The scheduling literature reveals that majority of the studied problems are for deterministic case where all parameters jobs known in advance and fixed. However, some real-world environments, assumption fixed is not valid since job uncertain. An uncertain parameter can be modelled as a random variable within interval with lower upper bounds, called bounded. objective this paper to review invest...

We introduce a heuristic method for finding good, feasible solutions for multiproduct lot sizing problems with general assembly structures, multiple constrained resources, and nonzero setup costs and setup times. We evaluate the performance of this heuristic by comparing its solutions to optimal solutions of small randomly generated problems and to time-truncated Optimization Subroutine Library...

The two-machine permutation flowshop scheduling problem to minimize makespan or total completion time criterion is addressed where setup times are considered to be separate from processing times. Setup times are relaxed to be random variables as opposed to the common assumption in the literature that setup times are exactly known (deterministic) in advance. The probability distributions of setu...

In this paper, the flow-shop scheduling problem with unrelated parallel machines at each stage as well as sequence-dependent setup times under minimization of the sum of earliness and tardiness are studied. The processing times, setup times and due-dates are known in advance. To solve the problem, we introduce a hybrid memetic algorithm as well as a particle swarm optimization algorithm combine...

This paper introduces a new notion related to the traveling salesperson problem (TSP) — the notion of the TSP ratio. The TSP ratio of a TSP instance I is the sum of the marginal values of the nodes of I divided by the length of the optimal TSP tour on I, where the marginal value of a node i ∈ I is the difference between the length of the optimal tour on I and the length of the optimal tour on I...

Consider the problem in which n jobs that are classified into k types are to be scheduled on m identical machines without preemption. A machine requires a proper setup taking s time units before processing jobs of a given type. The objective is to minimize the makespan of the resulting schedule. We design and analyze an approximation algorithm that runs in time polynomial in n,m and k and compu...

In this paper, we study a Capacitated Lot Sizing Problem with Stochastic Setup Times (CLSP-SST).We describe a mathematical model that considers both regular costs (including production, setup and inventory holding costs) and expected overtime costs (related to the excess usage of capacity). The CLSP-SST is formulated as a two-stage stochastic programming problem. A procedure is proposed to effe...