Modeling and analysis of build-to-order supply chains

The build-to-order supply chain (BTO-SC) or make-to-order (MTO) system has received a great deal of attention in recent years because of the success of high-tech companies such as Dell, BMW, Compaq, and Gateway. Some auto companies have also implemented BTO-SC. Quite a few research articles have been written on BTO-SC and MTO. However, those that explicitly address the problems of BTO-SCM with modeling are rather limited in number. Considering the growing importance of more informed and timely decision making in these areas, there is a need to encourage further research on the modeling and analysis of global outsourcing, optimization between product variants and the cost of production, the point of differentiation along the production/assembly process, the selection of suppliers, logistics costs, and customer relationship management. Traditional operations research models have been used to solve supply chain management problems. Considering the importance of BTO or MTO, an attempt has been made to review the selected literature on the modeling and analysis of BTO-SC with the objectives of providing assistance to and motivating both researchers and practitioners to design, develop, and manage BTO-SC effectively; and suggesting some future research directions on BTO supply chain management (BTO-SCM). The literature available on BTO-SCM has been classified based on the nature of the decision-making areas and then sub-classified to focus on solving problems with modeling and analysis. We have focused mostly on the modeling aspect of the BTO-SC, but have not extended our efforts to empirical research. We have developed a unified framework for modeling and analyzing BTO-SCM and suggest some future research directions.     

Rich routing problems arising in supply chain management

The purpose of this paper is to provide basic models for highly relevant extensions of the classical vehicle routing problem in the context of supply chain management. The classical vehicle routing problem is extended in various ways. We will especially focus on extensions with respect to lotsizing, scheduling, packing, batching, inventory and intermodality. The proposed models allow for a more efficient use of resources, while explicitly taking into account interdependencies among the subproblems. The contribution of this survey is twofold: (i) it provides an overview of recent and suitable literature for the interested scholar and (ii) it presents six integrative models for the above mentioned extensions.     

Fair transfer price and inventory holding policies in two-enterprise supply chains

A key issue in supply chain optimisation involving multiple enterprises is the determination of policies that optimise the performance of the supply chain as a whole while ensuring adequate rewards for each participant.In this paper, we present a mathematical programming formulation for fair, optimised profit distribution between echelons in a general multi-enterprise supply chain. The proposed formulation is based on an approach applying the Nash bargaining solution for finding optimal multi-partner profit levels subject to given minimum echelon profit requirements.The overall problem is first formulated as a mixed integer non-linear programming (MINLP) model. A spatial and binary variable branch-and-bound algorithm is then applied to the above problem based on exact and approximate linearisations of the bilinear terms involved in the model, while at each node of the search tree, a mixed integer linear programming (MILP) problem is solved. The solution comprises inter-firm transfer prices, production and inventory levels, flows of products between echelons, and sales profiles.The applicability of the proposed approach is demonstrated by a number of illustrative examples based on industrial processes.     

Integrated design and operation of remnant inventory supply chains under uncertainty

We consider the simultaneous design and operation of remnant inventory supply chains. Remnant inventory is generated when demand for various lengths of a product may be satisfied by existing inventory, or by cutting a large piece into smaller pieces. We formulate our problem as a two-stage stochastic mixed-integer program. In solving our stochastic program, we enhance the standard L-shaped method in two ways. Our computational experiments demonstrate that these enhancements are effective, dramatically reducing the solution time for large instances.     

An integrated guaranteed- and stochastic-service approach to inventory optimization in supply chains

Multi-echelon inventory optimization literature distinguishes stochastic- (SS) and guaranteed-service (GS) approaches as mutually exclusive frameworks. While the GS approach considers flexibility measures at the stages to deal with stockouts, the SS approach only relies on safety stock. Within a supply chain, flexibility levels might differ between stages rendering them appropriate candidates for one approach or the other. The existing approaches, however, require the selection of a single framework for the entire supply chain instead of a stage-wise choice. We develop an integrated hybrid-service (HS) approach which endogenously determines the overall cost-optimal approach for each stage and computes the required inventory levels. We present a dynamic programming optimization algorithm for serial supply chains that partitions the entire system into subchains of different types. From a numerical study we find that, besides implicitly choosing the better of the two pure frameworks, whose cost differences can be considerable, the HS approach enables additional pipeline and on-hand stock cost savings. We further identify drivers for the preferability of the HS approach.     

Using and extending fix-and-relax to solve maritime inventory routing problems

The paper presents a new way of optimising maritime inventory routing problems (IRP) by using a heuristic approach based on fix-and-relax time decomposition extended with two new features. The purpose of the extensions is to reduce computation time during the fix-and-relax process and to improve solution quality after a first solution is found. The feature which improves solution quality is independent of the method used for calculating the first solution. In this study, the algorithm and extensions have been tested on four liquefied natural gas (LNG) cases and the impacts on computational time and objective function value are reported. The results show that using fix-and-relax reduces computing time considerably while the objective function value is only slightly worse compared to a general MILP solver. Furthermore, the results confirm that the extensions work according to the intentions when compared to the original fix-and-relax heuristic. For relatively complex cases, it appears advantageous to use the extensions developed.     

Bilateral information sharing in two supply chains with complementary products

Information sharing has been regarded as a major way to promote collaboration or to optimize overall supply chain performance. Most of the literature has focused on unilateral information sharing in a supply chain with single or substitutable products. This paper investigates bilateral information sharing in two supply chains with complementary products, and formulates four decision models based on different information sharing patterns. Our results show that (i) information sharing always benefits the manufacturer, and benefits the retailer and the whole supply chain under certain conditions; (ii) information sharing increases/decreases the positive effect of the retailer’s/manufacturer’s forecast on the optimal pricing strategies in its own supply chain; however, its impact depends on the parameter conditions in the other complementary supply chain.     

A queuing approach for inventory planning with batch ordering in multi-echelon supply chains

This paper presents stylized models for conducting performance analysis of the manufacturing supply chain network (SCN) in a stochastic setting for batch ordering. We use queueing models to capture the behavior of SCN. The analysis is clubbed with an inventory optimization model, which can be used for designing inventory policies . In the first case, we model one manufacturer with one warehouse, which supplies to various retailers. We determine the optimal inventory level at the warehouse that minimizes total expected cost of carrying inventory, back order cost associated with serving orders in the backlog queue, and ordering cost. In the second model we impose service level constraint in terms of fill rate (probability an order is filled from stock at warehouse), assuming that customers do not balk from the system. We present several numerical examples to illustrate the model and to illustrate its various features. In the third case, we extend the model to a three-echelon inventory model which explicitly considers the logistics process.     

A continuous approximation procedure for determining inventory distribution schemas within supply chains

This paper presents an integrated inventory distribution optimization model that simultaneously incorporates the issues of location, production, inventory, and transportation within a supply chain. The objective is to determine the optimal number and size of shipments under varying but commonly practiced production and shipping scenarios. A continuous approximation procedure is proposed to determine the optimal number and size of shipments. Three production and shipping scenarios are investigated and closed form expressions for the optimal number of shipments for each scenario are obtained. A numerical example is presented to demonstrate the usefulness of the model.     

Particle swarm optimization for bi-level pricing problems in supply chains

With rapid technological innovation and strong competition in hi-tech industries such as computer and communication organizations, the upstream component price and the downstream product cost usually decline significantly with time. As a result, an effective pricing supply chain model is very important. This paper first establishes two bi-level pricing models for pricing problems with the buyer and the vendor in a supply chain designated as the leader and the follower, respectively. A particle swarm optimization (PSO) based algorithm is developed to solve problems defined by these bi-level pricing models. Experiments illustrate that this PSO based algorithm can achieve a profit increase for buyers or vendors if they are treated as the leaders under some situations, compared with the existing methods.     

Adaptive fuzzy vendor managed inventory control for mitigating the Bullwhip effect in supply chains

This paper proposes an adaptive fuzzy control application to support a vendor managed inventory (VMI). The methodology applies fuzzy control to generate an adaptive smoothing constant in the forecast method, production and delivery plan to eliminate, for example, the rationing and gaming or the Houlihan effect and the order batching effect or the Burbidge effects and finally the Bullwhip effect. The results show that the adaptive fuzzy VMI control surpasses fuzzy VMI control and traditional VMI in terms of mitigating the Bullwhip effect and lower delivery overshoots and backorders. This paper also guides management in allocating inventory by coordinating suppliers and buyers to ensure minimum inventory levels across a supply chain. Adaptive fuzzy VMI control is the main contribution of this paper.     

A new model and hybrid approach for large scale inventory routing problems

This paper studies an inventory routing problem (IRP) with split delivery and vehicle fleet size constraint. Due to the complexity of the IRP, it is very difficult to develop an exact algorithm that can solve large scale problems in a reasonable computation time. As an alternative, an approximate approach that can quickly and near-optimally solve the problem is developed based on an approximate model of the problem and Lagrangian relaxation. In the approach, the model is solved by using a Lagrangian relaxation method in which the relaxed problem is decomposed into an inventory problem and a routing problem that are solved by a linear programming algorithm and a minimum cost flow algorithm, respectively, and the dual problem is solved by using the surrogate subgradient method. The solution of the model obtained by the Lagrangian relaxation method is used to construct a near-optimal solution of the IRP by solving a series of assignment problems. Numerical experiments show that the proposed hybrid approach can find a high quality near-optimal solution for the IRP with up to 200 customers in a reasonable computation time.     

New and efficient algorithms for transfer prices and inventory holding policies in two-enterprise supply chains

We consider a multi-period problem of fair transfer prices and inventory holding policies in two enterprise supply chains. This problem was formulated as a mixed integer non-linear program by Gjerdrum et al. (Eur J Oper Res 143:582–599, 2002). Existing global optimization methods to solve this problem are computationally expensive. We propose a continuous approach based on difference of convex functions (DC) programming and DC Algorithms (DCA) for solving this combinatorial optimization problem. The problem is first reformulated as a DC program via an exact penalty technique. Afterward, DCA, an efficient local approach in non-convex programming framework, is investigated to solve the resulting problem. For globally solving this problem, we investigate a combined DCA-Branch and Bound algorithm. DCA is applied to get lower bounds while upper bounds are computed from a relaxation problem. The numerical results on several test problems show that the proposed algorithms are efficient: DCA provides a good integer solution in a short CPU time although it works on a continuous domain, and the combined DCA-Branch and Bound finds an \(\epsilon \) -optimal solution for large-scale problems in a reasonable time.     

Maritime inventory routing with multiple products: A case study from the cement industry

This paper considers a maritime inventory routing problem faced by a major cement producer. A heterogeneous fleet of bulk ships transport multiple non-mixable cement products from producing factories to regional silo stations along the coast of Norway. Inventory constraints are present both at the factories and the silos, and there are upper and lower limits for all inventories. The ship fleet capacity is limited, and in peak periods the demand for cement products at the silos exceeds the fleet capacity. In addition, constraints regarding the capacity of the ships’ cargo holds, the depth of the ports and the fact that different cement products cannot be mixed must be taken into consideration. A construction heuristic embedded in a genetic algorithmic framework is developed. The approach adopted is used to solve real instances of the problem within reasonable solution time and with good quality solutions.     

Evaluation of cycle-count policies for supply chains with inventory inaccuracy and implications on RFID investments

Inventory record inaccuracy leads to ineffective replenishment decisions and deteriorates supply chain performance. Conducting cycle counts (i.e., periodic inventory auditing) is a common approach to correcting inventory records. It is not clear, however, how inaccuracy at different locations affects supply chain performance and how an effective cycle-count program for a multi-stage supply chain should be designed. This paper aims to answer these questions by considering a serial supply chain that has inventory record inaccuracy and operates under local base-stock policies. A random error, representing a stock loss, such as shrinkage or spoilage, reduces the physical inventory at each location in each period. The errors are cumulative and are not observed until a location performs a cycle count. We provide a simple recursion to evaluate the system cost and propose a heuristic to obtain effective base-stock levels. For a two-stage system with identical error distributions and counting costs, we prove that it is more effective to conduct more frequent cycle counts at the downstream stage. In a numerical study for more general systems, we find that location (proximity to the customer), error rates, and counting costs are primary factors that determine which stages should get a higher priority when allocating cycle counts. However, it is in general not effective to allocate all cycle counts to the priority stages only. One should balance cycle counts between priority stages and non-priority stages by considering secondary factors such as lead times, holding costs, and the supply chain length. In particular, more cycle counts should be allocated to a stage when the ratio of its lead time to the total system lead time is small and the ratio of its holding cost to the total system holding cost is large. In addition, more cycle counts should be allocated to downstream stages when the number of stages in the supply chain is large. The analysis and insights generated from our study can be used to design guidelines or scorecard systems that help managers design better cycle-count policies. Finally, we discuss implications of our study on RFID investments in a supply chain.     

Bundling decisions in supply chains

Firms often sell products in bundles to extract consumer surplus. While most bundling decisions studied in the literature are geared to integrated firms, we examine a decentralized supply chain where the suppliers retain decision rights. Using a generic distribution of customers’ reservation price we establish equilibrium solutions for three different bundling scenarios in a supply chain, and generate interesting insights for distributions with specific forms. We find that (i) in supply chain bundling the retailer’s margin equals the margin of each independent supplier, and it equals the combined margin when the suppliers are in a coalition, (ii) when the suppliers form a coalition to bundle their products the bundling gain in the supply chain is higher and retail price is lower than when the retailer bundles the products, (iii) the supply chain has more to gain from bundling relative to an integrated firm, (iv) the first-best supply chain bundling remains viable over a larger set of parameter values than those in the case of the integrated firm, (v) supplier led bundling is preferable to separate sales over a wider range of parameter values than if the retailer led the bundling, and (vi) if the reservation prices are uniformly distributed bundling can be profitable when the variable costs are low and valuations of the products are not significantly different from one another. For normally distributed reservation prices, we show that the bundling set is larger and the bundling gain is higher than that for a uniform distribution.     

Modeling and optimization of biomass quality variability for decision support systems in biomass supply chains

Annals of Operations Research - A feasible alternative to the production of fossil fuels is the production of biofuels. In order to minimize the costs of producing biofuels, we developed a...