A two warehouse inventory model for deteriorating items with a linear trend in demand and shortages
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Haldia Institute of Technology and 2 Vidyasagar University, India
In this paper, we develop a deterministic inventory model with two warehouses (one is the existing storage known as own warehouse (OW) and the other is hired on rental basis known as rented warehouse (RW). The model allows different levels of item deterioration in both warehouses. The demand rate is supposed to be a linear (increasing) function of time and the replenishment rate is in®nite. The stock is transferred from RW to OW in continuous release pattern and the associated transportation cost is taken into account. Shortages in OW are allowed and excess demand is backlogged. For the general model, we give the equations for the optimal policy and cost function and we discuss some special cases. A numerical example is given to illustrate the solution procedure of the model. Finally, based on this example, we conduct a sensitivity analysis of the model. Keywords: demand; deterioration; inventory; warehouse
Introduction In real life, the harvest of food grains like paddy, wheat, etc. is periodic. As there are a large number of landless people in the rural areas of India, there will be a constant demand for these food grains throughout the year. Due to various reasons, some of the farmers are forced to sell some part of their food grains and as a result, they buy the food grains from the market towards the end of production cycle. Therefore, the rate of demand for food grains remains partly constant and increases partly with time. Traditional inventory models for deteriorating items are developed mainly for a single warehouse. In practice, due to the limited capacity of the available showroom facility (existing storage, own warehouse, (OW)), an additional storage which is assumed to be available with abundant space is required to hold a large stock. This additional storage facility may be a rented warehouse (RW) with better preserving facility. This situation arises when the management gets an attractive price discount for purchasing grain or if the acquisition costs are higher than using a RW. Also, because of its better preserving facility, the holding cost in RW is greater than that of OW. So, for economic reasons, the goods of RW are consumed ®rst and next the goods of OW. The two warehouse inventory models have been considered by various authors in recent years. This type of model was ®rst discussed by Hartely.1 Sarma2 developed a model with in®nite production rate, but without shortages. Dave3 discussed the inventory models for ®nite and in®nite rate of Correspondence: Dr AK Bhunia, Department of Mathematics, Haldia Institute of Technology, Haldia, Midnapore, India.
replenishment, rectifying the errors for the model given by Sarma2 and gave a complete solution. Further, Goswami and Chaudhuri4 considered the models with or without shortages taking linearly increasing time dependent demand. Correcting and modifying the assumptions of Goswami and Chaudhuri,4 Bhunia and Maiti5 analysed the same inventory model and graphically presented a sensitiv
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