The Assortment Packing Problem: Multiperiod Assortment Planning for Short-Lived Products

Motivated by retailers ’ frequent introduction of new items to refresh product lines and maintain their market shares, we present the assortment packing problem in which a firm must decide, in advance, the release date of each product in a given collection over a selling season. Our formulation models the trade-offs among profit margins, preference weights, and limited life cycles. A key aspect of the problem is that each product is short-lived in the sense that, once introduced, its attractiveness lasts only a few periods and vanishes over time. The objective is to determine when to introduce each product to maximize the total profit over the selling season. Even for two periods, the corresponding optimization problem is shown to be NP-complete. As a result, we study a continuous relaxation of the problem that approximates the problem well, when the number of products is large. When margins are identical and product preferences decay exponentially, its solution can be characterized: it is optimal to introduce products with slower decays earlier. The structural properties of the relaxation also help us to develop several heuristics, for which we establish performance guarantees. We test our heuristics with data on sales and release dates of woman handbags from an accessories retailer. The numerical experiments show that the heuristics perform very well and can yield significant improvements in profitability. 1

Durvalumab Plus Carboplatin/Paclitaxel Followed by Maintenance Durvalumab With or Without Olaparib as First-Line Treatment for Advanced Endometrial Cancer: The Phase III DUO-E Trial

PURPOSE Immunotherapy and chemotherapy combinations have shown activity in endometrial cancer, with greater benefit in mismatch repair (MMR)-deficient (dMMR) than MMR-proficient (pMMR) disease. Adding a poly(ADP-ribose) polymerase inhibitor may improve outcomes, especially in pMMR disease. METHODS This phase III, global, double-blind, placebo-controlled trial randomly assigned eligible patients with newly diagnosed advanced or recurrent endometrial cancer 1:1:1 to: carboplatin/paclitaxel plus durvalumab placebo followed by placebo maintenance (control arm); carboplatin/paclitaxel plus durvalumab followed by maintenance durvalumab plus olaparib placebo (durvalumab arm); or carboplatin/paclitaxel plus durvalumab followed by maintenance durvalumab plus olaparib (durvalumab + olaparib arm). The primary end points were progression-free survival (PFS) in the durvalumab arm versus control and the durvalumab + olaparib arm versus control. RESULTS Seven hundred eighteen patients were randomly assigned. In the intention-to-treat population, statistically significant PFS benefit was observed in the durvalumab (hazard ratio [HR], 0.71 [95% CI, 0.57 to 0.89]; P = .003) and durvalumab + olaparib arms (HR, 0.55 [95% CI, 0.43 to 0.69]; P < .0001) versus control. Prespecified, exploratory subgroup analyses showed PFS benefit in dMMR (HR [durvalumab v control], 0.42 [95% CI, 0.22 to 0.80]; HR [durvalumab + olaparib v control], 0.41 [95% CI, 0.21 to 0.75]) and pMMR subgroups (HR [durvalumab v control], 0.77 [95% CI, 0.60 to 0.97]; HR [durvalumab + olaparib v control] 0.57; [95% CI, 0.44 to 0.73]); and in PD-L1-positive subgroups (HR [durvalumab v control], 0.63 [95% CI, 0.48 to 0.83]; HR [durvalumab + olaparib v control], 0.42 [95% CI, 0.31 to 0.57]). Interim overall survival results (maturity approximately 28%) were supportive of the primary outcomes (durvalumab v control: HR, 0.77 [95% CI, 0.56 to 1.07]; P = .120; durvalumab + olaparib v control: HR, 0.59 [95% CI, 0.42 to 0.83]; P = .003). The safety profiles of the experimental arms were generally consistent with individual agents. CONCLUSION Carboplatin/paclitaxel plus durvalumab followed by maintenance durvalumab with or without olaparib demonstrated a statistically significant and clinically meaningful PFS benefit in patients with advanced or recurrent endometrial cancer

Demand seasonality in retail inventory management

We investigate the value of accounting for demand seasonality in inventory control. Our problem is motivated by discussions with retailers who admitted to not taking perceived seasonality patterns into account in their replenishment systems. We consider a single-location, single-item periodic review lost sales inventory problem with seasonal demand in a retail environment. Customer demand has seasonality with a known season length, the lead time is shorter than the review period and orders are placed as multiples of a fixed batch size. The cost structure comprises of a fixed cost per order, a cost per batch, and a unit variable cost to model retail handling costs. We consider four different settings which differ in the degree of demand seasonality that is incorporated in the model: with or without within-review period variations and with or without across-review periods variations. In each case, we calculate the policy which minimizes the long-run average cost and compute the optimality gaps of the policies which ignore part or all demand seasonality. We find that not accounting for demand seasonality can lead to substantial optimality gaps, yet incorporating only some form of demand seasonality does not always lead to cost savings. We apply the problem to a real life setting, using Point-of-Sales data from a European retailer. We show that a simple distinction between weekday and weekend sales can lead to major cost reductions without greatly increasing the complexity of the retailer’s automatic store ordering system. Our analysis provides valuable insights on the trade-off between the complexity of the automatic store ordering system and the benefits of incorporating demand seasonality

Assortment Planning and Inventory Decisions Under a Locational Choice Model

We consider a single-period assortment planning and inventory management problem for a retailer, using a locational choice model to represent consumer demand. We first determine the optimal variety, product location, and inventory decisions under static substitution, and show that the optimal assortment consists of products equally spaced out such that there is no substitution among them regardless of the distribution of consumer preferences. The optimal solution can be such that some customers prefer not to buy any product in the assortment, and such that the most popular product is not offered. We then obtain bounds on profit when customers dynamically substitute, using the static substitution for the lower bound, and a retailer-controlled substitution for the upper bound. We thus define two heuristics to solve the problem under dynamic substitution and numerically evaluate their performance. This analysis shows the value of modeling dynamic substitution and identifies conditions in which the static substitution solution serves as a good approximation.product variety, inventory management, consumer choice models, assortment planning, retail operations