmark (i.e., the use of SOP1 in all the nodes), the final performance achieved with our methodology is 1.06 (benchmark performance is 1; values close to 1 indicate better performance than values significantly larger than 1). 5.2. Results for Case Study 2: Nonstationary Demand. The three-stage procedure was implemented for performance improvement. The performance improvement obtained during the assessment stages and the optimized performance attained using the various heuristic rules are as follows: starting from the base overall cost of 92440, the cost reduces to 72235 (after stage 1), 49885 (after stage 2), and 5888 (after stage 3). In this case, significant improvements have been achieved with each stage. The maximum change occurs in stage 3; in this phase, the conflict nodes are made responsive to demand and the PI policy is implemented instead of order-up-to policy. The benchmark performances are 5268 (PI), 44168 (SOP1), and 5470 (SOP2). SOP2 strategy outperforms SOP1 strategy by a significant margin. PI strategy provides the best performance. With reference to the benchmark performance (obtained with the use of PI replenishment policy in all the nodes), the final performance achieved with our methodology is 1.12, compared to the initial performance measure of 17.55. This shows the effectiveness of the proposed strategy. Because of space limitations, only limited information is provided here. We can make further details available to interested readers upon request. Despite the fact that the method is shown to provide a workable supply-chain improvement strategy that is minimally intrusive, it suffers from the limitation of being a heuristic approach. Our current work is focused on making the approach more formal and sophisticated while retaining its minimally intrusive nature. This will be the subject of our future publications. 6. Conclusions We have proposed a heuristic three-stage approach to improve the performance of decentralized supply chains. Workability of the proposed strategy was demonstrated using a realistic multiechelon multi-product decentralized supply-chain system under two different demand trends. The proposed improvement method was intended to provide performance that is similar to the achievable performance. The novelty of the presented work is in identifying bottleneck nodes that cause performance deterioration (from the analysis of supply-chain data) and using a staged approach to effect significant improvements in the supply-chain performance. The improvement is achieved by tuning the replenishment parameters or by altering the replenishment strategies practiced by the problematic nodes. The ability to improve the performance of the distribution network (contingent on the implementation limitations at the distribution nodes) in a minimally intrusive manner makes the proposed methodology attractive and straightforward to implement. Literature Cited (1) Lee, H. L.; Padmanabhan, V.; Whang, S. The Bullwhip Effect in Supply Chains. Sloan Manage. ReV. 1997, 38, 93-102.

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ReceiVed for reView February 18, 2007 ReVised manuscript receiVed October 10, 2007 Accepted October 17, 2007 IE070256E

Enhancement Methodology for Supply

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