Track: Operations Research

Abstract

With immense competition, coupled with short and unpredictable shelf life of products in some cases, companies rely upon diversifying their product range to disperse risk associated with failure of one product. Since pricing is also dynamic, varying with time, there is also a need for the companies to formulate appropriate pricing policies to maximize profits as against expenses incurred in promotion of multiple products. In this paper we device and analyze policies for promoting sales of multiple products in the market through optimal control theory problems. The main aim is to maximize profits while considering multiple product range, demand requirements and optimum pricing policy for an available budget for promotion. To be as near as possible to a real-life situation, the total available budget is taken to be imprecise. Further, optimal control model with fuzzy parameter is converted into crisp form by using both necessity and possibility constraints. The solution is derived using Pontryagin Maximum principle and the entire technique is illustrated by giving a numerical example.