Dynamic Pricing and Inventory Control of Substitute Products

Abstract

We study dynamic pricing and inventory control of substitute products for a retailer who faces a long supply lead time and a short selling season. Within a multinomial logit model of consumer choice over substitutes, we develop a stochastic dynamic programming formulation and derive the optimal dynamic pricing policy. We prove that dynamic pricing converges to static pricing as inventory levels of all variates approach the number of remaining selling periods (assuming at most one customer arrival within each period). Our extensive numerical study of the effects of time and inventory depletion on the optimal pricing reveals two fundamental underlying driving forces of the complex price behavior: the level of inventory scarcity and the quality difference among products. We also compare the performance of three restricted pricing strategies: static, unified dynamic, and mixed dynamic pricing. We find that full-scale dynamic pricing is of great value in the presence of inventory scarcity, and initial inventory decisions are quite robust in the pricing scheme employed in the selling season. Based on the above insights, we propose a computationally efficient approach to the initial inventory decision, which delivers close-to-optimal inventory levels for all testing cases.dynamic pricing, inventory control, substitute products, multinomial logit model

Assortment Optimization Under Variants of the Nested Logit Model

“…The objective is to maximize the expected revenue per customer. For the pricing problem, Hanson and Martin (1996) notice that the expected revenue function fails to be concave in prices for the multinomial logit model, but significant progress was made by formulating the pricing problem in terms of market shares, as this results in a concave expected revenue function; see Song and Xue (2007) and Dong et al (2009). Li and Huh (2011) extend the concavity result to the nested logit model by assuming that the price sensitivities of the products are constant within each nest and the nest dissimilarity parameters are all between zero and one.…”

Yield Management Models for Two Substitutable Products

“…Inventory-driven substitution research has been studied by many Kuyumcu and Popescu [14] studied joint pricing and inventory control by considering deterministic optimization models for multiple substitutable products, and they showed that the optimization problem could be reduced to a pure pricing problem. Karakul and Chan [3] considered stochastic optimization problems, which are a joint pricing and inventory decision, for an existing product and a new improved production decisions. The authors developed an in-depth mathematical procedure for finding optimal solutions for the stochastic problem with inventory-driven substitution.…”

“…1～8 (in 100,000s). 3 The expected profit of the capacity level decision model when     ,     ,     . 4 The expected profit of joint pricing and capacity level decision without inventory-driven substitution 5 The expected profit of the pricing decision model when 3 The expected profit of the capacity level decision model when         ,     .…”

“…3 The expected profit of the capacity level decision model when     ,     ,     . 4 The expected profit of joint pricing and capacity level decision without inventory-driven substitution 5 The expected profit of the pricing decision model when 3 The expected profit of the capacity level decision model when         ,     . 4 The expected profit of joint pricing and capacity level decision without inventory-driven substitution 5 The expected profit of the pricing decision model when     ,     ,     .…”

Consumer Choice Under Limited Attention When Options Have Different Information Costs

“…We refer to Anderson et al (1992) for a comprehensive coverage of MNL models in general and to Wierenga (2008) for their use in marketing science. MNL and its variations (e.g., nested logit) have been extensively used to model consumer behavior in the operations management literature as well, in particular in the context of pricing, revenue management and assortment planning (Hanson and Martin 1996, van Ryzin and Mahajan 1999, Dong et al 2009, Zhang and Adelman 2009, Davis et al 2014. In this stream, the need for richer and more general choice models has also been recognized and some propositions have been made, such as Talluri and van Ryzin (2004), Alptekinoğlu and Semple (2015), Blanchet et al (2016), Srikanth and Rusmevichientong (2016).…”