Some Studies in Multi-Storage Inventory System: Using Genetic Algorithm

1.0 Introduction

In the field of inventory management, an important problem associated with the inventory maintenance is to decide where to stock the goods. This problem does not seem to have attracted much attention of researchers in this field. In this regard, the basic assumption in the traditional inventory models is that the management owns a store (warehouse) with unlimited capacity. However, in some situations, it is not always true. In the busy markets like super market, corporation market, municipality market etc., the storage space of a show – room is limited. When an attractive price discount for bulk purchase is available or the cost of procuring goods is higher than the inventory related other costs or there are some problems in frequent procurement or the demand of items is very high, management then decides to purchase (or produce) a large amount of items at a time. These items may not be accommodated in the existing storage (viz., the owned warehouse, OW) due to limited capacity. Then for storing the excess items, one (sometimes more than one) additional warehouse is hired on rental basis. This rented warehouse (RW) may be located near the OW or a little away from it. It is generally assumed that the holding cost in RW is greater than that in OW. Moreover, items should be always available at OW for the convenience of business as the actual service to the customer is carried out at OW only. Hence, the items are stored first in OW and only excess stock is stored in RW. As the holding cost in RW is greater than that in the OW, the stocks of RW are emptied first by transporting the stocks from RW to OW in order to reduce the holding cost. Generally, the items of RW are transferred to OW in a continuous / bulk release pattern to meet up the demand until the stock level in RW is emptied and lastly the items of OW are released. This type of problem is known as multi – storage (warehouse) problem.

Approximately twenty eight years before, Hartely (1976) in U.S.A., first introduced two storage problem in his book “Operations Research –A Managerial Emphasis”. In his analysis, he ignored the cost of transportation for transferring the goods from RW to OW. After Hartely, Sarma(1983) in India, first investigated two storage inventory model in the year 1983. Murdeswar and Sathi (1985) extended this model by assuming a finite rate of replenishment. Dave (1989) modified the EOQ models of Sarma (1983). Dave (1989) considered finite as well as infinite rate of replenishment under some assumptions and gave an algorithm for each model to get a complete solution. The above models were formulated for non-deteriorating items without allowing the shortages. Considering the shortages, Sarma (1987) formulated a model of deteriorating items with infinite replenishment rate. Next, Pakhala and Achary (1992) developed the two warehouse models with finite rate of replenishment and shortages taking time as discrete and continuous variable respectively. In their models, the scheduling period was taken as constant and prescribed and the transportation cost for transferring the stocks from RW to OW was not taken into account. All these models discussed earlier were developed for uniform demand only. Taking linearly time dependent demand, Goswami and Chaudhuri (1992) formulated two models for non-deteriorating items with or without shortages. Shah N.H.(2006) formulated a inventory model for deteriorating items and time value of money for a finite time horizon under the permissible delay in payments. Correcting and modifying the assumptions of Goswami and Chaudhuri (1992), Bhunia and Maiti (1994) analyzed the same and graphically presented a sensitivity analysis on the optimal average cost and the cycle length for the variations