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

Optimal Expediting Decisions in a Continuous-Stage Serial Supply Chain.

In this paper, we analyze expediting decisions in a continuous-time, continuous-stage serial supply chain facing a Poisson demand process. For each unit in the chain, one must decide at which speed it should be moved downstream, given the state of the system, so as to minimize total supply chain costs. We decompose the problem into a set of one-dimensional subproblems that can be easily solved and characterize the optimal expediting policy: under quite general assumptions, the optimal speed of a given unit accelerates upstream, and then slows down downstream. We finally provide a case study where we estimate the benefits of expediting compared to a fixed transportation speed and show them to be significant

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 share, 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 relaxation also helps us to develop several heuristics, for which we establish performance guarantees. Numerical experiments show that these heuristics perform very well, yielding profits within 1% of the optimal in most cases