Juan José Miranda-Bront

A branch-and-cut algorithm for the latent-class logit assortment problem

We study the product assortment problem of a retail operation that faces a stream of customers who are heterogeneous with respect to preferences. Each customer belongs to a market segment characterized by a consideration set that includes the alternatives viewed as options, and by the preference weights that the segment assigns to each of those alternatives. Upon arrival, he checks the offer set displayed by the firm, and either chooses one of those products or quits without purchasing according to a multinomial-logit (MNL) criterion. The firms goal is to maximize the expected revenue extracted during a fixed time horizon. This problem also arises in the growing area of choice-based, network revenue management, where computational speed is a critical factor for the practical viability of a solution approach. This so-called latent-class, logit assortment problem is known to be NP-Hard. In this paper, we analyze unconstrained and constrained (i.e., with a limited number of products to display) versions of it, and propose a branch-and-cut algorithm that is computationally fast and leads to (nearly) optimal solutions.

An integer programming approach for the time-dependent TSP

The Time-Dependent Travelling Salesman Problem (TDTSP) is a generalization of the traditional TSP where the travel cost between two cities depends on the moment of the day the arc is travelled. In this paper, we focus on the case where the travel time between two cities depends not only on the distance between them, but also on the position of the arc in the tour. We consider the formulations proposed in Picard and Queryanne [J.C. Picard and M. Queyranne. The time-dependent traveling salesman problem and its application to the tardiness problem in one-machine scheduling. Operations Res., 26(1):86–110, 1978] and Vander Wiel and Sahinidis [R.J. Vander Wiel and N.V. Sahinidis. An exact solution approach for the time-dependent traveling-salesman problem. Naval Res. Logist., 43(6):797–820, 1996], analyze the relationship between them and derive some valid inequalities and facets. Computational results are also presented for a Branch and Cut algorithm (B&C) that uses these inequalities, which showed to be very effective.

A cluster-first route-second approach for the swap body vehicle routing problem

The swap body vehicle routing problem (SB-VRP) is a generalization of the classical vehicle routing problem where a particular structure as well as several operational aspects for the trucks composing the fleet are considered. This research has been motivated by the VeRoLog Solver Challenge 2014, organized together by VeRoLog and PTV group, aiming to motivate the study of real-world logistic problems. A truck can carry either only one swap body or, in addition, an extra trailer with an extra swap body. For the latter, special depots, called swap locations, can be used to drop and pickup the swap bodies. These operations may affect the feasibility and the cost of a route, and therefore the overall operational cost. In this paper, we propose a cluster-first route-second heuristic for the SB-VRP. Computational experiments are conducted over the benchmark instances proposed for the competition, simulating a practical environment by considering limited resources and execution time. The results obtained are of very good quality, where our approach ended as runner-up in the final set of instances and performs similarly to the other algorithms in the remaining cases, showing its potential to be applied in practice.

Facets and valid inequalities for the time-dependent travelling salesman problem

The Time-Dependent Travelling Salesman Problem (TDTSP) is a generalization of the traditional TSP where the travel cost between two cities depends on the moment of the day the arc is travelled. In this paper, we focus on the case where the travel time between two cities depends not only on the distance between them, but also on the position of the arc in the tour. We consider two formulations proposed in the literature, we analyze the relationship between them and derive several families of valid inequalities and facets. In addition to their theoretical properties, they prove to be very effective in the context of a Branch and Cut algorithm.

A Branch-and-Cut Algorithm for the Latent Class Logit Assortment Problem

Abstract We study the product assortment problem of a retail operation that faces a stream of customers heterogeneous with respect to preferences. Upon arrival, each customer checks the offer set displayed by the firm, and either chooses one of those products according to a multinomial-logit (MNL) criterion or quits without purchasing. The firms goal is to maximize the expected revenue extracted from each customer. The general version of the logit assortment problem is known to be NP-Hard. In this paper, we analyze uncapacitated and capacitated (i.e., with a limited number of products to display) versions of it, and propose a branch-and-cut algorithm that is computationally feasible and leads to high-quality solutions.

An ILP based heuristic for a generalization of the post-enrollment course timetabling problem

We consider a new timetabling problem arising from a real-world application in a private university in Buenos Aires, Argentina. In this paper we describe the problem in detail, which generalizes the Post-Enrollment Course Timetabling Problem (PECTP), propose an ILP model and a heuristic approach based on this formulation. This algorithm has been implemented and tested on instances obtained from real data, showing that the approach is feasible in practice and produces good quality solutions. HighlightsWe tackle a difficult optimization problem, arising from a real world application.We define a new problem in the context of the university timetabling problems.The problem generalizes two other problems from the related literature.We propose an ILP formulation and develop a heuristic algorithm based on this model.The algorithm is used in practice, providing good quality results.

A branch-and-price algorithm for the k,c-coloring problem

In this article, we study the k,c-coloring problem, a generalization of the vertex coloring problem where we have to assign k colors to each vertex of an undirected graph, and two adjacent vertices can share at most c colors. We propose a new formulation for the k,c-coloring problem and develop a Branch-and-Price algorithm. We tested the algorithm on instances having from 20 to 80 vertices and different combinations for k and c, and compare it with a recent algorithm proposed in the literature. Computational results show that the overall approach is effective and has very good performance on instances where the previous algorithm fails.

An integer programming approach for the time-dependent traveling salesman problem with time windows

Abstract Congestion in large cities and populated areas is one of the major challenges in urban logistics, and should be addressed at different planning and operational levels. The Time Dependent Travelling Salesman Problem (TDTSP) is a generalization of the well known Traveling Salesman Problem (TSP) where the travel times are not assumed to be constant along the day. The motivation to consider the time dependency factor is that it enables to have better approximations to many problems arising from practice. In this paper, we consider the Time-Dependent Traveling Salesman Problem with Time Windows (TDTSP-TW), where the time dependence is captured by considering variable average travel speeds. We propose an Integer Linear Programming model for the problem and develop an exact algorithm, which is compared on benchmark instances with another approach from the related literature. The results show that the approach is able to solve instances with up to 40 customers.

(k,c) – coloring via Column Generation

Abstract In this paper we study the ( k , c ) – coloring problem, a generalization of the well known Vertex Coloring Problem (VCP). We propose a new formulation and compare it computationally with another formulation from the literature. We also develop a diving heuristic that provides with good quality results at a reasonable computational effort.

Integer programming formulations for the time-dependent elementary shortest path problem with resource constraints

Abstract The impact of congestion in transportation has become one of the main concerns regarding urban planing in large cities. Time-Dependent Vehicle Routing Problems (TDVRPs) is the name given to a broad family of VRPs that explicitly incorporate the congestion by considering variable travel times. In this paper we study the Time-Dependent Elementary Shortest Path Problem with Resource Constraints (TDESPPRC), that appears as the pricing sub-problem in column generation-based approaches for TDVRPs. We consider two integer programming formulations which exploit the characteristics of the time-dependent travel time function and are evaluated on benchmark instances. On preliminary computational experiments, the approach is able to effectively solve instances with up to 25 vertices in reasonable times, showing its potential to be used within a Branch and Price algorithm.