Joint replenishment models with ramp demands and price dependent substitute ratio during stock-out Online publication date: Thu, 23-Aug-2018
by Raghu Nandan Giri; Shyamal Kumar Mondal; Manoranjan Maiti
International Journal of Operational Research (IJOR), Vol. 33, No. 1, 2018
Abstract: The paper deals with a single period joint replenishment model (JRM) of two substitutable items with ramp type demands in an inventory system. Here customers' demands are a dynamic, quadratic function of time, t. It is assumed that when an item is out of stock, demand for this item is partially met by the other available substitute item on the basis of items' prices difference. A new substitute function is presented here for this purpose. We determine the optimal order quantities of each item for maximum average total profit. Also attention is paid to maintain a balance between stocks of the items - i.e. not to have too much or very insufficient stock of the items at the end of a cycle. The models are illustrated with numerical data and some sensitivity analyses, and managerial insights are presented. Results of several particular models including the correct results of Salameh et al.'s (2014) model are derived from the general model.
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