A stochastic integer programming approach to reserve staff scheduling with preferences

Nowadays, reaching a high level of employee satisfaction in efficient schedules is an important and difficult task faced by companies. We tackle a new variant of the personnel scheduling problem under unknown demand by considering employee satisfaction via endogenous uncertainty depending on the combination of their preferred and received schedules. We address this problem in the context of reserve staff scheduling, an unstudied operational problem from the transit industry. To handle the challenges brought by the two uncertainty sources, regular employee and reserve employee absences, we formulate this problem as a two-stage stochastic integer program with mixed-integer recourse. The first-stage decisions consist in finding the days off of the reserve employees. After the unknown regular employee absences are revealed, the second-stage decisions are to schedule the reserve staff duties. We incorporate reserve employees' days-off preferences into the model to examine how employee satisfaction may affect their own absence rates.Comment: 25 pages, 4 figures, submitted to International Transactions in Operational Researc

Two decomposition algorithms for solving a minimum weight maximum clique model for the air conflict resolution problem

International audienceIn this article, 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 maneuvers and the edges connect conflict-free maneuvers. A maximum clique of minimal weight yields a conflict-free situation that involves all the aircraft and minimizes the costs induced. The innovation of the model is its cost structure: the costs of the vertices cannot be determined a priori, since they depend on the vertices in the clique. We formulate the problem as a mixed integer linear program. Since the modeling of the aircraft dynamics and the computation of trajectories is separated from the solution process, the model is flexible. As a consequence, our mathematical framework is valid for any hypotheses. In particular, the aircraft can perform dynamic velocity, heading, and flight-level changes. To solve instances involving a large number of aircraft spread over several flight levels, we introduce two decomposition algorithms. The first is a sequential mixed integer linear optimization procedure that iteratively refines the discretization of the maneuvers to yield a trade-off between computational time and cost. The second is a large neighborhood search heuristic that uses the first procedure as a subroutine. The best solutions for the available set of maneuvers are obtained in less than 10 seconds for instances with up to 250 aircraft randomly allocated to 20 flight levels

The pickup and delivery problem with time windows and handling operations

This paper introduces the pickup and delivery problem with time windows and handling operations. In this problem, the loading compartment of a vehicle is modeled as a linear LIFO stack. When an item is picked up, it is positioned on top of the stack. When it is on top of the stack, it can be delivered without additional handling. Otherwise, items on top must be unloaded before the delivery and reloaded afterwards, which requires time. We define two rehandling policies. For both policies, rehandling is only allowed at delivery locations and there is no specific reloading order for the rehandled items. Under the first policy, only compulsory rehandling is allowed. Under the second policy, in addition to compulsory rehandling, preventive rehandling is allowed. For each policy, we propose a branch-price-and-cut algorithm with an ad hoc dominance criterion for the labeling algorithm used to generate routes. Computational results are reported on benchmark instances for the pickup and delivery problem with time windows. (C) 2016 Elsevier Ltd. All rights reserved

Column generation with dynamic duty selection for railway crew rescheduling

The Dutch railway network experiences about three large disruptions per day on average. In this paper, we present an algorithm to reschedule the crews when such a disruption occurs. The algorithm is based on column generation techniques combined with Lagrangian heuristics. Since the number of duties is very large in practical instances, we first define a core problem of tractable size. If some tasks remain uncovered in the solution of the core problem, we perform a neighborhood exploration to improve the solution. Computational experiments with real-life instances show that our method is capable of producing good solutions within a couple of minutes of Computation time

Explainable prediction of Qcodes for NOTAMs using column generation

A NOtice To AirMen (NOTAM) contains important flight route related information. To search and filter them, NOTAMs are grouped into categories called QCodes. In this paper, we develop a tool to predict, with some explanations, a Qcode for a NOTAM. We present a way to extend the interpretable binary classification using column generation proposed in Dash, Gunluk, and Wei (2018) to a multiclass text classification method. We describe the techniques used to tackle the issues related to one vs-rest classification, such as multiple outputs and class imbalances. Furthermore, we introduce some heuristics, including the use of a CP-SAT solver for the subproblems, to reduce the training time. Finally, we show that our approach compares favorably with state-of-the-art machine learning algorithms like Linear SVM and small neural networks while adding the needed interpretability component

Comparison of heuristic approaches for the multiple depot vehicle scheduling problem

Given a set of timetabled tasks, the multi-depot vehicle scheduling problem is a well-known problem that consists of determining least-cost schedules for vehicles assigned to several depots such that each task is accomplished exactly once by a vehicle. In this paper, we propose to compare the performance of five different heuristic approaches for this problem, namely, a heuristic \\mip solver, a Lagrangian heuristic, a column generation heuristic, a large neighborhood search heuristic using column generation for neighborhood evaluation, and a tabu search heuristic. The first three methods are adaptations of existing methods, while the last two are novel approaches for this problem. Computational results on randomly generated instances show that the column generation heuristic performs the best when enough computational time is available and stability is required, while the large neighborhood search method is the best alternative when looking for a compromise between computational time and solution quality