Demand uncertainty and supplier's returns policies for a multi-store style-good retailer

As demand uncertainty grows in the marketplace, a critical issue today in most purchase contract negotiations between an independent retailer of a style-good and its supplier is the provision of a returns policy, i.e., a commitment by the supplier to buy back unsold inventory of the good at the end of its selling season. Management science research on the strategic role and optimal design of returns policies has grown in recent years but so far offers little treatment of how exactly the retailer's optimal order quantity decisions are affected by demand uncertainty and how a supplier's returns policy can influence these decisions. Employing the traditional “newsboy problem” modeling framework, the authors investigate these issues considering a supplier who faces a retailer with two or more store outlets with normally distributed and possibly correlated demands. To facilitate their analyses, the authors employ a methodology based on special error function representations of the highly nonlinear objective functions of the retailer and supplier. Utilizing this approach, the authors are able to provide explicit insights into how: (a) the buyer's total order quantity decision is affected by the variability in demand; (b) buyback prices in combination with wholesale prices can influence the buyer's order quantity response to demand uncertainty; (c) demand uncertainty moderates the effects of the buyback and wholesale prices; (d) supplier's optimal combination of actions are affected by demand variability; (e) retailer's and supplier's expected profits behave in response to changes in the supplier's actions under different levels of demand variability.