Integrated Supply Chain Optimization Models: Reformulation and Piecewise Linear Approximation

  • Abdulla Saif Al Shamsi

Student thesis: Master's Thesis


Supply chain management decisions are divided into three categories: strategic, such as facility location decisions; tactical, such as inventory management decisions; and operational, such as routing decisions. The effectiveness and efficiency of supply chain management depends primarily on the approach to modeling these decisions. The traditional technique is to model these decisions independently, for two reasons. First, these decisions are made over different time frames. Strategic decisions are typically made over years, tactical decisions over months or weeks, and operational decisions over days or hours, so it is intuitive to model these decisions separately. Secondly, most real supply chain optimization problems are complicated and cannot be easily solved using commercial optimization software. Hence, considering two or three different decision levels simultaneously may result in a problem so complex it cannot be solved even with very specialized solution algorithms. Recently, researchers and practitioners have become more interested in integrating the three supply chain decision levels. First, the three categories of decisions are interdependent. For example, the strategic decision to open a new warehouse impacts the tactical decision to maintain an inventory sufficient to satisfy required demand. If one made these decisions independently, one might make decisions that are not optimal. Second, many real-world business problems can be modeled as integrated problems, and although it may appear that decisions are made at different levels, in reality all these decisions belong to the same category. In this thesis, we consider a published integrated location-inventory problem that was formulated as a mixed integer nonlinear program (MINLP). The linear programming relaxation of that problem is a nonconvex problem that was solved to optimality, even in a small size, by the use of the General Algebraic Modeling System (GAMS). We first present a novel reformulation of the problem as a Quadratically Constrained Program (QCP). We then test the new formulation in GAMS and determine that GAMS is able to solve small- to medium-sized problems of that specific problem. However, to solve problems of a large size, we develop a linear piece wise approximation to the quadratic constraint, resulting in a mixed integer program (MIP). Then, we demonstrate through computational experiments that the linear piece wise approximation is close to the original problem and that GAMS is able to solve the MIP even with very large-sized problems. In order for us to make this problem look more realistic, we add new constraints to the problem, which are called capacity constraints. We then progress in the same order we did for the non-capacitated problem. Finally, we demonstrate through computational experiments that the values using capacitated problems are near optimal solutions when compared to other data points.
Date of AwardAug 2015
Original languageAmerican English
SupervisorAli Diabat (Supervisor)


  • Supply Chain
  • Location–Inventory
  • Integer Programming
  • Piecewise Linearization.

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