Capacitated Assortment Optimization: Hardness and Approximation

Assortment optimization is an important problem arising in various applications. In many practical settings, the assortment is subject to a capacity constraint. In “Capacitated Assortment Optimization: Hardness and Approximation,” Désir, Goyal, and Zhang study the capacitated assortment optimization problem. The authors first show that adding a general capacity constraint makes the problem NP-hard even for the simple multinomial logit model. They also show that under the mixture of multinomial logit model, even the unconstrained problem is hard to approximate within any reasonable factor when the number of mixtures is not constant. In view of these hardness results, the authors present near-optimal algorithms for a large class of parametric choice models including the mixture of multinomial logit, Markov chain, nested logit, and d-level nested logit choice models. In fact, their approach extends to a large class of objective functions that depend only on a small number of linear functions.

Asset Selling Under Debt Obligations

We extend the classical asset-selling problem to include debt repayment obligation, selling capacity constraint, and Markov price evolution. Specifically, we consider the problem of selling a divisible asset that is acquired through debt financing. The amount of asset that can be sold per period may be limited by physical constraints. The seller uses part of the sales revenue to repay the debt. If unable to pay off the debt, the seller must go bankrupt and liquidate the remaining asset. Our analysis reveals that in the presence of debt, the optimal asset-selling policy must take into account two opposing forces: an incentive to sell part of the asset early to secure debt payment and an incentive to delay selling the asset to capture revenue potential under limited liability. We analyze how these two forces, originating from debt financing, will distort the seller’s optimal policy.

Precision Scheduled Railroading and the Need for Improved Estimates of Yard Capacity and Performance Considering Traffic Complexity

Multiple North American freight railroads have adopted concepts of Precision Scheduled Railroading (PSR) that attempt to reduce costs by maximizing train length and minimizing railcar transit time. To achieve these objectives, PSR emphasizes pre-blocking traffic and operating general-purpose trains. These changes have altered the nature of operations at many classification yards, leading to yard closures and conversions to different yard types. Difficulty in implementing PSR-inspired operating practices at yards suggests the industry requires improved estimates of classification yard performance and capacity. While volume-based approaches may be adequate when yard operations are consistent with historical experience, it is hypothesized that approaches considering overall traffic complexity will offer improved predictions when changes are also made to the number of blocks and trains assembled in the yard. An original simulation model of a classification yard pull-down process is used to investigate this hypothesis. The simulation results suggest that a combination of factors describing yard traffic complexity can be a better predictor of yard performance than volume alone. The results are also transformed into a capacity constraint that describes the interaction between the maximum allowable daily number of railcars, blocks, and trains processed by a classification yard. Better understanding of these relationships can aid practitioners and researchers in improving network blocking models and developing train plans that properly use available yard capacity under PSR and other operating plans, reducing the likelihood of future network disturbances and congestion events.