Time-bound product returns and optimal order quantities for mass merchandisers

The return guidelines for a mass merchandiser usually entail a grace period, a markdown on the original price and the condition of the returned items. This research utilises eight scenarios formed from the variation of possible return guidelines to model the cost functions of single-product categories for a typical mass merchandiser. Models for the eight scenarios are developed and solved with the objective of maximising the expected profit so as to obtain closed form solutions for the associated optimal order quantity. An illustrative example and sensitivity analysis are provided to demonstrate the applicability of the model. Our results show that merchandisers who allow for returns within a time window, albeit with a penalty cost imposed and the returned products being recoverable, should plan for larger order amounts as such products do not affect the business. Similarly, the merchandisers who allow for returns beyond a grace period and without any penalty charges, but where the returned products are irrecoverable, should manage their stocks in this category more judiciously by ordering as little as possible so as to limit the number of returns and carefully consider the effects of their customer satisfaction-guaranteed policies, if any.