Abstract
In selecting the best mixed integer linear programming (MILP) formulation the important issue is to figure out how to evaluate the performance of each candidate formulation in terms of selected criteria. The main objective of this study is to propose a systematic approach to guide the selection of the best MILP formulation among the alternatives according to the needs of the decision maker. For this reason we consider the problem of “selecting the most appropriate MILP formulation for a certain type of decision maker” as a multi-criteria decision making problem and present an integrated AHP-TOPSIS decision making methodology to select the most appropriate formulation. As an example the proposed decision making methodology is implemented on the selection of the MILP formulations of the Capacitated Vehicle Routing Problem (CVRP). A numerical example is provided for illustrative purposes. As a result, the proposed decision model can be a tool for the decision makers (here they are the scientists, engineers and practitioners) who intend to choose the appropriate mathematical model(s) among the alternatives according to their needs on their studies. The integrated AHP-TOPSIS approach can simply be incorporated into a computer-based decision support system since it has simplicity in both computation and application.
Highlights
The modeling and optimization concepts are important for scientists, engineers and industrial practitioners
The proposed decision model is implemented on the selection of the mixed integer linear programming (MILP) formulations of the Capacitated Vehicle Routing Problem (CVRP)
The distance of all alternatives to the positive ideal solution Dj* and the negative ideal solution Dj– results are determined for all formulations and with these solutions the relative closeness of each alternative to the ideal solution is obtained for each type of decision maker
Summary
The modeling and optimization concepts are important for scientists, engineers and industrial practitioners. As computers are getting cheaper and more powerful and they are used more widespread, mathematical models play an increasingly important role in engineering optimization and it has become an increasingly cost-effective alternative to the experimentation. Kececi et al A comparative study of the capability of alternative mixed integer programming. In most studies in the area of operations research (Luss, Rosenwein 1997; Pannirselvam et al 1999), the combinatorial optimization problems (COPs) are formulated as a mixed integer linear programming (MILP) formulation and they are solved by using either exact or meta-heuristic solution approaches. The solution of a COP can be obtained by solving the MILP formulation directly using an integer linear programming solver, as well
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