An economic order quantity model with demand-dependent unit cost

The point is demonstrated that GP has potential as a viable mathematical tool for the analysis of a certain class of inventory control problems and is solved analytically to obtain a closed-form optimal solution.

Abstract

For the classical EOQ problem a relationship between demand and unit cost may exist under certain circumstances. We propose an EOQ model with demand-dependent unit cost and formulate the optimization problem as a geometric program (GP). We solve the GP analytically to obtain a closed-form optimal solution. An illustrative example is provided to show the working procedures of applying GP to solve a given problem. We also touch on some aspects of sensitivity analysis based on the GP approach. We demonstrate in this paper the point that GP has potential as a viable mathematical tool for the analysis of a certain class of inventory control problems.