Costing partial order cycles in the temporary sale price problem

The selection of a special order quantity in response to a temporary price reduction is usually derived by comparing the benefits of a special order in terms of a lower purchase price, with the additional holding cost if the offer is rejected. The analysis is usually carried out over a finite planning horizon, under various cost-allocation specifications, thus neglecting the longer-term effects of these offers. In contrasting the different solutions, this paper shows (i) that the basic differences among the various earlier formulations centre around the evaluation of the cost of a partial inventory cycle, within the average cost (AVC) approach; (ii) that the net present value (NPV) approach eliminates the partial order cycle problem by evaluating cash flows always at the time of occurrence, thus obviating the need for considering partial order cycles; and (iii) that the various AVC specifications presented in this paper yield excellent approximations to the theoretically correct but harder to use NPV formulation. Numerical examples highlight the main features of the paper.