Multi-product economic inventory policy with time varying power demand, shortages and complete backordering

Abstract

The present article elaborates a multi-product economic inventory model in which multiple items are considered with demand, which depends on time, abides power law, shortages, and complete backordering. The rate of production is greater than the rate of demand for each item. This type of demand pattern is accessible to various kinds of practical problems in the present modern era. In this paper, the production rate is assumed to be directly proportional to the rate of demand. In real situations, demand is always dependent on the price of any product, so it is also assumed that demand is depleted linearly with the price. This paper aims to fulfill the requirement of products and maximize the overall profit in any organization. Optimal values of involved costs, price, re-order point, and scheduling period are also calculated. In this work, the objective is to maximize the total profit and optimize production quantity. Optimization methods are used to obtain the maximum profit. Shortages are permitted and completely backordered. Total cost and production quantity models for deteriorating items have been developed. The study is validated with a numerical example, and sensitive analysis of the optimal solutions concerning main parameters is carried out using the software Mathematica. The tables are also shown for optimal values of the present model.