performance of a supply chain highly depends on its suppliers and therefore, appropriate selection of them is of great importance. this paper presents an integrated model of an mcdm method and a mathematical programming in order to select suppliers and determine lot sizes in the supply chain. the proposed framework comprises two main sub-models; the qualitative sub-model seeks to evaluate the s...

Multi-objective optimization is the simultaneous consideration of two or more objective functions that are completely or partially inconflict with each other. The optimality of such optimizations is largely defined through the Pareto optimality. Multiple objective integer linear programs (MOILP) are special cases of multiple criteria decision making problems. Numerous algorithms have been desig...

Mixed integer programming (MIP) is a powerful modelling tool for decision-making in the industry and in the public sector. Integer requirements are essential to model a wide variety of situations involving assignment restrictions, logical constraints and yes/no decisions, to name a few. Usually real-life applications result in mixed integer programs that are large in size and that are beyond th...

We study the mixed-integer rounding (MIR) closures of polyhedral sets. The MIR closure of a polyhedral set is equal to its split closure and the associated separation problem is NP-hard. We describe a mixed-integer programming (MIP) model with linear constraints and a non-linear objective for separating an arbitrary point from the MIR closure of a given mixed-integer set. We linearize the objec...

design of a logistics network in proper way provides a proper platform for efficient and effective supply chain management. this paper studies a multi-period, multi echelon and multi-product integrated forward-reverse logistics network under uncertainty. first, an efficient complex mixed-integer linear programming (milp) model by considering some real-world assumptions is developed for the inte...