Mathematical modelling for convertible items with rework using particle swarm optimisation

Abstract

Conversion of milk into butter, debenture into share, sovereign bond into Dollar and currency exchange are need of hours. For example, milk cannot be stored for a long time, but after converted into butter, it could be stored for more little time and again its conversion in the form of Ghee could be stored for long time. Also, the converted product becomes costlier after conversion than earlier state and hence the conversion of the item is also considered profitable for the business. The aim of this paper is to find that when to convert, how much to convert, conversion cost and conversion time to get optimum profit. The objective of the proposed model is also to find the selling price of converted items and sale seasons. The complete conversion process is analytically and numerically discussed for two scenarios: homogeneous conversion and heterogeneous conversion. Profit function and other output parameters are optimised by Particle Swarm Optimisation. This tool is much better than the classical optimisation method due to searching for the optimal solution in entire search space and able to optimise large number of variables at a time. For best course of action, the model is simulated and managerial insights are given accordingly. Also the theoretical implications are suggested and compared between both types of conversions. On the basis of analysis, it is suggested to inventory managers that only higher selling price is not guaranty to get optimal profit, but optimal strategy and determined selling price with the help of proposed model provide optimal profit.

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