Using JIT in a Green Supply Chain

Find Solutions through Pareto's Multi-Objective Integer Programming

In previous studies involving finding multi-objective solutions, the weighting method was developed to convert multi-objective elements into the same units for comparison. The multi-objective problem in this study was adopted by Pareto to derive the most efficient multi-objective optimized solution. The normalized limitation method is one that features the following advantages: (1) Ability to produce an even Pareto solution; (2) Ability to produce all the points of Pareto infeasible solutions.

Messac et al. proposed a standardized, normalized limitation method to resolve multi-objective models. This method does not require a weight to be provided for each objective to produce an evenly distributed Pareto boundary solution. Since this calculation method involves gradient-based optimization algorithms, it will generate convex and non-convex. Then, it can be used to filter the non-optimized solution into the Pareto curve using the Pareto filter algorithm, thereby producing evenly distributed Pareto feasible solutions.

In this research, we used ILOG CPLEX12.4 to solve the problem. The IBM ILOG COLEX Optimization Studio is the analytical decision support toolkit for rapid development and solving mathematical optimization problems. This software combines the Integrated Development Environment (IDE), the Optimized Programming Language (OPL), and the High-Performance ILOG COLEX Optimized Program Solver to provide the fastest way to solve the problem. The OPL is an algebraic modeling language that makes it easier for users to understand the constraints, assumptions, goals, and costs of the problem. The following are the types of problems that can be solved: 1. Linear Programming; 2. Mixed-integer Linear Programming; 3. Quadratic Programming; 4. Quadratic Constrained Programming.