Production optimization of a soap and cosmetic industry by using mixed integer linear programing

Abstract

This research presents a mathematical formulation for production optimization of soap and cosmetic industry named Mega Sornali Soap and Cosmetics Industry (MSSCI). The entire model is constructed by several parameters such as labor cost, machine cost, raw material cost and other cost. This study consists of the formulated Mixed Integer Linear Programming (MILP) model. In order to validate and calibrate the model, related real data from a soap industry named (MSSCI) has been collected. MILP model exhibits rapid conversion and a global optimum with well-defined solution methods. The model has been solved using A Mathematical Programming Language (AMPL) which is an algebraic modeling language to describe and solve high-complexity problems for large-scale mathematical computing. One advantage of AMPL is the similarity of its syntax to the mathematical notation of optimization problems. The results display significant effective model with optimal solution.

In order to validate the model, the sensitivity analysis of different cost parameters such as labor cost, raw material cost and machine cost have been considered. From the sensitivity analysis, the decision makers of the factory will be able to find out the ranges of cost coefficients and all the resources. As a result, they will be able to see how any change can affect the production. From the numerical results, it is clear that raw material cost and machine cost are the most sensitive cost. If the raw material cost and machine cost can be decreased the production will also be increased. Finally, the result of the optimal solution will be represented in tabular form in addition to the graphs.