stochastic approach to vehicle routing problem: development and theories abstract in this article, a chance constrained (ccp) formulation of the vehicle routing problem (vrp) is proposed. the reality is that once we convert some special form of probabilistic constraint into their equivalent deterministic form then a nonlinear constraint generates. knowing that reliable computer software for lar...

We present an in-depth theoretical, algorithmic and computational study of a linear programming (LP) relaxation to the precedence constrained single machine scheduling problem 1jprecj P j wjCj to minimize a weighted sum of job completion times. On the theoretical side, we study the structure of tight parallel inequalities in the LP relaxation and show that every permutation schedule which is co...

In the last decade, the PSE community has achieved remarkable results in relation to the problem of short-term scheduling of batch processes. Numerous optimization models, able to solve different problem variants, have been reported. Currently, the great majority of the formulations adopt a continuoustime approach given its advantages over other alternative representations. This contribution pr...

This paper considers the single machine scheduling problem with precedence constraints and deteriorating jobs. A mathematical model based on binary integer programming (BIP) is developed. By these precedence constraints, jobs can not start before completion of its all predecessors. The represented model is in two steps, in step one the earliest starting time of each job is computed, then the re...

This study addresses the resource-constrained project scheduling problem with precedence relations, and aims at minimizing two criteria: the makespan and the total weighted start time of the activities. To solve the problem, five multi-objective metaheuristic algorithms are analyzed, based on Multi-objective GRASP (MOG), Multiobjective Variable Neighborhood Search (MOVNS) and Pareto Iterated Lo...

In this paper we consider a labour constrained scheduling problem (LCSP) which is a simpliication of a practical problem arising in industry. Jobs are subject to precedence constraints and have speciied processing times. Moreover, for each job the labour requirement varies as the job is processed. Given the amount of labour available in each period, the problem is to nish all the jobs as soon a...

Abstract It is the purpose of this article to introduce a linear approximation technique for solving a fractional chance constrained programming (CC) problem. For this purpose, a fuzzy goal programming model of the equivalent deterministic form of the fractional chance constrained programming is provided and then the process of defuzzification and linearization of the problem is started. A sam...

In an article entitled “Optimal sequencing of a single machine subject to precedence constraints” E.L. Lawler presented a now classical minmax result for job scheduling. In essence, Lawler’s proof demonstrated that the properties of partially ordered sets were sufficient to solve the posed scheduling problem. These properties are, in fact, common to a more general class of combinatorial structu...

We consider a single-machine scheduling problem with each job having an uncertain processing time which can take any real value within each corresponding closed interval before completing the job. The scheduling objective is to minimize the total weighted flow time of all n jobs, where there is a weight associated with each job. We establish the necessary and sufficient condition for the existe...