An economic order quantity model for two deteriorating items with mutually complementary price and time dependent demand

Document Type : Article


University of Pretoria, South Africa


We present an inventory model to determine the optimal selling price and cycle time for two mutually complementary commodities that are subject to deterioration. Each commodity's demand is influenced by its own selling price, the selling price of the complementary product, and the passage of time. Numerical examples and sensitivity analysis results are presented to demonstrate the usefulness of the inventory model. We conducted sensitivity analysis on the impacts of the changes in key parameters of the model on the decision variables and the objective (profitability) of the inventory system. We observed that as the deterioration rate of either item increases, the model proposes shorter replenishment cycle length, which reduces the profit. Our model’s novelty is the inclusion of mutual (two-way) complementarity in the Economic Order Quantity model, where both items are deteriorating and have time-dependent demands.


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