The Effects of Selling Packaged Goods on Inventory Decisions

Abstract

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.inventory with substitution, bundling policies, newsvendor problem, retail inventories, product line design

Centralized and Competitive Inventory Models with Demand Substitution

“…For the model that we employ, the contributions of this paper are as follows: (i) we obtain necessary optimality conditions (which may not be sufficient due to the potential existence of multiple local maxima) for the noncompetitive case with n products, thus extending the work of Parlar and Goyal (1984, 2 products), Ernst and Kouvelis (1999, 3 products with partial substitution), and Noonan (1995, n products but no analytical expression for the optimality conditions); (ii) we show that concavity of the objective function in the noncompetitive setting established by Parlar and Goyal (1984, 2 products) and Ernst and Kouvelis (1999, 3 products with partial substitution) does not extend to n products with full substitution structure; (iii) we establish uniqueness of the equilibrium for the competitive n-product case, thus extending the work of Parlar (1988, 2 products) and Wang and Parlar (1994, 3 products but no proof of uniqueness); (iv) we obtain optimality conditions for the competitive n-product case, thus extending the work of Parlar (1988, 2 products) and Wang and Parlar (1994, 3 products); (v) we provide comparison between noncompetitive and competitive solutions; and (vi) we characterize the impact of demand correlation on profits under demand substitution for the centralized case, thus analytically confirming the numerical results of Rajaram and Tang (2001) and Ernst and Kouvelis (1999). A nonintuitive result is the finding that competition might lead to understocking some of the substitutable products, as compared to the centralized solution.…”

“…For certain problem parameters, Parlar and Goyal (1984) have demonstrated that the objective function in the case of two products is jointly concave. Ernst and Kouvelis (1999) have shown that the problem with three partially substitutable products is jointly concave as well. However, we will verify analytically and through numerical experiments that the objective function with more than two products and full substitution structure might not be concave and not even quasiconcave, which parallels a finding of Mahajan and van Ryzin (2001a) in a different setting.…”

“…If this product is out of stock, the consumer might choose one of the other products as a substitute. In modeling the substitution process we employ an abstraction that is frequently used in the literature (see McGillivray and Silver 1978, Parlar and Goyal 1984, Noonan 1995, Parlar 1988, Wang and Parlar 1994, Rajaram and Tang 2001, Ernst and Kouvelis 1999. Specifically, for each product there is a random demand that is exogenously specified.…”

Bundle pricing of inventories with stochastic demand

“…Although not directly related to our study, see also Ansari et al (1996) for the determination of the optimal number of items to be included in a service bundle, Ben-Akiva and Gershenfeld (1998) for customer choice behavior for bundles with correlated demand, Carbajo et al (1990) for incentives for bundling under imperfect competition, Hanson and Martin (1990) for the calculation of optimal bundle prices in a deterministic setting, using mixed integer linear programming, Ernst and Kouvelis (1999) for the effect of selling product bundles (as opposed to price bundles in our case) on inventory decisions, and Stremersch and Tellis (2002) for a clear discussion of bundling terms which are used in marketing, economics and law literature in a somewhat unclear way. Finally, we note the growing literature on bundling of information goods (see, for example, Bakos and Brynjolfsson (1999)).…”

Optimal ordering quantities for substitutable deteriorating items under joint replenishment with cost of substitution

“…In this sequence, Drezner et al (1995) developed an EOQ model with substitution for two substitutable products and compare the results with no substitution. Ernst and Kouvelis (1999) suggested an efficient numerical search algorithm for the optimal stocking levels for three partially substitutable products. Gurnani and Drezner (2000) extended the model of Drezner et al (1995) for multiple products.…”