Effects of selling packaged goods on inventory decisions

In this paper, we study within a newsboy type modeling framework the common business practice of retail firms to sell products not only as independent items, but also as part of multiproduct packets (packaged goods). Our emphasis is on understanding the effects of such practices on the inventory decisions of the firm. We provide insights on the resulting level of suboptimality when inventory decisions are made with demand information only on the independent items and without accounting for the demand substitution structure induced between independent items and packaged goods. Our stylized model studies an environment with two products that are not direct substitutes for each other, sold either independently or as part of a packet that contains one unit of each. We provide necessary and sufficient optimality conditions for this model and suggest an efficient numerical search for obtaining the optimal stocking levels. An extensive computational study allowed us to provide insights on the nature of the optimal stocking policies, the suboptimality of independent newsboy policies, the effects of demand correlation among individual products and multiproduct packets, and the determining role of induced substitution structure among products during stockout occasions on the profitability of the inventory system.