C onsider a retailer who sells perishable seasonal products with uncertain demand. Due to the short sales season and long replenishment lead times associated with such products, the retailer is unable to update demand forecasts by using actual sales data generated from the early part of the season and to respond by replenishing stocks during the season. To overcome this limitation, we examine the case in which the retailer develops a program called the "advance booking discount" (ABD) program that entices customers to commit to their orders at a discount price prior to the selling season. The time between placement and fulfillment of these precommitted orders provides an opportunity for the retailer to update demand forecasts by utilizing information generated from the precommitted orders and to respond by placing a cost-effective order at the beginning of the selling season. In this paper, we evaluate the benefits of the ABD program and characterize the optimal discount price that maximizes the retailer's expected profit.

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We model a situation in which two retailers consider launching an "Advance Booking Discount" (ABD) program. In this program, customers are enticed to precommit their orders at a discount price prior to the regular selling season. However, these precommitted orders are filled during the selling season. While the ABD program enables the retailers to lock in a portion of the customer demand and use this demand information to develop more accurate forecasts and supply plans, the ABD price reduces profit margin. We analyze the four possible scenarios wherein each of the two firms offer an ABD program or not, and establish conditions under which the unique equilibrium calls for launching the ABD program at both retailers.retailing, competition, pricing, inventory management

Eppen (1979) showed that inventory costs in a centralized system increase with the correlation between multivariate normal product demands. Using multivariate stochastic orders, we generalize this statement to arbitrary distributions. We then describe methods to construct models with arbitrary dependence structure, using the copula of a multivariate distribution to capture the dependence between the components of a random vector. For broad classes of distributions with arbitrary marginals, we confirm that centralization or pooling of inventories is more valuable when demands are less positively dependent.inventory control, pooling effect, multivariate dependence, copula

W e consider a patient admission problem to a hospital with multiple resource constraints (e.g., OR and beds) and a stochastic evolution of patient care requirements across multiple resources. There is a small but significant proportion of emergency patients who arrive randomly and have to be accepted at the hospital. However, the hospital needs to decide whether to accept, postpone, or even reject the admission from a random stream of non-emergency elective patients. We formulate the control process as a Markov decision process to maximize expected contribution net of overbooking costs, develop bounds using approximate dynamic programming, and use them to construct heuristics. We test our methods on data from the Ronald Reagan UCLA Medical Center and find that our intuitive newsvendor-based heuristic performs well across all scenarios.

We consider the problem of minimizing daily expected resource usage and overtime costs across multiple parallel resources such as anesthesiologists and operating rooms, which are used to conduct a variety of surgical procedures at large multispecialty hospitals. To address this problem, we develop a two-stage, mixed-integer stochastic dynamic programming model with recourse. The first stage allocates these resources across multiple surgeries with uncertain durations and prescribes the sequence of surgeries to these resources. The second stage determines actual start times to surgeries based on realized durations of preceding surgeries and assigns overtime to resources to ensure all surgeries are completed using the allocation and sequence determined in the first stage. We develop a data-driven robust optimization method that solves large-scale real-sized versions of this model close to optimality. We validate and implement this model as a decision support system at the UCLA Ronald Reagan Medical Center. This system effectively incorporates the flexibility in the resources and uncertainty in surgical durations, and explicitly trades off resource usage and overtime costs. This has increased the average daily utilization of the anesthesiologists by 3.5% and of the operating rooms by 3.8%. This has led to an average daily cost savings of around 7% or estimated to be $2.2 million on an annual basis. In addition, the insights based on this model have significantly influenced decision making at the operating services department at this hospital. The e-companion is available at https://doi.org/10.1287/opre.2017.1634 .

In a merchandise depth test, a retail chain introduces new products at a small sample of selected stores for a short period prior to the primary selling season and uses the observed sales to forecast demand for the entire chain. We describe a method for resolving two key questions in merchandise testing: (1) which stores to use for the test and (2) how to extrapolate from test sales to create a forecast of total season demand for each product for the chain. Our method uses sales history of products sold in a prior season, similar to those to be tested, to devise a testing program that would have been optimal if it had been applied to this historical sample. is defined as minimizing the cost of conducting the test, plus the cost of over- and understocking of the products whose supply is to be guided by the test. To determine the best set of test stores, we apply a -median model to cluster the stores of the chain based on a store similarity measure defined by sales history, and then choose one test store from each cluster. A linear programming model is used to fit a formula that is then used to predict total sales from test sales. We applied our method at a large retailer that specializes in women's apparel and at two major shoe retailers, comparing results in each case to the existing process used by the apparel retailer and to some standard statistical approaches such as forward selection and backward elimination. We also tested a version of our method in which clustering was based on a combination of several store descriptors such as location, type of store, ethnicity of the neighborhood of location, total store sales, and average temperature of the store location. We found that relative to these other methods, our approach could significantly improve forecasts and reduce markdowns that result from excessive inventory, and lost margins resulting from stockouts. At the apparel retailer the improvement was enough to increase profits by more than 100%. We believe that one reason our method outperforms the forward selection and backward elimination methods is that these methods seek to minimize squared errors, while our method optimizes the true cost of forecast errors. In addition, our approach, which is based purely on sales, outperforms descriptor variables because it is not always clear which are the best store descriptors and how best to combine them. However, the sales-based process is completely objective and directly corresponds to the retailer's objective of minimizing the understock and overstock costs of forecast error. We examined the stores within each of the clusters formed by our method to identify common factors that might explain their similar sales patterns. The main factor was the similarity in climate within a cluster. This was followed by the ethnicity of the neighborhood where the store is located, and the type of store. We also found that, contrary to popular belief, store size and location had little impact on sales patterns. In addition, this technique could also be used to determine the inv...

We consider the problem of determining (for a short lifecycle) retail product initial and replenishment order quantities that minimize the cost of lost sales, back orders, and obsolete inventory. We model this problem as a two-stage stochastic dynamic program, propose a heuristic, establish conditions under which the heuristic finds an optimal solution, and report results of the application of our procedure at a catalog retailer. Our procedure improves on the existing method by enough to double profits. In addition, our method can be used to choose the optimal reorder time, to quantify the benefit of leadtime reduction, and to choose the best replenishment contract.Retailing, Inventory Replenishment, Stochastic Dynamic Programming, Heuristics