François Soumis

• Polytechnique Montréal

Operations research specialists at the OCP Group, the Mohammed VI Polytechnic University, and Polytechnique Montreal operationalized a system that optimizes the OCP downstream supply chain operations. The system simultaneously schedules production, inventory, and vessels, ensuring the highest demand fulfillment level. To operationalize the system,...

The crew rostering problem (CRP) for pilots is a complex crew scheduling task assigning pairings, or sequences of flights starting and ending at the same airport, to pilots to create a monthly schedule. In this paper, we propose an innovative solution method for the CRP that uses a windowing approach. First, using a combination of machine learning...

The crew rostering problem (CRP) for pilots is a complex crew scheduling task assigning pairings, or sequences of flights starting and ending at the same airport, to pilots to create a monthly schedule. In this paper, we propose an innovative solution method for the CRP that uses a windowing approach. First, using a combination of machine learning...

Crew scheduling is typically performed in two stages. First, solving the crew pairing problem generates sequences of flights called pairings. Then, the pairings are assigned to crew members to provide each person with a full schedule. A common way to do this is to solve an optimization problem called the crew rostering problem (CRP). However, befor...

In this paper we address the problem of designing the logistics network of a fertilizers manufacturing firm operating in a developing country. The objective of this study is to establish a transportation and warehouse development plan to support the new distribution chain of a world-class manufacturing firm in Ethiopia. We focus on the distribution...

The personalized crew rostering problem (CRP) consists of assigning pairings (sequences of flights, deadheads, connections, and rests, forming one or several days of work) to individual crew members to create a feasible roster that maximizes crew satisfaction. This problem is often solved using a branch-and-price algorithm. In this paper, we propos...

Motivated by the needs from an airline crew scheduling application, we introduce structured convolutional kernel networks (Struct-CKN), which combine CKNs from Mairal et al. (2014) in a structured prediction framework that supports constraints on the outputs. CKNs are a particular kind of convolutional neural networks that approximate a kernel feat...

The crew pairing problem (CPP) is generally modelled as a set partitioning problem where the flights have to be partitioned in pairings. A pairing is a sequence of flight legs separated by connection time and rest periods that starts and ends at the same base. Because of the extensive list of complex rules and regulations, determining whether a seq...

We present a case study of using machine learning classification algorithms to initialize a large scale commercial operations research solver (GENCOL) in the context of the airline crew pairing problem, where small savings of as little as 1% translate to increasing annual revenue by millions of dollars in a large airline. We focus on the problem of...

The monthly crew pairing problem (CPP) consists of determining a least-cost set of feasible crew pairings (sequences of flights starting and ending at a crew base) such that each flight is covered once and side constraints are satisfied. This problem has been widely studied but most works have tackled daily or weekly CPP instances with up to 3500 f...

The shortest path problem with resource constraints (SPPRC) is often used as a subproblem within a column-generation approach for routing and scheduling problems. It aims to find a least-cost path between the source and the destination nodes in a network while satisfying the resource consumption limitations on every node. The SPPRC is usually solve...

The primal adjacency‐based algorithm and the multidirectional dynamic programming algorithm are two exact methods that have recently been developed to efficiently solve the shortest path problem with resource constraints (SPPRCs). These methods are primal in the sense that they are able to produce sequences of feasible solutions using iterative exp...

In this paper, we introduce a general framework for vector space decompositions that decompose the set partitioning problem into a reduced problem, defined in the vector subspace generated by the columns corresponding to nonzero variables in the current integer solution, and a complementary problem, defined in the complementary vector subspace. We...

In this paper, we suggest a new approach called the return function to deal with the determination of Bayesian–Nash equilibria in games of incomplete information. Whereas in the traditional approach players reply to each others’ strategies, here each player replies to his own return function. In short, given a player’s choice of action and the othe...

In large commercial airlines, the monthly schedule (roster) of the crew members is usually determined by solving two problems sequentially, namely, the crew pairing problem (CPP) and the crew rostering problem (CRP). While the CPP finds a set of low-cost feasible anonymous pairings, the CRP assigns these pairings to the crew members to create a val...

A common strategy used by airlines to improve employee satisfaction is to create schedules that take into account crew preferences such as preferred legs or desired off-periods. Air crew scheduling usually involves two steps: the crew pairing problem (CPP) and the crew rostering problem (CRP). A pairing is a sequence of legs and deadheads separated...

We consider a personalized employee scheduling problem with characteristics present in retail stores consisting of multiple departments. In the setting under study, each department generally covers its demand in employees over the planning horizon of a week by assigning shifts to its own staff. However, the employees can also be transferred to othe...

In this paper, we address a personalized multi-department multi-day shift scheduling problem with a multi-skill heterogeneous workforce where employees can be transferred between departments under some restrictions. The objective is to construct a schedule that minimizes under-coverage, over-coverage, transfer and labor costs. We propose a novel tw...

Synchronization of workers and vehicles plays a major role in many industries such as logistics, healthcare or airport ground handling. In this paper, we focus on operational ground handling planning and model it as an archetype of vehicle routing problems with multiple synchronization constraints, coined as “abstract vehicle routing problem with w...

We consider a multi-activity shift scheduling problem where the objective is to construct anonymous multi-activity shifts that respect union rules, satisfy the demand and minimize workforce costs. An implicit approach using adapted forward and backward constraints is proposed that integrates both the shift construction and the activity assignment p...

Integral simplex using decomposition (ISUD) is a method that efficiently solves set partitioning problems. It is an iterative method that starts from a known integer solution and moves through a sequence of integer solutions, decreasing the cost at each iteration. At each iteration, the method decomposes the original problem into a reduced problem...

The tail assignment problem is a critical part of the airline planning process that assigns specific aircraft to sequences of flights, called lines-of-flight, to satisfy operational constraints. The aim of this paper is to develop an operationally flexible method, based upon the one-day routes business model, to compute tail assignments that satisf...

The aircraft trajectory optimization problem can be approached by first considering a large set of possible spatial aircraft trajectories that connect a departure point and an arrival point. For each spatial trajectory in this set, the minimization of the total flight cost leads unavoidably to the problem of selecting a minimal-cost speed-profile,...

Starting from the improved primal simplex (IPS) decomposition, introduced by Elhallaoui et al. [Elhallaoui, I., A. Metrane, G. Desaulniers, and F. Soumis (2011). An Improved Primal Simplex Algorithm for Degenerate Linear Problems. INFORMS Journal on Computing 23(4), 569–577]. to tackle degeneracy in general linear programs, we introduce and discuss...

This paper concentrates on the addition of cutting planes to the integral simplex using decomposition (ISUD) of Zaghrouti et al. (Operations Research, 2014, 62(2):435--449). This method solves the set partitioning problem by iteratively improving an existing feasible solution. We present the algorithm in a primal language and relate it to existing...

In this paper, we tackle the aircraft conflict resolution problem under uncertainties. We consider errors due to the wind effect, the imprecision of aircraft speed prediction, and the delay in the execution of maneuvers. Using a geometrical approach, we derive an analytical expression for the minimum distance between aircraft, along with the corres...

This paper introduces an exact method to schedule the internal transshipment process at cross-docks in less-than-truckload industries. An integer programming formulation is presented to minimize the cost of double handling by synchronizing two types of decisions: (1) products’ internal transferring route, and (2) the order of processing trucks at t...

Airline crew scheduling is typically performed in two steps : crew pairing followed by crew assignment. The crew pairing problem (CPP) finds a set of pairings (sequences of flights separated by connections or rests starting and ending at the same crew base) that covers a set of flights at minimum cost. The crew assignment problem consists of assign...

This paper presents a method based on dynamic constraint aggregation concept to solve the monthly crew pairing problem which consists of determining a minimum cost set of feasible pairings such that each flight is covered exactly once and side constraints are satisfied. Given its high complexity, This problem is traditionally decomposed in three pr...

In this paper, we tackle the conflict resolution problem using a new variant of the minimum-weight maximum-clique model. The problem involves identifying maneuvers that maintain the required separation distance between all pairs of a set of aircraft while minimizing fuel costs. We design a graph in which the vertices correspond to a finite set of m...

Air traffic in Europe is predicted to increase considerably over the next decades. In this context, we present a study of the interactions between the costs due to ground-holding regulations and the costs due to en-route air traffic control. We describe a traffic simulator that considers the regulation delays, aircraft trajectories, and air conflic...

This paper presents a scheduling model to enhance cross-docking operations. It attempts to reduce the transshipment workload by minimizing the total number of products that require double-handling. We formalize the problem and represent its mathematical form. Moreover, we develop a variable neighborhood search heuristic to tackle large problems. Co...

To solve integer linear programs, primal algorithms follow an augmenting sequence of integer solutions leading to an optimal solution. In this work, we focus on a particular primal algorithm, the integral simplex using decomposition (ISUD). To find the next point, one solves a linear program to select an augmenting direction for the current point f...

In this paper, we develop the two-dimensional positive edge criterion for the dual simplex. This work extends a similar pricing rule implemented by Towhidi et al. (2014) [24] to reduce the negative effects of degeneracy in the primal simplex. In the dual simplex, degeneracy occurs when nonbasic variables have a zero reduced cost, and it may lead to...

The improved primal simplex (IPS) was recently developed by Elhalaloui et al. to take advantage of degeneracy when solving linear programs with the primal simplex. It implements a dynamic constraint reduction based on the compatible columns, i.e., those that belong to the span of a given subset of basic columns including the nondegenerate ones. The...

Various disturbances such as adverse weather conditions may result in delayed or canceled flights and affect the optimized schedules planned for airline crew members. In this paper, we solve the recovery problem via an integrated approach to reoptimize both the pairings and the personalized monthly plans. We solve this problem simultaneously for th...

In this article, we present a new formulation for the air conflict detection and resolution problem. Given the current position, speed and acceleration of a set of aircraft, we identify the maneuvers required to avoid all possible conflicts and such that the fuel costs are minimized. To this end, we design a graph whose vertices correspond to discr...

The airline crew scheduling problem has received extensive attention, particularly in the last 60 years. This problem is frequently divided into crew pairing and crew assignment because of its large size and the complex safety agreements and contractual rules. Several solution methodologies have been developed, but many objectives and constraints a...

In this article, we formulate a new variant of the problem of finding a maximum clique of minimum weight in a graph applied to the detection and resolution of conflicts between aircraft. The innovation of the model relies on the cost structure: the cost of the vertices cannot be determined a priori, since they depend on the vertices in the clique....

Aircraft maintenance planning is of critical importance to the safe and efficient operations of an airline. It is common to solve the aircraft routing and maintenance planning problems many months in advance, with the solution spanning multiple days. An unfortunate consequence of this approach is the possible infeasibility of the maintenance plan d...

Since its introduction in 1969, the set partitioning problem has received much attention, and the structure of its feasible domain has been studied in detail. In particular, there exists a decreasing sequence of integer feasible points that leads to the optimum, such that each solution is a vertex of the polytope of the linear relaxation and adjace...

Air traffic in Europe is predicted to increase considerably over the next decades. In this context, we present a study of the interactions between the costs due to ground-holding regulations and the costs due to en-route air traffic control. We describe a traffic simulator that considers the regulation delays, aircraft trajectories, and air conflic...

The integral simplex using decomposition (ISUD) algorithm [22] is a dynamic constraint reduction method that aims to solve the popular set partitioning problem (SPP). It is a special case of primal algorithms, i.e. algorithms that furnish an improving sequence of feasible solutions based on the resolution, at each iteration, of an augmentation prob...

Air traffic in Europe is predicted to largely increase over the next decades. In such a context, this paper presents a study of the interactions between costs due to ground holding regulation and costs due to en-route air traffic control. With that in mind, a traffic simulator including the computations of regulation delays, aircraft trajectories a...

Since the 1970s, several authors have studied the structure of the set partitioning polytope and proposed adaptations of the simplex algorithm that find an optimal solution via a sequence of basic integer solutions. Balas and Padberg in 1972 proved the existence of such a sequence with nonincreasing costs, but degeneracy makes it difficult to find...

In this article, we propose a general framework for an algorithm derived from the primal simplex that guarantees a strict improvement in the objective after each iteration. Our approach relies on the identification of compatible variables that ensure a nondegenerate iteration if pivoted into the basis. The problem of finding a strict improvement in...

In this paper, a mixed integer programming model for solving the short term planning problem in surface mining is presented. This model will establish the sequence of mining for a period ranging from days to several months. This involves determining which blocks of the geological model will be extracted and in what order, indicating the movement of...

A crew pairing is a sequence of flights, connections and rests that starts and ends at a crew base and is assigned to a single crew. The crew pairing problem consists of determining a minimum cost set of feasible crew pairings such that each flight is covered exactly once and side constraints are satisfied. Traditionally, this problem has been solv...

Traditionally, the airline crew scheduling problem has been decomposed into a crew pairing problem and a crew assignment problem, both of which are solved sequentially. The first consists of generating a set of least-cost crew pairings (sequences of flights starting and ending at the same crew base) that cover all flights. The second aims at findin...

Abstract Since its appearance in 1947, the primal simplex algorithm has been one of the most popular algorithm for solving linear programs. It is very efficient when there is very little degeneracy, but it often struggles in the presence of high degeneracy, executing many pivots without improving the objective function value. In this paper, we prop...

The integrated crew scheduling (ICS) problem consists of determining, for a set of available crew members, least-cost schedules that cover all flights and respect various safety and collective agreement rules. A schedule is a sequence of pairings interspersed by rest periods that may contain days off. A pairing is a sequence of flights, connections...

This paper presents a prototype method for optimally solving the rostering problem, i.e., constructing work schedules for airline crew members. The main goal is to show the possibilities of solving the rostering problem using optimal methods. The prototype uses a column generation approach embedded in a branch and bound algorithm to solve the roste...

This paper considers the placement of components onto printed circuit boards (PCBs) using surface mount technology. Multiple automatic placement machines, a variety of PCB types and a large volume for each PCB type characterize the environment studied. The problem addressed is that of allocating and arranging the components on several placement mac...

In this paper, we propose a new Dantzig–Wolfe decomposition for degenerate linear programs with the non degenerate constraints in the master problem and the degenerate ones in the subproblem. We propose three algorithms. The first one, where some set of variables of the original problem are added to the master problem, corresponds to the Improved P...

Given a set of scheduled flights that must be operated by the same aircraft type, the aircraft routing problem consists of building anonymous aircraft routes that respect maintenance requirements and cover each flight exactly once. This paper looks at the nature of the problem and introduces a classification according to three business processes th...

Dynamic constraint aggregation is an iterative method that was recently introduced to speed up the linear relaxation solution process of set partitioning type problems. This speed up is mostly due to the use, at each iteration, of an aggregated problem defined by aggregating disjoint subsets of constraints from the set partitioning model. This aggr...

This paper considers a shift scheduling problem that includes different forms of flexibility in terms of shift starting times, break lengths and break placement. Two particular forms are studied: fractionable breaks and work stretch duration restrictions. For some instances the use of fractionable breaks results in considerable labor savings. In ad...

The Improved Primal Simplex (IPS) algorithm [Elhallaoui I, Metrane A, Desaulniers G, Soumis F. An Improved Primal Simplex algorithm for degenerate linear programs. SIAM Journal of Optimization, submitted for publication] is a dynamic constraint reduction method particularly effective on degenerate linear programs. It is able to achieve a reduction...

We consider a widespread branch-and-price approach to solve the multiple depot vehicle scheduling problem with time windows. We describe a dynamic time window reduction technique to speed up this approach. The time windows are transferred from nodes to arcs in order to take advantage of dual information and to tighten as much as possible the time v...

The crew pairing problem (CPP) is one step of the airline crew scheduling process. The CPP consists of determining a minimum cost set of feasible pairings such that each flight is covered exactly once and side constraints are satisfied. In the industry, this problem has been traditionally solved by a heuristic three-phase (TP) approach that solves...

Most fleet assignment problem (FAP) formulations use a leg-based estimation of revenue loss to derive the passenger revenue component of their objective function. This neglects the leg interdependency of revenues, caused by multileg itineraries. We tackle this problem by modifying the objective function using information provided by a passenger flo...

In some companies such as large retail stores, the employees perform different activities (e.g., cashier or clerk in a specific department) to respond to a customer demand for each activity that varies over the planning horizon and must be fulfilled as soon as possible. For a given time period, this demand translates into an ideal number of employe...

Abstract We present a model that rapidly finds an approximation of the expected passenger flow on an airline network, given forecast data concerning 1) the distribution of the demand for each itinerary, seen as a random variable; 2) the time distribution of book- ing requests for each itinerary; and 3) the proportion of spill (from an itinerary) th...

Dynamic constraint aggregation was recently introduced by Elhallaoui et al. [Dynamic aggregation of set partitioning constraints in column generation. Operations Research 2005; 53: 632–45] for efficiently solving the linear relaxation of a class of set partitioning type problems in a column generation context. It reduces the master problem size by...

This paper considers large shift scheduling problems with different shift start times and lengths, fractionable breaks and work stretch duration restrictions. Two solution approaches are proposed to solve the problems over a multiple-day planning horizon. The first approach is based on a local branching strategy and the second one is based on a tem...

In a transit authority bus depot, buses of different types arrive in the evening to be parked in the depot for the night, and then dispatched in the morning to a set of routes, each of which requests a specific bus type. A type mismatch occurs when the requested type is not assigned to a morning route. We consider the problem of assigning the buses...

In constructing working shifts, the classical Dantzig (Operation Research 2:339–341, 1954) set covering model uses a great number of variables which makes computation very complicated for some cases that incorporate a high degree of break-placement flexibility. Bechtold and Jacobs (Management Science 36:1339–1351, 1990) proposed an implicit model u...

This paper introduces the first exact approach for constructing aircrew member personalized monthly work schedules when a preferential bidding system (PBS) is used. With such a system, each employee bids for his/her preferred activities, yielding a bidding score for each feasible schedule. The PBS problem thus consists of assigning to each employee...

In the integrated aircraft routing, crew scheduling and flight retiming problem, a minimum-cost set of aircraft routes and crew pairings must be constructed while choosing a departure time for each flight leg within a given time window. Linking constraints ensure that the same schedule is chosen for both the aircraft routes and the crew pairings, a...

Given buses of different types arriving at a depot during the evening, the bus parking problem consists of assigning these buses to parking slots in such a way that they can be dispatched adequately to the next morning routes without moving them between their arrivals and departures. In practice, the bus arrival times deviate stochastically from th...

Consider a set of trips where each trip is specified a priori by a place of origin, a destination, a duration, a cost, and a time interval within which the trip must begin. The trips may include visits to one or more specific points. Our problem is to determine the number of vehicles required, together with their routes and schedules, so that each...

Given a linear program, we describe an approach for crossing over from an optimal dual solution to an optimal basic primal solution. It consists in restricting the dual problem to a small box around the available optimal dual solution then, resolving the associated modified primal problem.

In this article we consider the problem of assigning parking slots to buses of different types so that the required buses can be dispatched easily in the morning. More precisely, if a bus of a certain type is needed at a given time, the buses that precede it in the lane must have departed already. Thus care must be taken to ensure that the buses ar...

The characterization of irregular objects with fractal methods often leads to the estimation of the slope of a function which is plotted versus a scale parameter. The slope is usually obtained with a linear regression. The problem is that the fit is usually not acceptable from the statistical standpoint. We propose a new approach in which we use tw...

This paper considers the locomotive assignment problem encountered during the planning of the operations of a freight railroad, which consists of providing sufficient motive power to pull a set of scheduled trains at minimum cost while satisfying locomotive availability and maintenance requirements. In 1997, Ziarati et al. proposed for this problem...

Given the flight schedule of an airline, the fleet assignment problem consists of determining the aircraft type to assign to each flight leg in order to maximize the total expected profits while satisfying aircraft routing and availability constraints. The profit for a leg is a function of the leg’s stochastic passenger demand, the capacity of the...

This chapter presents a formulation for the job shop problem based on Dantzig-Wolfe decomposition with a subproblem for each machine. Each subproblem is a sequencing problem on a single machine with time windows. The formulation is used within an exact algorithm capable of solving problems with objectives Cmax, Tmax, as well as an objective consist...

We consider the multiple depot vehicle scheduling problem (MDVSP) and propose a branch-and-bound algorithm for solving it that combines column generation, variable fixing, and cutting planes. We show that the solutions of the linear relaxation of the MDVSP contain many ”odd cycles.” We derive a class of valid inequalities by extending the notion of...

Given the sets of flights and aircraft of an airline carrier, the fleet assignment problem consists of assigning the most profitable aircraft type to each flight. In this paper we propose a model for the periodic fleet assignment problem with time windows in which departure times are also determined. Anticipated profits depend on the schedule and t...

The shortest path problem with resource constraints consists of finding the minimum cost path between two specified points while respecting constraints on resource consumption. Its solving by a dynamic programming algorithm requires a computation time increasing with the number of resources. With the aim of producing rapidly a good heuristic soluti...

Column generation is often used to solve problems involving set-partitioning constraints, such as vehicle-routing and crew-scheduling problems. When these constraints are in large numbers and the columns have on average more than 8-12 nonzero elements, column generation often becomes inefficient because solving the master problem requires very long...

The integrated aircraft routing and crew scheduling problem consists in determining a minimum-cost set of aircraft routes and crew pairings such that each flight leg is covered by one aircraft and one crew, and side constraints are satisfied. While some side constraints involve only crews or aircraft, linking constraints impose minimum connection t...

The fractional aircraft market is the fastest growing segment of the business aircraft industry. A fractional aircraft operation is complex—essentially an unscheduled airline in a constantly changing environment. Bombardier Flexjet implemented a comprehensive three-module optimization system to simultaneously maximize its use of aircraft, crews, an...

Column generation has become a powerful tool in solving large scale integer programs. It is well known that most of the often reported compatibility issues between pricing subproblem and branching rule disappear when branching decisions are based on imposing constraints on the subproblem's variables. This can be generalized to branching on variable...

This paper introduces a new kind of operational multi-crew scheduling problem which consists in simultaneously modifying, as necessary, the existing flight departure times and planned individual work days (duties) for the set of crew members, while respecting predefined aircraft itineraries. The splitting of a planned crew is allowed during a day o...

This paper introduces a new integrated model for the combined days-off and shift scheduling problem (the tour scheduling problem). This model generalizes the forward and backward constraints, previously introduced by Bechtold and Jacobs for the shift scheduling problem, to the tour scheduling problem. This results in a general and compact formulati...

Column generation has become a powerful tool in solving large scale integer programs. We argue that most of the often reported compatibility issues between pricing oracle and branching rules disappear when branching decisions are based on the reduction of the oracle's domain. This can be generalized to branching on variables of a so-called compact...