Heuristics for short route job shop scheduling problems

Abstract not available

Investigating a Hybrid Metaheuristic For Job Shop Rescheduling

Previous research has shown that artificial immune systems can be used to produce robust schedules in a manufacturing environment. The main goal is to develop building blocks (antibodies) of partial schedules that can be used to construct backup solutions (antigens) when disturbances occur during production. The building blocks are created based upon underpinning ideas from artificial immune systems and evolved using a genetic algorithm (Phase I). Each partial schedule (antibody) is assigned a fitness value and the best partial schedules are selected to be converted into complete schedules (antigens). We further investigate whether simulated annealing and the great deluge algorithm can improve the results when hybridised with our artificial immune system (Phase II). We use ten fixed solutions as our target and measure how well we cover these specific scenarios.

Scheduling techniques to optimise sugarcane rail transport systems

In Australia, railway systems play a vital role in transporting the sugarcane crop from farms to mills. In this paper, a novel job shop approach is proposed to create a more efficient integrated harvesting and sugarcane transport scheduling system to reduce the cost of sugarcane transport. There are several benefits that can be attained by treating the train scheduling problem as a job shop problem. Job shop is generic and suitable for all trains scheduling problems. Job shop technique prevents operating two trains on one section at the same time because it considers that the section or the machine is unique. This technique is more promising to find better solutions in reasonable computation times.

Metaheuristics for minimizing the makespan of the dynamic shop scheduling problem

For the shop scheduling problems such as flow-shop, job-shop, open-shop, mixed-shop, and group-shop, most research focuses on optimizing the makespan under static conditions and does not take into consideration dynamic disturbances such as machine breakdown and new job arrivals. We regard the shop scheduling problem under static conditions as the static shop scheduling problem, while the shop scheduling problem with dynamic disturbances as the dynamic shop scheduling problem. In this paper, we analyze the characteristics of the dynamic shop scheduling problem when machine breakdown and new job arrivals occur, and present a framework to model the dynamic shop scheduling problem as a static group-shop-type scheduling problem. Using the proposed framework, we apply a metaheuristic proposed for solving the static shop scheduling problem to a number of dynamic shop scheduling benchmark problems. The results show that the metaheuristic methodology which has been successfully applied to the static shop scheduling problems can also be applied to solve the dynamic shop scheduling problem efficiently.

A fast tabu search algorithm for the group shop scheduling problem

Three types of shop scheduling problems, the flow shop, the job shop and the open shop scheduling problems, have been widely studied in the literature. However, very few articles address the group shop scheduling problem introduced in 1997, which is a general formulation that covers the three above mentioned shop scheduling problems and the mixed shop scheduling problem. In this paper, we apply tabu search to the group shop scheduling problem and evaluate the performance of the algorithm on a set of benchmark problems. The computational results show that our tabu search algorithm is typically more efficient and faster than the other methods proposed in the literature. Furthermore, the proposed tabu search method has found some new best solutions of the benchmark instances.

Scheduling batches with simultaneous job processing for two-machine shop problems

We consider the problem of scheduling independent jobs on two machines in an open shop, a job shop and a flow shop environment. Both machines are batching machines, which means that several operations can be combined into a batch and processed simultaneously on a machine. The batch processing time is the maximum processing time of operations in the batch, and all operations in a batch complete at the same time. Such a situation may occur, for instance, during the final testing stage of circuit board manufacturing, where burn-in operations are performed in ovens. We consider cases in which there is no restriction on the size of a batch on a machine, and in which a machine can process only a bounded number of operations in one batch. For most of the possible combinations of restrictions, we establish the complexity status of the problem.

Approximation algorithms for two-machine flow shop scheduling with batch setup times

In many practical situations, batching of similar jobs to avoid setups is performed while constructing a schedule. This paper addresses the problem of non-preemptively scheduling independent jobs in a two-machine flow shop with the objective of minimizing the makespan. Jobs are grouped into batches. A sequence independent batch setup time on each machine is required before the first job is processed, and when a machine switches from processing a job in some batch to a job of another batch. Besides its practical interest, this problem is a direct generalization of the classical two-machine flow shop problem with no grouping of jobs, which can be solved optimally by Johnson's well-known algorithm. The problem under investigation is known to be NP-hard. We propose two O(n logn) time heuristic algorithms. The first heuristic, which creates a schedule with minimum total setup time by forcing all jobs in the same batch to be sequenced in adjacent positions, has a worst-case performance ratio of 3/2. By allowing each batch to be split into at most two sub-batches, a second heuristic is developed which has an improved worst-case performance ratio of 4/3. © 1998 The Mathematical Programming Society, Inc. Published by Elsevier Science B.V.

Minimizing total weighted completion time in a proportionate flow shop

We study the special case of the m machine flow shop problem in which the processing time of each operation of job j is equal to pj; this variant of the flow shop problem is known as the proportionate flow shop problem. We show that for any number of machines and for any regular performance criterion we can restrict our search for an optimal schedule to permutation schedules. Moreover, we show that the problem of minimizing total weighted completion time is solvable in O(n2) time. © 1998 John Wiley & Sons, Ltd.

Shop-scheduling problems with fixed and non-fixed machine orders of the jobs

The paper deals with the determination of an optimal schedule for the so-called mixed shop problem when the makespan has to be minimized. In such a problem, some jobs have fixed machine orders (as in the job-shop), while the operations of the other jobs may be processed in arbitrary order (as in the open-shop). We prove binary NP-hardness of the preemptive problem with three machines and three jobs (two jobs have fixed machine orders and one may have an arbitrary machine order). We answer all other remaining open questions on the complexity status of mixed-shop problems with the makespan criterion by presenting different polynomial and pseudopolynomial algorithms.

Scheduling batches with sequential job processing for two-machine flow and open shops

In this paper, we study a problem of scheduling and batching on two machines in a flow-shop and open-shop environment. Each machine processes operations in batches, and the processing time of a batch is the sum of the processing times of the operations in that batch. A setup time, which depends only on the machine, is required before a batch is processed on a machine, and all jobs in a batch remain at the machine until the entire batch is processed. The aim is to make batching and sequencing decisions, which specify a partition of the jobs into batches on each machine, and a processing order of the batches on each machine, respectively, so that the makespan is minimized. The flow-shop problem is shown to be strongly NP-hard. We demonstrate that there is an optimal solution with the same batches on the two machines; we refer to these as consistent batches. A heuristic is developed that selects the best schedule among several with one, two, or three consistent batches, and is shown to have a worst-case performance ratio of 4/3. For the open-shop, we show that the problem is NP-hard in the ordinary sense. By proving the existence of an optimal solution with one, two or three consistent batches, a close relationship is established with the problem of scheduling two or three identical parallel machines to minimize the makespan. This allows a pseudo-polynomial algorithm to be derived, and various heuristic methods to be suggested.

Three-machine shop scheduling with partially ordered processing routes

This paper considers the problem of sequencing n jobs in a three-machine shop with the objective of minimising the maximum completion time. The shop consists of three machines, M1,M2 and M_{3}. A job is first processed on M1 and then is assigned either the route (M2,M_{3}) or the route (M_{3},M2). Thus, for our model the processing route is given by a partial order of machines, as opposed to the linear order of machines for a job shop, or to an arbitrary sequence of machines for an open shop. The main result is on O(nlog n) time heuristic, which generates a schedule with the makespan that is at most 5/3 times the optimum value.

Two-machine shop scheduling: Compromise between flexibility and makespan value

In this paper, we consider the problem of providing flexibility to solutions of two-machine shop scheduling problems. We use the concept of group-scheduling to characterize a whole set of schedules so as to provide more choice to the decision-maker at any decision point. A group-schedule is a sequence of groups of permutable operations defined on each machine where each group is such that any permutation of the operations inside the group leads to a feasible schedule. Flexibility of a solution and its makespan are often conflicting, thus we search for a compromise between a low number of groups and a small value of makespan. We resolve the complexity status of the relevant problems for the two-machine flow shop, job shop and open shop. A number of approximation algorithms are developed and their worst-case performance is analyzed. For the flow shop, an effective heuristic algorithm is proposed and the results of computational experiments are reported.

An improved approximation algorithm for the two-machine flow shop scheduling problem with an interstage transporter

We study the two-machine flow shop problem with an uncapacitated interstage transporter. The jobs have to be split into batches, and upon completion on the first machine, each batch has to be shipped to the second machine by a transporter. The best known heuristic for the problem is a –approximation algorithm that outputs a two-shipment schedule. We design a –approximation algorithm that finds schedules with at most three shipments, and this ratio cannot be improved, unless schedules with more shipments are created. This improvement is achieved due to a thorough analysis of schedules with two and three shipments by means of linear programming. We formulate problems of finding an optimal schedule with two or three shipments as integer linear programs and develop strongly polynomial algorithms that find solutions to their continuous relaxations with a small number of fractional variables

The order selection and lot sizing problem in the make-to-order environment

This research is motivated by the need for considering lot sizing while accepting customer orders in a make-to-order (MTO) environment, in which each customer order must be delivered by its due date. Job shop is the typical operation model used in an MTO operation, where the production planner must make three concurrent decisions; they are order selection, lot size, and job schedule. These decisions are usually treated separately in the literature and are mostly led to heuristic solutions. The first phase of the study is focused on a formal definition of the problem. Mathematical programming techniques are applied to modeling this problem in terms of its objective, decision variables, and constraints. A commercial solver, CPLEX is applied to solve the resulting mixed-integer linear programming model with small instances to validate the mathematical formulation. The computational result shows it is not practical for solving problems of industrial size, using a commercial solver. The second phase of this study is focused on development of an effective solution approach to this problem of large scale. The proposed solution approach is an iterative process involving three sequential decision steps of order selection, lot sizing, and lot scheduling. A range of simple sequencing rules are identified for each of the three subproblems. Using computer simulation as the tool, an experiment is designed to evaluate their performance against a set of system parameters. For order selection, the proposed weighted most profit rule performs the best. The shifting bottleneck and the earliest operation finish time both are the best scheduling rules. For lot sizing, the proposed minimum cost increase heuristic, based on the Dixon-Silver method performs the best, when the demand-to-capacity ratio at the bottleneck machine is high. The proposed minimum cost heuristic, based on the Wagner-Whitin algorithm is the best lot-sizing heuristic for shops of a low demand-to-capacity ratio. The proposed heuristic is applied to an industrial case to further evaluate its performance. The result shows it can improve an average of total profit by 16.62%. This research contributes to the production planning research community with a complete mathematical definition of the problem and an effective solution approach to solving the problem of industry scale.

Minimizing makespan for hybrid flowshops with batch, discrete processing machines and arbitrary job sizes

This research aims at a study of the hybrid flow shop problem which has parallel batch-processing machines in one stage and discrete-processing machines in other stages to process jobs of arbitrary sizes. The objective is to minimize the makespan for a set of jobs. The problem is denoted as: FF: batch1,sj:Cmax. The problem is formulated as a mixed-integer linear program. The commercial solver, AMPL/CPLEX, is used to solve problem instances to their optimality. Experimental results show that AMPL/CPLEX requires considerable time to find the optimal solution for even a small size problem, i.e., a 6-job instance requires 2 hours in average. A bottleneck-first-decomposition heuristic (BFD) is proposed in this study to overcome the computational (time) problem encountered while using the commercial solver. The proposed BFD heuristic is inspired by the shifting bottleneck heuristic. It decomposes the entire problem into three sub-problems, and schedules the sub-problems one by one. The proposed BFD heuristic consists of four major steps: formulating sub-problems, prioritizing sub-problems, solving sub-problems and re-scheduling. For solving the sub-problems, two heuristic algorithms are proposed; one for scheduling a hybrid flow shop with discrete processing machines, and the other for scheduling parallel batching machines (single stage). Both consider job arrival and delivery times. An experiment design is conducted to evaluate the effectiveness of the proposed BFD, which is further evaluated against a set of common heuristics including a randomized greedy heuristic and five dispatching rules. The results show that the proposed BFD heuristic outperforms all these algorithms. To evaluate the quality of the heuristic solution, a procedure is developed to calculate a lower bound of makespan for the problem under study. The lower bound obtained is tighter than other bounds developed for related problems in literature. A meta-search approach based on the Genetic Algorithm concept is developed to evaluate the significance of further improving the solution obtained from the proposed BFD heuristic. The experiment indicates that it reduces the makespan by 1.93 % in average within a negligible time when problem size is less than 50 jobs.