Cut generation for an employee timetabling problem

Motivated by an industrial application, we study a specific employee timetabling problem. Several investigations are being conducted: a lower bound by Lagrangian relaxation, a heuristic based on a cut generation process and an exact method by Benders decomposition. Experimental results on real and generated instances are reported

Cut generation for an integrated employee timetabling and production scheduling problem

International audienceThis paper investigates the integration of the employee timetabling and production scheduling problems. At the first level, we manage a classical employee timetabling problem. At the second level, we aim at supplying a feasible production schedule for a set of interruptible tasks with qualification requirements and time-windows. Instead of hierarchically solving these two problems as in the current practice, we try here to integrate them and propose two exact methods to solve the resulting problem. The former is based on a Benders decomposition while the latter relies on a specific decomposition and a cut generation process. The relevance of these different approaches is discussed here through experimental results

Near Optimal and Optimal Solutions for an Integrated Employee Timetabling and Production Scheduling Problem

This paper deals with integrated employee timetabling and production scheduling problem. At the first level, we have to manage a classical employee timetabling problem. At the second level, we aim at supplying a feasible production schedule for a set of interruptible tasks with qualification requirements and time-windows. Instead of using a hierarchical approach, we try here to integrate the two stages and propose an exact method based on a specific decomposition and a cut generation process to solve the resulting problem. This exact two-stage procedure has the double advantage to converge to optimal solutions but also to find quickly near optimal solutions. The relevance of this approach is discussed here through experimental results

Solving an integrated Job-Shop problem with human resource constraints

This paper investigates the integration of the employee timetabling and production scheduling problems. At the first level, we have to manage a classical employee timetabling problem. At the second level, we aim at supplying a feasible production schedule for a job-shop scheduling problem (NP-hard problem). Instead of using a hierarchical approach as in the current practice, we here integrate the two decision stages and propose two exact methods for solving the resulting problem. The former is similar to the cut generation algorithm proposed in Guyon et. al. 2010) for a problem integrating a classical employee timetabling problem and a polynomially solvable production scheduling problem. The latter is based on a Branch-And-Cut process that exploits the same feasibility cuts than the first approach. Preliminar experimental results on instances proposed in (Artigues et al. 2009) reveal a real interest for the approaches described here

Solving an integrated job-shop problem with human resource constraints

International audienceWe propose two exact methods to solve an integrated employee-timetable and job-shop-scheduling problem. The problem is to find a minimum cost employee-timetable, where employees have different competences and work during shifts, so that the production, that corresponds to a job-shop with resource availability constraints, can be achieved. We introduce two new exact procedures: (1) a decomposition and cut generation approach and (2) a hybridization of a cut generation process with a branch and bound strategy. We also propose initial cuts that strongly improve these methods as well as a standard MIP approach. The computational performances of those methods on benchmark instances are compared to that of other methods from the literature

The Maraca: a tool for minimizing resource conflicts in a non-periodic railway timetable

While mathematical optimization and operations research receive growing attention in the railway sector, computerized timetabling tools that actually make significant use of optimization remain relatively rare. SICS has developed a prototype tool for non-periodic timetabling that minimizes resource conflicts, enabling the user to focus on the strategic decisions. The prototype is called the Maraca and has been used and evaluated during the railway timetabling construction phase at the Swedish Transport Administration between April and September 2010

Solving Challenging Real-World Scheduling Problems

This work contains a series of studies on the optimization of three real-world scheduling problems, school timetabling, sports scheduling and staff scheduling. These challenging problems are solved to customer satisfaction using the proposed PEAST algorithm. The customer satisfaction refers to the fact that implementations of the algorithm are in industry use. The PEAST algorithm is a product of long-term research and development. The first version of it was introduced in 1998. This thesis is a result of a five-year development of the algorithm. One of the most valuable characteristics of the algorithm has proven to be the ability to solve a wide range of scheduling problems. It is likely that it can be tuned to tackle also a range of other combinatorial problems. The algorithm uses features from numerous different metaheuristics which is the main reason for its success. In addition, the implementation of the algorithm is fast enough for real-world use.Siirretty Doriast

Operations research in passenger railway transportation

In this paper, we give an overview of state-of-the-art OperationsResearch models and techniques used in passenger railwaytransportation. For each planning phase (strategic, tactical andoperational), we describe the planning problems arising there anddiscuss some models and algorithms to solve them. We do not onlyconsider classical, well-known topics such as timetabling, rollingstock scheduling and crew scheduling, but we also discuss somerecently developed topics as shunting and reliability oftimetables.Finally, we focus on several practical aspects for each of theseproblems at the largest Dutch railway operator, NS Reizigers.passenger railway transportation;operation research;planning problems

Allocation of Classroom Space Using Linear Programming (A Case Study: Premier Nurses Training College, Kumasi)

The use of linear programming to solve the problem of over-allocation and under-allocation of the scarce classroom space was considered with particular reference to the Premier Nurse’s Training College, Kumasi. Data was collected from the College on the classroom facilities and the number of students per programme. A linear programming model was formulated based on the data collected to maximize the usage of the limited classroom space. POM-QM for Windows 4 (Software for Quantitative Methods, Production and Operation Management by Howard J. Weiss) was used based on the simplex algorithm to obtain optimal solution.Analysis of the results showed that six (50%) of the twelve classrooms could be used to create a maximum classroom space of six hundred and forty.  It was also observed that the management could use two hundred and eighty (280) surplus spaces to increase its student’s intake from three hundred and sixty (360) to six hundred and forty (640) students, an increase of about 77.78% with only 50% of the total number of classrooms. Again management could cut down the number of classrooms used from twelve to six and reduce the cost of maintaining the classrooms by 50% and still have as many as six extra classrooms for other equally important purposes, hence maximize its profit margin. Keywords: Linear programming, Allocation, Optimal solution, Simplex Algorithm, Premier Nurse’s Training College.