Assortment Planning and Inventory Decisions Under a Locational Choice Model
Management Science
Outsourcing via Service Competition
Management Science
Dynamic Assortment with Demand Learning for Seasonal Consumer Goods
Management Science
Retail Assortment Planning in the Presence of Consumer Search
Manufacturing & Service Operations Management
Dynamic Pricing and Inventory Control of Substitute Products
Manufacturing & Service Operations Management
Industrial strength COMPASS: A comprehensive algorithm and software for optimization via simulation
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Assortment Planning and Inventory Decisions Under Stockout-Based Substitution
Operations Research
On the Interaction Between Demand Substitution and Production Changeovers
Manufacturing & Service Operations Management
Computing Bid Prices for Revenue Management Under Customer Choice Behavior
Manufacturing & Service Operations Management
Optimal Algorithms for Assortment Selection Under Ranking-Based Consumer Choice Models
Manufacturing & Service Operations Management
A PTAS for capacitated sum-of-ratios optimization
Operations Research Letters
An Adaptive Hyperbox Algorithm for High-Dimensional Discrete Optimization via Simulation Problems
INFORMS Journal on Computing
Manufacturing & Service Operations Management
Optimal Dynamic Assortment Planning with Demand Learning
Manufacturing & Service Operations Management
Marketing Science
A branch-and-cut algorithm for the latent-class logit assortment problem
Discrete Applied Mathematics
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We analyze a single-period, stochastic inventory model (newsboy-like model) in which a sequence of heterogeneous customers dynamically substitute among product variants within a retail assortment when inventory is depleted. The customer choice decisions are based on a natural and classical utility maximization criterion. Faced with such substitution behavior, the retailer must choose initial inventory levels for the assortment to maximize expected profits.Using a sample path analysis, we analyze structural properties of the expected profit function. We show that, under very general assumptions on the demand process, total sales of each product are concave in their own inventory levels and possess the so-calleddecreasing differences property, meaning that the marginal value of an additional unit of the given product is decreasing in the inventory levels of all other products. For a continuous relaxation of the problem, we then show, via counterexamples, that the expected profit function is in general not even quasiconcave. Thus, global optimization may be difficult. However, we propose and analyze a stochastic gradient algorithm for the problem, and prove that it converges to a stationary point of the expected profit function under mild conditions. Finally, we apply the algorithm to a set of numerical examples and compare the resulting inventory decisions to those of some simpler, naive heuristics. The examples show that substitution effects can have a significant impact on an assortment's gross profits. The examples also illustrate some systematic distortions in inventory decisions if substitution effects are ignored. In particular, under substitution one should stock relatively more of popular variants and relatively less of unpopular variants than a traditional newsboy analysis indicates.