Stocking Under Random Demand and Product Variety: Exact Models and Heuristics

Abstract

E fficient inventory management in the face of product variety is an important part of retail operations management. In this study, we analyze the optimal stocking policy for a retailer, in a setup with a single horizontally differentiated product with an arbitrary number of product variants, stochastic demand, and two-level consumer choice. The demands for individual product variants are negatively correlated conditional on the total demand. We assume that each customer will purchase one unit of a preferred product variant, if it is in stock, and will seek to buy a second choice product, if the former is not in stock. We formulate an exact model, with Poisson customer arrivals. In order to maintain tractability and characterize an optimal policy analytically, we develop a benchmark model which does not explicitly account for the stochastic nature of customer arrival times. In this model, which is a heuristic approximation of the exact model, we find simple conditions under which the objective of maximizing expected profit is jointly concave in the stocking levels of the product variants; under these conditions we prove that the optimal stocking levels are simply scaled versions of the optimal newsvendor quantities. We then analytically establish a connection between the exact and benchmark models. We develop a dynamic Monte Carlo simulation experiment to gain further insights on the impact of different performance measures on the effectiveness of the optimal policy in the benchmark model and its performance in reference to the exact optimal policy.

An Economic Order Quantity (EOQ) Model for Chemotherapy Drugs Using New Patients’ Arrival Rates

“…Dobson et al (2015) optimized the inventory policy for compound sterile products by considering time-varying holding and ordering costs. Dewi et al (2020) Several previous studies used a demand quantity of one unit per customer so that the demand rate equals the arrival rate and can replace the demand rate directly in the inventory model (Ghosh et al 2022;Lyu et al 2010;Marand et al 2019). Then for the arrival of customers with more than one unit demand (Hill and Dominey 2001), the total demand is estimated by multiplying the expected value of the customer arrival rate and the quantity per customer.…”

“…This study uses a different approach when using the arrival rates in the inventory model. Previous studies used arrival rates directly as demand in the inventory model (Ghosh et al 2022;Hill and Dominey 2001;Khedlekar et al 2014;Lyu et al 2010;Marand et al 2019), whereas the current study uses new patients' arrival rates to estimate demand in all CT cycles in the future.…”

“…customer arrival rate for a continuous review model, with the probabilistic demand quantity from each customer must be fulfilled in full or not at all Lyu et al (2010). used the customer arrival rate for a replenishment simulation model in collaborative supplier and retailer conditions,Marand et al (2019) used the customer arrival rate for a continuous review inventory model integrated with the queuing model, andGhosh et al (2022) used customer arrival in the retail inventory model by considering customer preferences.…”