Abdelaziz Dammak

CLASSROOM ASSIGNMENT FOR EXAM TIMETABLING

Abstract We consider the problem of assigning a set of independent (non-conflicting) exams having a given size to a set of classrooms having certain capacities. We formulate the problem as a zero–one linear integer program for both cases where each classroom contains no more than one exam and for the case where this constraint is relaxed. For the second case, the problem is also formulated as a transportation problem. We already presented two working papers that consider the problem of assigning exams to timeslots at the Faculty of Economics and Management Sciences of Sfax using several heuristics based on graph colouring. This paper is a supplement of the earlier ones, where the solution obtained in these papers (i.e., timetables composed of non-conflicting exams) serves as an input to the problem treated here. Some elementary results are proved and a simple heuristic procedure is developed to solve the problem.

A Goal Programming model for Aggregate Production Planning problem

Aggregate Production Planning (APP) involves the simultaneous determination of companys production, inventory and employment levels over a finite time horizon to minimise the total costs while meeting the forecasted demand. Other objectives can be to minimise the fluctuation on the employment levels, the inventory levels or to reach some standard on the performance levels. The objective of this paper is to propose an effective method to elaborate an aggregate plan which takes into account the managers preferences. We propose a Goal Programming (GP) approach, with satisfaction functions. This latter has not been used in the field of APP. Applied to a real case problem, weighted GP has initially been used; the results were not satisfactory for the manager. Our GP with satisfaction function gives, very satisfactory results for the manager.

The classroom assignment problem: Complexity, size reduction and heuristics

In this paper, we investigate a compound of the exam timetabling problems which consists of assigning a set of independent exams to a certain number of classrooms. We can define the exam timetabling problem as the scheduling of exams to time slots in first stage and at a second stage, the assignment of a set of exams extracted from one time slot to some available classrooms. Even though the formulation of this problem looks simple as it contains only two sets of constraints including only binary variables, we show that it belongs to the class of NP hard problems by reduction from the Numerical Matching with Target Sum problems (NMTS). In order to reduce the size of this problem and make it efficiently solvable either by exact method or heuristic approaches, a theorem is rigorously demonstrated and a reduction procedure inspired from the dominance criterion is developed. The two methods contribute in the search for a feasible solution by reducing the size of the original problem without affecting the feasibility. Since the reduction procedures do not usually assign all exams to classrooms, we propose a Variable Neighbourhood Search (VNS) algorithm in order to obtain a good quality complete solution. The objective of VNS algorithm is to reduce the total classroom capacity assigned to exams. A numerical result concerning the exam of the main session of the first semester of the academic year 2009-2010 of the Faculty of Economics and Management Sciences of Sfax shows the good performance of our approach compared with lower bound defined as the sum of the total capacity of all assigned classrooms and the total size of the remaining exams after reduction.

The genetic algorithm with two point crossover to solve the resource-constrained project scheduling problems

In the last few decades, the resource-constrained project-scheduling problem has become the key of the success of researching project in the enterprises and has become a popular problem type in operations research. However, due to its strongly NP-hard status, the effectiveness of exact optimization procedures is restricted to relatively small instances. In this paper, we present a genetic algorithm (GA), the so called genetic algorithm with two-point crossover (GA2P), for this problem that is able to provide near-optimal heuristic solutions. A full factorial computational experiment was set up using the well-known standard instances in PSPLIB, and the results reveal that the algorithm is effective for the RCPSP.

Lecture timetabling at a Tunisian university

This paper deals with the lecture timetabling problem at an institution in a Tunisian university. The objective is to construct a feasible timetable for all the lectures taken by the students sections in the institution. For this, we give a formulation of the problem as a set of linear constraints. Then we develop a heuristic procedure that starts by assigning student sections having the biggest size to classrooms with the smallest capacity that can fit the students. This heuristic is illustrated with real data of one section at the Faculty of Economics and Management Sciences of Sfax (FEMSS) in Tunisia. In addition, it is fully implemented to solve the lecture timetabling problem for all the students sections in the same faculty.

An optimization and simulation approach for Operating room scheduling under stochastic durations

Several variants of the Operating room scheduling problem are provided in literature for different contexts. In Tunisia, especially in Habib Bourguiba Hospital in Sfax, Open scheduling policy is considered to schedule elective surgeries. In the orthopedic service, operating room scheduling is carried out weekly. Three operating rooms are available and one of them is assigned to a special kind of surgeries called septic. At the tactical level, elective operations are assigned to weeks so that the workload (average) by week is approximately equal to the weekly capacity. In the selection of surgeries the variation of surgery duration is not taken into account. The average of the operations durations are considered for planning and scheduling. This situation can lead to either an overtime which is unwelcome by surgeons and surgical team. Or an underutilization of OR resources which generate an additional cost for hospital. To deal with this problem, we propose two stochastic MILP models that take into account the stochastic aspect of the surgery duration. Once the set of operations to be carried out in a week are selected, we choose at the operational level to which day and which room the operations are assigned and in which order. As patients are asked to come to the hospital in the morning, the best scheduling is the one that minimizes the patients waiting time. In this paper, we provide two MILP to model this problem. In the first one an additive slack is given to the total duration of surgery to deal with any possible overtime. The other one try to equilibrate the total charge between room/day and the total surgery variations during the week. The two models are solved using Cplex and then a simulation model is used to evaluate the robustness of the provided solutions.

New variants of the covering location problem: Modeling and a two-stage genetic algorithm

In this paper, we are interested to develop new models with reference to classical ones existent for covering and location problems. These models aim to improve the coverage and the satisfaction of demand on Radio Network of Cellular Mobile Communication Systems and wireless sensors networks. First, we propose a new definition of a General Covering Problem that generalizes both the classical total and maximal covering problems. We propose two mathematical linear models that take into account station assignment capacity and signal degradation constraints. In order to solve this proposed problem variant, we propose in addition a two-stage Genetic Algorithm (GA) combining location decisions and heuristic-based Base Stations (BS) allocation for users. Experimental study is conducted to compare Mathematical models and GA methods showing satisfactory results.

A genetic algorithm to minimize the makespan on two dedicated processors

The studied problem is to optimize a production system where these systems have two dedicated processors. The assignment of tasks to these processors is fixed. For this problem, we have three types of tasks. Some tasks must be processed only by the first processor, a few others by the second processor and the remaining tasks need simultaneously both processors. This NP-hard problem requires the use of well-adapted methods. We have studied the design of genetic algorithms which have been very successful in solving optimization problems. This can be justified by the quality of the solution obtained by such methods and the efficiency in terms of computation time.

A genetic algorithm to minimize the total of tardiness multiprocessing tasks on two dedicated processors

In this work, we study the problem of scheduling multi-processor tasks on two dedicated processors with release date. Our objective is to minimize the sum of the tasks tardiness. This NP-hard problem in the strong sense requires the use of well-adapted methods. Thus, to solve this problem, a genetic algorithm was designed and a lower bound was constructed to evaluate the experimental results.

An enterprise system component based on graph colouring for exam timetabling

Purpose – This paper aims to consider the exam timetabling of the re‐sit session in the Faculty of Economics and Management Sciences of Sfax. The objective is to find a timetable which minimizes the number of timeslots for exams required by the enrolled students.Design/methodology/approach – Two heuristic procedures based on graph colouring are developed and tested on real data to solve the exam timetabling problem at the faculty.Findings – These heuristics were tested on a simple example which shows the out‐performance of the second heuristic compared with the first one. When tested with the real data of the faculty, exam size heuristic provides a timetable with a shorter timeframe; however, the timetable obtained from the second heuristic is of better quality.Originality/value – The main contribution of this paper is to create an automated exam timetabling that helps the faculty to manage its own enterprise system.