An Economic Order Quantity Model with Demand-Dependent Unit Production Cost and Imperfect Production Processes

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Abstract
The classical economic order quantity (EOQ) model assumes that items produced are of perfect quality and that die unit cost of production is independent of demand. Product quality is not always perfect but directly affected by the reliability of the production process used to produce the products. In addition, a relationship between unit production cost and demand may exist under certain circumstances. We propose an EOQ model with demand-dependent unit production cost and imperfect production processes. We formulate this inventory decision problem as a geometric program (GP) and solve it to obtain closed-form optimal solutions. An illustrative example is provided to demonstrate the point that GP has potential as a valuable analytical tool for studying a certain class of inventory control problems. We also discuss the aspect of sensitivity analysis based on the GP approach.