Accelerated sample average approximation method for two-stage stochastic programming with binary first-stage variables

This paper proposes an accelerated solution method to solve two-stage stochastic programming problems with binary variables in the first stage and continuous variables in the second stage. To develop the solution method, an accelerated sample average approximation approach is combined with an accelerated Benders’ decomposition algorithm. The accelerated sample average approximation approach improves the main structure of the original technique through the reduction in the number of mixed integer programming problems that need to be solved. Furthermore, the recently accelerated Benders’ decomposition approach is utilized to expedite the solution time of the mixed integer programming problems. In order to examine the performance of the proposed solution method, the computational experiments are performed on developed stochastic supply chain network design problems. The computational results show that the accelerated solution method solves these problems efficiently. The synergy of the two accelerated approaches improves the computational procedure by an average factor of over 42%, and over 12% in comparison with the original and the recently modified methods, respectively. Moreover, the betterment of the computational process increases substantially with the size of the problem.     

A stochastic programming approach for supply chain network design under uncertainty

This paper proposes a stochastic programming model and solution algorithm for solving supply chain network design problems of a realistic scale. Existing approaches for these problems are either restricted to deterministic environments or can only address a modest number of scenarios for the uncertain problem parameters. Our solution methodology integrates a recently proposed sampling strategy, the sample average approximation (SAA) scheme, with an accelerated Benders decomposition algorithm to quickly compute high quality solutions to large-scale stochastic supply chain design problems with a huge (potentially infinite) number of scenarios. A computational study involving two real supply chain networks are presented to highlight the significance of the stochastic model as well as the efficiency of the proposed solution strategy.     

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.     

Development of a new approach for deterministic supply chain network design

This paper proposes a mixed integer linear programming model and solution algorithm for solving supply chain network design problems in deterministic, multi-commodity, single-period contexts. The strategic level of supply chain planning and tactical level planning of supply chain are aggregated to propose an integrated model. The model integrates location and capacity choices for suppliers, plants and warehouses selection, product range assignment and production flows. The open-or-close decisions for the facilities are binary decision variables and the production and transportation flow decisions are continuous decision variables. Consequently, this problem is a binary mixed integer linear programming problem. In this paper, a modified version of Benders’ decomposition is proposed to solve the model. The most difficulty associated with the Benders’ decomposition is the solution of master problem, as in many real-life problems the model will be NP-hard and very time consuming. In the proposed procedure, the master problem will be developed using the surrogate constraints. We show that the main constraints of the master problem can be replaced by the strongest surrogate constraint. The generated problem with the strongest surrogate constraint is a valid relaxation of the main problem. Furthermore, a near-optimal initial solution is generated for a reduction in the number of iterations.     

Designing a two-echelon distribution network under demand uncertainty

This paper proposes a comprehensive methodology for the stochastic multi-period two-echelon distribution network design problem (2E-DDP) where product flows to ship-to-points are directed from an upper layer of primary warehouses to distribution platforms (DPs) before being transported to the ship-to-points. A temporal hierarchy characterizes the design level dealing with DP location and capacity decisions, as well as the operational level involving transportation decisions as origin-destination flows. These design decisions must be calibrated to minimize the expected distribution cost associated with the two-echelon transportation schema on this network under stochastic demand. We consider a multi-period planning horizon where demand varies dynamically from one planning period to the next. Thus, the design of the two-echelon distribution network under uncertain customer demand gives rise to a complex multi-stage decisional problem. Given the strategic structure of the problem, we introduce alternative modeling approaches based on two-stage stochastic programming with recourse. We solve the resulting models using a Benders decomposition approach. The size of the scenario set is tuned using the sample average approximation (SAA) approach. Then, a scenario-based evaluation procedure is introduced to post-evaluate the design solutions obtained. We conduct extensive computational experiments based on several types of instances to validate the proposed models and assess the efficiency of the solution approaches. The evaluation of the quality of the stochastic solution underlines the impact of uncertainty in the two-echelon distribution network design problem (2E-DDP).     

Formation of a strategic manufacturing and distribution network with transfer prices

We propose a profit maximization model for the decision support system of a firm that wishes to establish or rationalize a multinational manufacturing and distribution network to produce and deliver finished goods from sources to consumers. The model simultaneously evaluates all traditional location factors in a manufacturing and distribution network design problem and sets intra-firm transfer prices that take account of tax and exchange rate differentials between countries. Utilizing the generalized Benders decomposition approach, we exploit the partition between the product flow and the cash allocation (i.e., the pricing and revenue assignment) decisions in the supply chain to find near optimal model solutions. Our proposed profit maximizing strategic planning model produces intuitive results. We offer computational experiments to illustrate the potential valuable guidance the model can provide to a firm's supply chain design strategic planning process.     

The research on optimization of auto supply chain network robust model under macroeconomic fluctuations

Considering the uncertainty of the macroeconomic environment, the robust optimization method is studied for constructing and designing the automotive supply chain network, and based on the definition of robust solution a robust optimization model is built for integrated supply chain network design that consists of supplier selection problem and facility location–distribution problem. The tabu search algorithm is proposed for supply chain node configuration, analyzing the influence of the level of uncertainty on robust results, and by comparing the performance of supply chain network design through the stochastic programming model and robustness optimize model, on this basis, determining the rational layout of supply chain network under macroeconomic fluctuations. At last the contrastive test result validates that the performance of tabu search algorithm is outstanding on convergence and computational time. Meanwhile it is indicated that the robust optimization model can reduce investment risks effectively when it is applied to supply chain network design.     

基于时间的随机需求二级分销网络物流系统集成优化研究

分销网络设计包括设施选址、库存控制、运输等方面的设计与优化,但以往只是从战略层、战术层、运作层来分别进行各自的研究。实际上,这三个层次的决策要素之间存在着复杂的互动关系,并存在着广泛的效益悖反关系,这些在变化的环境下显得尤为突出。本文充分考虑时间因素的重要性,从物流系统的集成优化高度出发,研究建立需求随机的多分销中心多顾客的设施选址———运输路线安排———库存控制问题(ILRIP)的模型,对此设计了一个两层粒子群优化(PSO)算法,并给出了计算实例。研究结果有助于供应链分销网络的集成优化,缩短商品流转周期,提高顾客服务水平,提升竞争力。     

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.     

An Approach for Strategic Supply Chain Planning under Uncertainty based on Stochastic 0-1 Programming

We present a two-stage stochastic 0-1 modeling and a related algorithmic approach for Supply Chain Management under uncertainty, whose goal consists of determining the production topology, plant sizing, product selection, product allocation among plants and vendor selection for raw materials. The objective is the maximization of the expected benefit given by the product net profit over the time horizon minus the investment depreciation and operations costs. The main uncertain parameters are the product net price and demand, the raw material supply cost and the production cost. The first stage is included by the strategic decisions. The second stage is included by the tactical decisions. A tight 0-1 model for the deterministic version is presented. A splitting variable mathematical representation via scenario is presented for the stochastic version of the model. A two-stage version of a Branch and Fix Coordination (BFC) algorithmic approach is proposed for stochastic 0-1 program solving, and some computational experience is reported for cases with dozens of thousands of constraints and continuous variables and hundreds of 0-1 variables.