Strategic supply chain optimization (SCO) problems are often modelled as a two-stage optimization problem, in which the first-stage variables represent decisions on the development of the supply chain and the second-stage variables represent decisions on the operations of the supply chain. When uncertainty is explicitly considered, the problem becomes an intractable infinite-dimensional optimization problem, which is usually solved approximately via a scenario or a robust approach. This paper proposes a novel synergy of the scenario and robust approaches for strategic SCO under uncertainty. Two formulations are developed, namely, naïve robust scenario formulation and affinely adjustable robust scenario formulation. It is shown that both formulations can be reformulated into tractable deterministic optimization problems if the uncertainty is bounded with the infinity-norm, and the uncertain equality constraints can be reformulated into deterministic constraints without assumption of the uncertainty region. Case studies of a classical farm planning problem and an energy and bioproduct SCO problem demonstrate the advantages of the proposed formulations over the classical scenario formulation. The proposed formulations not only can generate solutions with guaranteed feasibility or indicate infeasibility of a problem, but also can achieve optimal expected economic performance with smaller numbers of scenarios.
This paper is concerned with strategic optimization of a typical industrial chemical supply chain, which involves a material purchase and transportation network, several manufacturing plants with on-site material and product inventories, a product transportation network, and several regional markets. In order to address large uncertainties in customer demands at the different regional markets, a novel robust scenario formulation, which has been recently developed by the authors, is tailored and applied for strategic optimization. Case study results show that the robust scenario formulation works well for this real industrial supply chain system, and it outperforms the deterministic formulation and the classical scenario-based stochastic programming formulation by generating better expected economic performance and solutions that are guaranteed to be feasible for all uncertainty realizations. The robust scenario problem exhibits a decomposable structure that can be taken advantage of by Benders decomposition for efficient solution, so the application of Benders decomposition to the solution of the strategic optimization is also discussed. The case study results show that Benders decomposition can reduce the solution time by almost an order of magnitude when the number of scenarios in the problem is large.Keywords: supply chain, uncertainty, stochastic programming, robust scenario formulation, Benders decomposition INTRODUCTION S upply chain optimization (SCO) is a set of approaches utilized to efficiently integrate suppliers, manufacturers, warehouses, and stores, so that merchandise is produced and distributed at the right quantities, to the right locations, and at the right time, in order to minimize system-wide costs while satisfying service level requirements.[1] SCO has emerged as a major research direction in the process systems engineering (PSE) community since the last decade; in the context of PSE, it is sometimes called enterprise-wide optimization if the emphasis is placed on the manufacturing stage. [2] In the PSE literature, SCO has been intensively studied for a variety of process industries, such as the petroleum industry, [3][4][5] bioenergy industry, [6][7][8] pharmaceutical industry, [9][10] and more. Papageorgiou gave a comprehensive summary and discussion of the advances and opportunities of supply chain optimization for the process industries. [11] Nikolopoulou and Ierapetritou presented a review on the optimization of sustainable chemical processes and supply chains for balanced economic, environmental, and social objectives. [12] SCO problems can be categorized into three levels: strategic, tactical, and operational problems, which are associated with the design, long-term/mid-term planning, and short-term operation of supply chains, respectively.[13] At any decision-making level in SCO, there may be factors that are not known exactly but can significantly impact supply chain performance, such as those related to raw material supplies, transportation and logistics, production and operation u...
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