Mathematics and Computer Science, Volume 2

17A Mathematical Representation for Deteriorating Goods with a Trapezoidal-Type Demand, Shortages and Time Dependent Holding Cost

Ruma Roy Chowdhury

Department of Basic Science and Humanities, University of Engineering & Management, Kolkata, India

Abstract

A production inventory model for a perishable good decaying at a constant rate has been devised in this research article. A ramp-type demand function has been considered, that is, the demand follows an accelerated growth initially for some time and finally becomes constant. The model allows shortage and is completely backlogged. The cost of holding the inventory is considered to vary linearly with time. Four cases have been developed depending on the position of time point at which the demand becomes constant in a trapezoidal-type demand. The production cycle restarts after a certain time. Optimal production stopping time and resuming time are calculated to optimize the expense of the production set-up per unit. The model is illustrated with a numerical.

Keywords: Trapezoidal demand, holding cost varying with time, completely backlogged short-ages, constant deterioration

17.1 Introduction

Demand is always fluctuating according to the requirements and preferences of customers and is quite unpredictable. In case of new launches of items like cosmetics, electronic gadgets with new technologies, trendy garments, etc. in the market, the items are in high demand initially. But, with the passage of time as more improvised items ...