Substitutable Inventory System with Partial Backlogging under Continuous Review

Introduction

Many practical multi-item inventory systems are concentrated on the coordination of replenishment orders for group of items. Presently, it is very much applicable to run a successful business and industries. These systems unlike those dealing with single commodity involve more complexities in the reordering procedures. The modelling of multi-item inventory system under joint replenishment has been receiving considerable attention for the past three decades.

In highly competitive business environment two branded items even though substitutable commodities like two different brands of super computers have almost same configuration and identical functioning may be sold by a single vendor. Because of brand affinity, some customers may seek a specific brand which is not in the stock in that case backordering is the right choice for the vendor even though the backlogging cost is more. This motivate the authors to consider the substitutable items with partial backlogging provision. Coordinated ordering policy is implemented to reduce the total expected cost rate since it is a vendor managed inventory control system.

In continuous review inventory systems, Ballintfy (1964) and Silver (1974) have considered a coordinated reordering policy which is represented by the triplet (S,c,s), where the three parameters S_i, c_i, and s_i are specified for each item i with s_i ≤ c_i ≤ S_i, under the unit sized Poisson demand and constant lead time. In this policy, if the level of i-th commodity at any time is below s_i, an order is placed for S_i-s_i items and at the same time, any other item j(≠i) with available inventory at or below its can-order level c_j, an order is placed so as to bring its level back to its maximum capacity S_j. Subsequently many articles have appeared with models involving the above policy and another article of interest is Federgruen, Groenevelt and Tijms (1984), which deals with the general case of compound Poisson demands and non-zero lead times. A review of inventory models under joint replenishment is provided by Goyal and Satir (1989).

Kalpakam and Arivarignan (1993) have introduced (s,S) policy with a single reorder level s defined in terms of the total number of items in the stock. This policy avoids separate ordering for each commodity and hence a single processing of orders for both commodities has some advantages in situation where in procurement is made from the same supplies, items produced on the same machine, or items have to be supplied by the same transport facility.

Krishnamoorthy, Iqbal Basha and Lakshmy (1994) have considered a two commodity continuous review inventory system without lead time. In their model, each demand is for one unit of first commodity or one unit of second commodity or one unit of each commodity 1 and 2, with prefixed probabilities. Krishnamoorthy and Varghese (1994) have considered a two commodity inventory problem without lead time and with Markov shift in demand for the type of commodity namely “commodity-1”, “commodity-2” or “both commodity”, using the direct Markov renewal theoretical results. And also for the same problem, Sivasamy and Pandiyan (1998) had derived various results by the application of filtering technique.

Anbazhagan and Arivarignan (2000) have considered a two commodity inventory system with Poisson demands and a joint reorder policy which placed fixed ordering quantities for both commodities whenever both inventory levels are less than or equal to their respective reorder levels.

Anbazhagan and Arivarignan (2001) have analysed the model with a joint ordering policy which places orders for both commodities whenever the total net inventory level drops to a prefixed level s.