Sequencing CONWIP flow-shops: Analysis and heuristics

In this paper, we address the backlog sequencing problem in a flow-shop controlled by a CON\VIP production control system with the objective to minimise the make span We characterise the problem and analyse its similarities and differences with the permutation flow-shop problem A comparison of same well-known flow-shop heuristics is carried out and a simple and fast dispatching rule is proposed. Regarding the more simple and faster heuristics, the proposed dispatching rule outperforms those commonly used for the permutation flow-shop problem. --Scheduling,Sequencing,Flow-Shop,Constant Work in Process (CONWIP),Heuristics,Dispatching Rules

Proportionate Flow Shop Games

In a proportionate flow shop problem several jobs have to be processed through a fixed sequence of machines and the processing time of each job is equal on all machines.By identifying jobs with agents, whose costs linearly depend on the completion time of their jobs, and assuming an initial processing order on the jobs, we face an additional problem: how to allocate the cost savings obtained by ordering the jobs optimally?In this paper, PFS games are defined as cooperative games associated to proportionate flow shop problems.It is seen that PFS games have a nonempty core.Moreover, it is shown that PFS games are convex if the jobs are initially ordered in decreasing urgency.For this case an explicit expression for the Shapley value and a specific type of equal gain splitting rule which leads to core elements of the PFS game are proposed.Proportionate flow shop problems;core;convexity

Applying Machine Based Decomposition in 2-Machine Flow Shops

The Shifting Bottleneck (SB) heuristic is among the most successful approximation methods for solving the Job Shop problem. It is essentially a machine based decomposition procedure where a series of One Machine Sequencing Problems (OMSPs) are solved. However, such a procedure has been reported to be highly ineffective for the Flow Shop problems (Jain and Meeran 2002). In particular, we show that for the 2-machine Flow Shop problem, the SB heurisitc will deliver the optimal solution in only a small number of instances. We examine the reason behind the failure of the machine based decomposition method for the Flow Shop. An optimal machine based decomposition procedure is formulated for the 2-machine Flow Shop, the time complexity of which is worse than that of the celebrated Johnsons Rule. The contribution of the present study lies in showing that the same machine based decomposition procedures which are so successful in solving complex Job Shops can also be suitably modified to optimally solve the simpler Flow Shops.

Efficient heuristics for the parallel blocking flow shop scheduling problem

We consider the NP-hard problem of scheduling n jobs in F identical parallel flow shops, each consisting of a series of m machines, and doing so with a blocking constraint. The applied criterion is to minimize the makespan, i.e., the maximum completion time of all the jobs in F flow shops (lines). The Parallel Flow Shop Scheduling Problem (PFSP) is conceptually similar to another problem known in the literature as the Distributed Permutation Flow Shop Scheduling Problem (DPFSP), which allows modeling the scheduling process in companies with more than one factory, each factory with a flow shop configuration. Therefore, the proposed methods can solve the scheduling problem under the blocking constraint in both situations, which, to the best of our knowledge, has not been studied previously. In this paper, we propose a mathematical model along with some constructive and improvement heuristics to solve the parallel blocking flow shop problem (PBFSP) and thus minimize the maximum completion time among lines. The proposed constructive procedures use two approaches that are totally different from those proposed in the literature. These methods are used as initial solution procedures of an iterated local search (ILS) and an iterated greedy algorithm (IGA), both of which are combined with a variable neighborhood search (VNS). The proposed constructive procedure and the improved methods take into account the characteristics of the problem. The computational evaluation demonstrates that both of them –especially the IGA– perform considerably better than those algorithms adapted from the DPFSP literature.Peer ReviewedPostprint (author's final draft

Flowshop Scheduling Using a Network Approach

In this paper, a network based formulation of a permutation flow shop problem is presented. Two nuances of flow shop problems with different levels of complexity are solved using different approaches to the linear programming formulation. Key flow shop parameters inclosing makespan of the flow shop problems were obtained without recourse to the traditional approach of using Gantt charts. The linear programming models of the flow shop problems considered were solved using LINGO 7.0. The present technique has been shown to be very effective and efficient.http://dx.doi.org/10.4314/njt.v34i2.1

Constructing a fuzzy flow-shop sequencing model based on statistical data

AbstractThis study investigated an approach for incorporating statistics with fuzzy sets in the flow-shop sequencing problem. This work is based on the assumption that the precise value for the processing time of each job is unknown, but that some sample data are available. A combination of statistics and fuzzy sets provides a powerful tool for modeling and solving this problem. Our work intends to extend the crisp flow-shop sequencing problem into a generalized fuzzy model that would be useful in practical situations. In this study, we constructed a fuzzy flow-shop sequencing model based on statistical data, which uses level (1−α,1−β) interval-valued fuzzy numbers to represent the unknown job processing time. Our study shows that this fuzzy flow-shop model is an extension of the crisp flow-shop problem and the results obtained from the fuzzy flow-shop model provides the same job sequence as that of the crisp problem

A genetic algorithm for the mixed flow shop problem

In this thesis we present a new interesting version of the mixed flow shop se-quencing problem, which at the same time is a version of the classic flow shop,a very common topic on operations research.We propose a genetic algorithm to solve it that we will compare at the endwith a simple initial genetic-based algorithm previously design. For that wefirst focus on the crossover operator as we consider it the most challenging parton a sequencing problem. We study and compare 5 different crossover operatorsand we choose the one that performs better. Finally we calibrate the populationsize, the weight of mutation and crossover operators on the algorithm and alsothe mutations operator itself.The goal of the thesis is to better understand the specific mixed flow shopproblem version presented and design a genetic algorithm that clearly improvesthe performance of the initial algorith