Outer Approximation and Super-modular Cuts for Constrained Assortment Optimization under Mixed-Logit Model

In this paper, we study the assortment optimization problem under the mixed-logit customer choice model. While assortment optimization has been a major topic in revenue management for decades, the mixed-logit model is considered one of the most general and flexible approaches for modeling and predicting customer purchasing behavior. Existing exact methods have primarily relied on mixed-integer linear programming (MILP) or second-order cone (CONIC) reformulations, which allow for exact problem solving using off-the-shelf solvers. However, these approaches often suffer from weak continuous relaxations and are slow when solving large instances. Our work addresses the problem by focusing on components of the objective function that can be proven to be monotonically super-modular and convex. This allows us to derive valid cuts to outer-approximate the nonlinear objective functions. We then demonstrate that these valid cuts can be incorporated into Cutting Plane or Branch-and-Cut methods to solve the problem exactly. Extensive experiments show that our approaches consistently outperform previous methods in terms of both solution quality and computation time.

Competitive Facility Location under Random Utilities and Routing Constraints

In this paper, we study a facility location problem within a competitive market context, where customer demand is predicted by a random utility choice model. Unlike prior research, which primarily focuses on simple constraints such as a cardinality constraint on the number of selected locations, we introduce routing constraints that necessitate the selection of locations in a manner that guarantees the existence of a tour visiting all chosen locations while adhering to a specified tour length upper bound. Such routing constraints find crucial applications in various real-world scenarios. The problem at hand features a non-linear objective function, resulting from the utilization of random utilities, together with complex routing constraints, making it computationally challenging. To tackle this problem, we explore three types of valid cuts, namely, outer-approximation and submodular cuts to handle the nonlinear objective function, as well as sub-tour elimination cuts to address the complex routing constraints. These lead to the development of two exact solution methods: a nested cutting plane and nested branch-and-cut algorithms, where these valid cuts are iteratively added to a master problem through two nested loops. We also prove that our nested cutting plane method always converges to optimality after a finite number of iterations. Furthermore, we develop a local search-based metaheuristic tailored for solving large-scale instances and show its pros and cons compared to exact methods. Extensive experiments are conducted on problem instances of varying sizes, demonstrating that our approach excels in terms of solution quality and computation time when compared to other baseline approaches.

A new constraint programming model and a linear programming-based adaptive large neighborhood search for the vehicle routing problem with synchronization constraints

We consider a vehicle routing problem which seeks to minimize cost subject to time window and synchronization constraints. In this problem, the fleet of vehicles is categorized into regular and special vehicles. Some customers require both vehicles' services, whose starting service times at the customer are synchronized. Despite its important real-world application, this problem has rarely been studied in the literature. To solve the problem, we propose a Constraint Programming (CP) model and an Adaptive Large Neighborhood Search (ALNS) in which the design of insertion operators is based on solving linear programming (LP) models to check the insertion feasibility. A number of acceleration techniques is also proposed to significantly reduce the computational time. The computational experiments show that our new CP model finds better solutions than an existing CP-based ANLS, when used on small instances with 25 customers and with a much shorter running time. Our LP-based ALNS dominates the cp-ALNS, in terms of solution quality, when it provides solutions with better objective values, on average, for all instance classes. This demonstrates the advantage of using linear programming instead of constraint programming when dealing with a variant of vehicle routing problems with relatively tight constraints, which is often considered to be more favorable for CP-based methods.