arXiv subjects

Jean-François Côté

Publications and source records attributed to Jean-François Côté.

7 recordsLinked to original sources

arXiv2026

The Stochastic Team Orienteering Problem

This paper analyses the Stochastic Team Orienteering Problem (STOP), a stochastic variant of the Team Orienteering Problem (TOP). In the STOP, travel times are represented by random variables. The objective is to determine a set of routes that maximises the expected collected profit. We model the problem as a two-stage stochastic integer program and propose an exact solution method based on the Integer L-shaped method. We also consider a set of non-linear chance constraints to restrict the search to highly reliable routes. In the first-stage, a set of routes is selected, while in the second-stage the recourse evaluates the expected profit of the selected routes. We present a new set of optimality cuts and strengthen the formulation by considering valid inequalities and constraints liftings. Computational results provide a comprehensive analysis of the algorithm using the standard TOP benchmark dataset from the literature.

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arXiv2026

The Car Resequencing Problem with Makespan Minimization

Problem definition: The car resequencing problem involves rearranging the sequence of cars between two adjacent production shops via an intermediate buffer. This study explores a new variant that aims to minimize the resequencing makespan when the buffer features several forward lanes and a return lane (RL). Both types of lanes follow first-in-first-out rules, but operate in opposite directions. Through the RL, cars can circulate between forward lanes, thereby increasing resequencing flexibility and complexity. The goal is to position cars over time to complete the target sequence change in the shortest possible time. Methodology/results: We prove the problem is NP-complete and develop an exact two-stage branch-and-price approach integrated with constraint programming (BP-CP). Three versions of the master problem (MP) are proposed for the first stage, each paired with a subproblem defined on a specific graph. Using partial integer solutions from branching, a constraint-programming model built in the second stage yields either a feasible solution to the problem or a feasibility cut added to the MP. Experimental results indicate that BP-CP greatly increases the scale of solvable instances for a production batch, especially with a moderately relaxed MP. A comparative analysis shows that the RL markedly enhances resequencing flexibility, enabling smaller buffers to attain makespans comparable to those of larger buffers without the RL across varying resequencing complexities. Managerial implications: Expanding lane capacity alone yields limited gains in resequencing performance and may even reduce efficiency. The RL acts as several forward lanes, supporting a smaller and cost-effective buffer design while maintaining efficient just-in-time operations.

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arXiv2026

An Exact Combinatorial Branch-and-Bound Algorithm for the Job Sequencing and Tool Switching Problem

The Job Sequencing and Tool Switching Problem (SSP) is a well-known combinatorial optimization problem arising in the context of flexible manufacturing. Since the seminal work of Tang and Denardo (1988), the SSP has received significant attention in the literature, leading to the development of numerous exact and heuristic approaches. Despite these efforts, several benchmark instances proposed decades ago and containing only 20 jobs have remained unsolved to proven optimality. In this work, we propose an exact algorithm for the SSP, namely the Combinatorial Branch-and-Bound (C-B\&B) algorithm, which combines two distinct branch-and-bound algorithms, each introducing novel features compared with the existing literature. The former relies on a new branching scheme designed to reduce the size of the implicit enumeration tree, together with a collection of new bounding functions. The latter builds on the branching scheme introduced by Laporte et al. (2004) and strengthens it with a new bounding function and two dominance rules. Within C-B\&B, these exact algorithms are complemented by a preprocessing phase that incorporates a new branch-and-bound-based heuristic capable of rapidly generating a high-quality initial incumbent solution. Extensive computational experiments show that C-B\&B represents a strong breakthrough over previously published approaches, proving optimality for more instances with significantly less computational effort and closing several benchmark instances that have remained open for decades.

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arXiv2026

Polynomial and Pseudopolynomial Algorithms for Two Classes of Bin Packing Instances

The Cutting Stock Problem (CSP) and Bin Packing Problem (BPP) are classical combinatorial optimization problems extensively studied since the 1960s. State-of-the-art exact algorithms are based on set-cover and arc-flow models whose linear relaxation, rounded up, matches the integer optimum for most benchmark instances, a condition known as the Integer Round-up Property (IRUP). In 2016, Delorme et al. showed that all existing instances could be solved within ten minutes by approaches exploiting this property. This motivated them to introduce two new classes, Augmented IRUP (AI) and Augmented Non-IRUP (ANI), designed to make IRUP less evident to state-of-the-art methods. Although these classes have motivated significant advances over the past decade, 13 out of 500 AI and ANI instances remain unsolved within standard time limits from the literature. In this paper, we show that while AI and ANI are particularly hard for MIP-based methods, the BPP restricted to these classes is not strongly NP-hard. We present polynomial-time algorithms for the AI class and pseudopolynomial-time algorithms for the ANI class, which solve all such instances orders of magnitude faster than previous approaches. They are also straightforward to adapt to the Skiving Stock Problem, the dual counterpart of the CSP. In addition, they can be used as preprocessing routines in exact methods, as their runtime is independent of the instance class, although they are guaranteed to return an optimality status only for instances belonging to the class for which they were designed.

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arXiv2026

Superadditivity-based valid inequalities and asymptotic bounds for the vehicle routing problem with stochastic demands

Over the past thirty years, the vehicle routing problem with stochastic demands (VRPSD) has emerged as a canonical application of the integer L-shaped method. Recently, the disaggregated integer L-shaped (DL-shaped) method, which decomposes the recourse function by customer rather than treating it as an aggregate cost, has been proposed for the VRPSD under the classical detour-to-depot policy. However, its generalizability to other recourse policies has not been investigated. In this work, we identify the property that characterizes the validity of the DL-shaped reformulation: the superadditivity of the recourse function under path concatenation. We show that superadditivity holds under the optimal restocking policy, and rectify an incorrect argument from the original paper on the DL-shaped method, rigorously establishing its validity under the detour-to-depot policy. We then introduce a new family of valid inequalities, the edge-set cuts, which generalize the original DL-shaped cuts and are analytically shown to provide structural advantages over existing inequalities. Building on these results, we develop a DL-shaped algorithm for the VRPSD with optimal restocking. Our algorithm outperforms existing methods in the high customer-to-vehicle ratio regime and solves 14 open single-route instances. We further derive asymptotic bounds on the optimal value of the VRPSD in a Euclidean setting with i.i.d. customers. This analysis reveals an asymptotic equivalence between the VRPSD and the split-delivery vehicle routing problem. It also yields tight bounds on the cost of requiring the total expected demand on each route not to exceed the vehicle capacity, resolving an open question in our asymptotic setting.

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arXiv2023

The disaggregated integer L-shaped method for the stochastic vehicle routing problem

This paper proposes a new integer L-shaped method for solving two-stage stochastic integer programs whose first-stage solutions can decompose into disjoint components, each one having a monotonic recourse function. In a minimization problem, the monotonicity property stipulates that the recourse cost of a component must always be higher or equal to that of any of its subcomponents. The method exploits new types of optimality cuts and lower bounding functionals that are valid under this property. The stochastic vehicle routing problem is particularly well suited to be solved by this approach, as its solutions can be decomposed into a set of routes. We consider the variant with stochastic demands in which the recourse policy consists of performing a return trip to the depot whenever a vehicle does not have sufficient capacity to accommodate a newly realized customer demand. This work shows that this policy can lead to a non-monotonic recourse function, but that the monotonicity holds when the customer demands are modeled by several commonly used families of probability distributions. We also present new problem-specific lower bounds on the recourse that strengthen the lower bounding functionals and significantly speed up the resolution process. Computational experiments on instances from the literature show that the new approach achieves state-of-the-art results.

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arXiv2019

A Primal Decomposition Algorithm for the Two-dimensional Bin Packing Problem

The Two-dimensional Bin Packing Problem calls for packing a set of rectangular items into a minimal set of larger rectangular bins. Items must be packed with their edges parallel to the borders of the bins, cannot be rotated and cannot overlap among them. The problem is of interest because it models many real-world applications, including production, warehouse management and transportation. It is, unfortunately, very difficult, and instances with just 40 items are unsolved to proven optimality, despite many attempts, since the 1990s. In this paper, we solve the problem with a combinatorial Benders decomposition that is based on a simple model in which the two-dimensional items and bins are just represented by their areas, and infeasible packings are imposed by means of exponentially-many no-good cuts. The basic decomposition scheme is quite naive, but we enrich it with a number of preprocessing techniques, valid inequalities, lower bounding methods, and enhanced algorithms to produce the strongest possible cuts. The resulting algorithm behaved very well on the benchmark sets of instances, improving on average upon previous algorithms from the literature and solving for the first time a number of open instances.

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