Supply chain design under uncertainty using sample average approximation and dual decomposition

We present a supply chain design problem modeled as a sequence of splitting and combining processes. We formulate the problem as a two-stage stochastic program. The first-stage decisions are strategic location decisions, whereas the second stage consists of operational decisions. The objective is to minimize the sum of investment costs and expected costs of operating the supply chain. In particular the model emphasizes the importance of operational flexibility when making strategic decisions. For that reason short-term uncertainty is considered as well as long-term uncertainty. The real-world case used to illustrate the model is from the Norwegian meat industry. We solve the problem by sample average approximation in combination with dual decomposition. Computational results are presented for different sample sizes and different levels of data aggregation in the second stage.     

Selection of contract suppliers under price and demand uncertainty in a dynamic market

In this paper, we consider a supply contracting problem in which the buyer firm faces non-stationary stochastic price and demand. First, we derive analytical results to compare two pure strategies: (i) periodically purchasing from the spot market; and (ii) signing a long-term contract with a single supplier. The results from the pure strategies show that the selection of suppliers can be complicated by many parameters, and is particularly affected by price uncertainty. We then develop a stochastic dynamic programming model to incorporate mixed strategies, purchasing commitments and contract cancellations. Computational results show that increases in price (demand) uncertainty favor long-term (short-term) suppliers. By examining the two-way interactions of contract factors (price, demand, purchasing bounds, learning and technology effect, salvage values and contract cancellation), both intuitive and non-intuitive managerial insights in outsourcing strategies are derived.     

Collaborative production planning of supply chain under price and demand uncertainty

This research is motivated by an automobile manufacturing supply chain network. It involves a multi-echelon production system with material supply, component fabrication, manufacturing, and final product distribution activities. We address the production planning issue by considering bill of materials and the trade-offs between inventories, production costs and customer service level. Due to its complexity, an integrated solution framework which combines scatter evolutionary algorithm, fuzzy programming and stochastic chance-constrained programming are combined to jointly take up the issue. We conduct a computational study to evaluate the model. Numerical results using the proposed algorithm confirm the advantage of the integrated planning approach. Compared with other solution methodologies, the supply chain profits from the proposed approach consistently outperform, in some cases up to 13% better. The impacts of uncertainty in demand, material price, and other parameters on the performance of the supply chain are studied through sensitivity analysis. We found the proposed model is effective in developing robust production plans under various market conditions.     

Integrated supply chain planning under uncertainty using an improved stochastic approach

This paper proposes an integrated model and a modified solution method for solving supply chain network design problems under uncertainty. The stochastic supply chain network design model is provided as a two-stage stochastic program where the two stages in the decision-making process correspond to the strategic and tactical decisions. The uncertainties are mostly found in the tactical stage because most tactical parameters are not fully known when the strategic decisions have to be made. The main uncertain parameters are the operational costs, the customer demand and capacity of the facilities. In the improved solution method, the sample average approximation technique is integrated with the accelerated Benders’ decomposition approach to improvement of the mixed integer linear programming solution phase. The surrogate constraints method will be utilized to acceleration of the decomposition algorithm. A computational study on randomly generated data sets is presented to highlight the efficiency of the proposed solution method. The computational results show that the modified sample average approximation method effectively expedites the computational procedure in comparison with the original approach.     

Supply chain structure in a market with deceptive counterfeits

Deceptive counterfeits differ from non-deceptive ones in that they are packaged and sold as authentic brand name products so that consumers may buy counterfeits unknowingly. When a distribution channel, referred to as the general channel, has been penetrated with deceptive counterfeits, a brand name company may need to restructure the way its products are distributed and rely on reliable channels such as certified stores or manufacturer-owned stores to guarantee 100% authenticity. In this paper, we first identify the conditions under which the general channel will carry deceptive counterfeits, and then analyze the optimal supply chain structure in the presence of counterfeits as well as by incorporating the wholesale price decisions, consumers’ risk attitude towards counterfeits and consumer loyalty towards the reliable stores. Our main finding is that the brand name company should continue to sell, sometimes exclusively, through the general channel despite deceptive counterfeiting under various conditions.     

Buyback contracts with price-dependent demands: Effects of demand uncertainty

We explore buyback contracts in a supplier–retailer supply chain where the retailer faces a price-dependent downward-sloping demand curve subject to uncertainty. Differentiated from the existing literature, this work focuses on analytically examining how the uncertainty level embedded in market demand affects the applicability of buyback contracts in supply chain management. To this end, we seek to characterize the buyback model in terms of only the demand uncertainty level (DUL). With this new research perspective, we have obtained some interesting new findings for buyback. For example, we find that (1) even though the supply chain’s efficiency will change over the DUL with a wholesale price-only contract, it will be maintained constantly at that of the corresponding deterministic demand setting with buyback, regardless of the DUL; (2) in the practice of buyback, the buyback issuer should adjust only the buyback price in reaction to different DULs while leave the wholesale price unchanged as that in the corresponding deterministic demand setting; (3) only in the demand setting with an intermediate level of the uncertainty (which is identified quantitatively in Theorem 5), buyback provision is beneficial simultaneously for the supplier, the retailer, and the supply chain system, while this is not the case in the other demand settings. This work reveals that DUL can be a critical factor affecting the applicability of supply chain contracts.     

Analysis of supply chain coordination under fuzzy demand in a two-stage supply chain

This paper considers a two-stage supply chain coordination problem and focuses on the fuzziness aspect of demand uncertainty. We use fuzzy numbers to depict customer demand, and investigate the optimization of the vertically integrated two-stage supply chain under perfect coordination and contrast with the non-coordination case. As in the traditional probabilistic analysis, we prove that the maximum expected supply chain profit in a coordination situation is greater than the total profit in a non-coordination situation.     

A robust optimization model for multi-site production planning problem in an uncertain environment

This paper addresses the multi-site production planning problem for a multinational lingerie company in Hong Kong subject to production import/export quotas imposed by regulatory requirements of different nations, the use of manufacturing factories/locations with regard to customers’ preferences, as well as production capacity, workforce level, storage space and resource conditions at the factories. In this paper, a robust optimization model is developed to solve multi-site production planning problem with uncertainty data, in which the total costs consisting of production cost, labor cost, inventory cost, and workforce changing cost are minimized. By adjusting penalty parameters, production management can determine an optimal medium-term production strategy including the production loading plan and workforce level while considering different economic growth scenarios. The robustness and effectiveness of the developed model are demonstrated by numerical results. The trade-off between solution robustness and model robustness is also analyzed.     

An optimal solution to a three echelon supply chain network with multi-product and multi-period

Recently, Kadadevaramath et al. (2012) [1] presented a mathematical model for optimizing a three echelon supply chain network. Their model is an integer linear programming (ILP) model. In order to solve it, they developed five algorithms; four of them are based on a particle swarm optimization (PSO) method and the other is a genetic algorithm (GA). In this paper, we develop a more general mathematical model that contains the model developed by Kadadevaramath et al. (2012) [1]. Furthermore, we show that all instances proved in Kadadevaramath et al. (2012) [1] can easily be solved optimally by any integer linear programming solver.     

Supply chain organization and e-commerce: a model to analyze store-picking, warehouse-picking and drop-shipping

Across many industries, e-commerce generates substantial modifications in supply chain structures. The aim of this article is to assess different forms of existing organizations when a store-based sales network coexists with a web site order network. Three main organizational models can be detected: “store-picking”, “dedicated warehouse-picking” and “drop-shipping”. We use a “newsboy” order policy model to compare the advantages of these different models and to note the impact of some parameters on inventory and flow management policies throughout the supply chain. Several effects are presented, particularly those linked to the size of the Internet market in relation to traditional market size and market demand hazards.      

Single machine scheduling under market uncertainty

This paper considers single machine scheduling problems where job processing times are known and deterministic but where the reward received upon completion of a job changes stochastically over time according to Brownian motion. The objectives of maximizing expected net-present-value (NPV), minimizing the variance of NPV and maximizing the probability of achieving a minimum benchmark NPV are considered. For non-preemptive static list policies complexity results and branch and bound procedures are presented. The branch and bound procedures are shown to be effective for problem instances with 20–25 jobs. For the problem of maximizing NPV with non-preemptive dynamic policies the optimal static schedule is shown through empirical testing to be as good as a greedy heuristic and to be near optimal when the variance is not large.     

Strategic robust supply chain design based on the Pareto-optimal tradeoff between efficiency and risk

The strategic design of a robust supply chain has to determine the configuration of the supply chain so that its performance remains of a consistently high quality for all possible future conditions. The current modeling techniques often only consider either the efficiency or the risk of the supply chain. Instead, we define the strategic robust supply chain design as the set of all Pareto-optimal configurations considering simultaneously the efficiency and the risk, where the risk is measured by the standard deviation of the efficiency. We model the problem as the Mean–Standard Deviation Robust Design Problem (MSD-RDP). Since the standard deviation has a square root expression, which makes standard maximization algorithms based on mixed-integer linear programming non-applicable, we show the equivalency to the Mean–Variance Robust Design Problem (MV-RDP). The MV-RDP yields an infinite number of mixed-integer programming problems with quadratic objective (MIQO) when considering all possible tradeoff weights. In order to identify all Pareto-optimal configurations efficiently, we extend the branch-and-reduce algorithm by applying optimality cuts and upper bounds to eliminate parts of the infeasible region and the non-Pareto-optimal region. We show that all Pareto-optimal configurations can be found within a prescribed optimality tolerance with a finite number of iterations of solving the MIQO. Numerical experience for a metallurgical case is reported.     

A multi-objective approach to supply chain visibility and risk

This paper investigates the twin effects of supply chain visibility (SCV) and supply chain risk (SCR) on supply chain performance. Operationally, SCV has been linked to the capability of sharing timely and accurate information on exogenous demand, quantity and location of inventory, transport related cost, and other logistics activities throughout an entire supply chain. Similarly, SCR can be viewed as the likelihood that an adverse event has occurred during a certain epoch within a supply chain and the associated consequences of that event which affects supply chain performance. Given the multi-faceted attributes of the decision making process which involves many stages, objectives, and stakeholders, it beckons research into this aspect of the supply chain to utilize a fuzzy multi-objective decision making approach to model SCV and SCR from an operational perspective. Hence, our model incorporates the objectives of SCV maximization, SCR minimization, and cost minimization under the constraints of budget, customer demand, production capacity, and supply availability. A numerical example is used to demonstrate the applicability of the model. Our results suggest that decision makers tend to mitigate SCR first then enhance SCV.     

An optimization approach for supply chain management models with quantity discount policy

Owing to the difficulty of treating nonlinear functions, many supply chain management (SCM) models assume that the average prices of materials, production, transportation, and inventory are constant. This assumption, however, is not practical. Vendors usually offer quantity discounts to encourage the buyers to order more, and the producer intends to discount the unit production cost if the amount of production is large. This study solves a nonlinear SCM model capable of treating various quantity discount functions simultaneously, including linear, single breakpoint, step, and multiple breakpoint functions. By utilizing the presented linearization techniques, such a nonlinear model is approximated to a linear mixed 0–1 program solvable to obtain a global optimum.     

Optimizing revenue in CDMA networks under demand uncertainty

Mathematical programming models for telecommunications network design are prevalent in the literature, but little research has been reported on stochastic models for cellular networks. We present a stochastic revenue optimization model for CDMA networks inspired by bid pricing models from the airline industry. We describe the optimality conditions for the model and develop a supergradient algorithm to solve it. We provide computational results that show the effects of the distribution and variance of demand. Finally, we discuss areas of future research, including a method to optimize the locations of the towers.     

Managing a dual-channel supply chain under price and delivery-time dependent stochastic demand

Several leading manufacturers recently combined the traditional retail channel with a direct online channel to reach a wider range of customers. We examine such a dual-channel supply chain under price and delivery-time dependent stochastic customer demand. We consider five decision variables, the price and order quantity for both the retail and the online channels and the delivery time for the online channel. Uncertainty frequently arises in both retail and online channels and so additional inventory management is required to control shortage or overstock and that has an effect on the optimal order quantity, price, and lead time. We developed mathematical models with the profit maximization motive. We analyze both centralized and decentralized systems for unknown distribution function of the random variables through a distribution-free approach and also for known distribution function. We examine the effect of delivery lead time and customers’ channel preference on the optimal operation. For supply chain coordination a hybrid all-unit quantity discount along a franchise fee contract is used. Moreover, we use the generalized asymmetric Nash bargaining for surplus profit distribution. A numerical example illustrates the findings of the model and the managerial insights are summarized for centralized, decentralized, and coordinated scenarios.     

Closed-loop supply chain network equilibrium under legislation

This paper expands previous work dealing with oligopolistic supply chains to the field of closed-loop supply chains. The model presented has been formulated with the intent of examining issues surrounding the recent European Union directive regarding waste of electric and electronic equipment (WEEE). The network modelled consists of manufacturers and consumer markets engaged in a Cournot pricing game with perfect information. Closed-loop supply chain network equilibrium occurs when all players agree on volumes shipped and prices charged. Certain properties of the model are examined analytically. Numeric examples are included and have been solved using an extragradient method with constant step size. The equilibrium solution obtained provide interesting insights that lead into a number of areas for future research.     

Supply chain analysis under a price-discount incentive scheme for electric vehicles

We investigate an automobile supply chain where a manufacturer and a retailer serve heterogeneous consumers with electric vehicles (EVs) under a government’s price-discount incentive scheme that involves a price discount rate and a subsidy ceiling. We show that the subsidy ceiling is more effective in influencing the optimal wholesale pricing decision of the manufacturer with a higher unit production cost. However, the discount rate is more effective for the manufacturer with a lower unit production cost. Moreover, the expected sales are increasing in the discount rate but may be decreasing in the subsidy ceiling. Analytic results indicate that an effective incentive scheme should include both a discount rate and a subsidy ceiling. We also derive the necessary condition for the most effective discount rate and subsidy ceiling that maximize the expected sales of EVs, and obtain a unique discount rate and subsidy ceiling that most effectively improve the manufacturer’s incentive for EV production.