Size stockouts in online fashion retailing occur when an item is not available in one of the sizes. In the size stockout cases, customers may opt to purchase a neighboring size (larger or smaller) rather than switching to a different style or leaving the store empty-handed. This customer choice pattern is known as the size substitution effect, and it has recently been revealed that it profoundly impacts customers' decisions. Size stockouts may also trigger fairness concerns among customers. In recent years, there has been substantial coverage of discrimination against plus-size customers as they cannot find the items they like in suitable sizes. Such concerns are increasingly important for retailers as “social inclusivity” gains traction among customers. Therefore, our goal in this research is to develop assortment optimization algorithms for an online fashion retailer in a static setting that, while considering the size substitution effect, are also fair toward different size groups.
We model this situation as a zero-sum game between the retailer and an adversary (nature) and then develop an exact algorithm and an efficient approximation algorithm to find the Nash equilibrium of this game. After calibrating our setup with the coefficients coming from a real-world dataset, we ran a series of simulations to evaluate the effectiveness of our approximation algorithm. Among other things, our results show that it is possible to drastically reduce unfairness with a minuscule drop in the retailer's revenue using our algorithm.

The cost of producing diverse cars depends on the sequence in which they are arranged in the body shop, paint shop, and assembly shop. Before entering the downstream assembly shop, the upstream car sequence shared by the body shop and paint shop is readjusted by a physical buffer named the painted body storage (PBS), which consists of several first-in-first-out lanes. The car resequencing problem (CRSP) addressed in this paper requires determining the upstream and downstream sequences and the car-to-lane assignment to minimize the total costs of the three shops. We propose a nested logic-based Benders decomposition (NLBBD) method with three levels, where the upstream sequence is determined in the first level by assigning each car a body and a color. By determining the configuration and the downstream sequence of each car, the cars are rearranged in the downstream sequence in the second level. A feasible assignment of cars to lanes is sought in the third level to respect this sequence change. We provide two shortest-path problem reformulations for the first level, which are applicable to general sequencing problems that aim to minimize the number of changeovers. Based on the first reformulation, the classical logic-based Benders decomposition iterative procedure is transformed into a k shortest simple path problem. We verify the corresponding stopping criteria and the existence of the global optimal solution. A lower bound, three valid inequalities, and a math-heuristic method are also proposed to enhance our NLBBD. In our CRSP, the number of cars to be resequenced is not limited by the PBS size. Computational results show that our NLBBD can handle real-world cases and instances of up to 120 cars in one hour, about ten times more than previous studies. A sensitivity analysis from three perspectives is performed to provide some managerial insights.

Cellular solids are porous materials used in sandwich panels, heat
exchangers, tissue engineering scaffolds and catalysts.
Advances in additive manufacturing have permitted the production of
triply periodic minimal surface (TPMS)–like cellular solids, which have
properties uniquely suited to these applications and have thus been the
focus of recent research.
Alas, the field of cellular solid design trails behind that of
mathematical optimization — much of the literature relies on variants of
grid search.
We are the first to apply the MADS blackbox optimization algorithm, as
implemented by the NOMAD optimizer, to cellular solid design.
We have developed a cellular solid generator suitable for use as input
to NOMAD, and a blackbox mimicking a problem in the literature
consisting of the compression of a block composed of a cellular solid,
with the goal of maximizing the cellular solid's relative Young's modulus.
We will present the cellular solid generator as well as the results we
obtained from applying NOMAD to the compression problem and a comparison
with those from the literature.
It is our hope that this will pave the way for researchers in cellular
solid design to employ more advanced methods of mathematical
optimization.