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A production inventory model with deteriorating items and shortages

A continuous production control inventory model for deteriorating items with shortages is developed. A number of structural properties of the inventory system are studied analytically. The formulae for the optimal average system cost, stock level, backlog level and production cycle time are derived when the deterioration rate is very small. Numerical examples are taken to illustrate the procedure of finding the optimal total inventory cost, stock level, backlog level and production cycle time. | Yugoslav Journal of Operations Research 14 (2004), Number 2, 219-230 A PRODUCTION INVENTORY MODEL WITH DETERIORATING ITEMS AND SHORTAGES G.P. SAMANTA, Ajanta ROY Department of Mathematics Bengal Engineering College (D. U.), Howrah – 711103, INDIA Received: October 2003 / Accepted: March 2004 Abstract: A continuous production control inventory model for deteriorating items with shortages is developed. A number of structural properties of the inventory system are studied analytically. The formulae for the optimal average system cost, stock level, backlog level and production cycle time are derived when the deterioration rate is very small. Numerical examples are taken to illustrate the procedure of finding the optimal total inventory cost, stock level, backlog level and production cycle time. Sensitivity analysis is carried out to demonstrate the effects of changing parameter values on the optimal solution of the system. Keywords: Deteriorating item, shortage, economic order quantity model. 1. INTRODUCTION In recent years, the control and maintenance of production inventories of deteriorating items with shortages have attracted much attention in inventory analysis because most physical goods deteriorate over time. The effect of deterioration is very important in many inventory systems. Deterioration is defined as decay or damage such that the item can not be used for its original purpose. Food items, drugs, pharmaceuticals, radioactive substances are examples of items in which sufficient deterioration can take place during the normal storage period of the units and consequently this loss must be taken into account when analyzing the system. Research in this direction began with the work of Whitin [16] who considered fashion goods deteriorating at the end of a prescribed storage period. Ghare and Schrader [7] developed an inventory model with a constant rate of deterioration. An order level inventory model for items deteriorating at a constant rate was discussed by