Makespan Value Research Articles

A genetic algorithm for minimizing makespan of block erection in shipbuilding

Purpose – The purpose of this paper is to propose an algorithm based on genetic algorithm (GA) to solve the block erection scheduling problem in shipbuilding.Design/methodology/approach – The block erection scheduling problem is defined as the identical parallel machine‐scheduling problem with precedence constraints and machine eligibility (PCME) restrictions. A GA is proposed to find near optimal solution, and a few lower bounds and the percentage of the reduced makespan are defined to evaluate the performance of the proposed algorithm. Finally, the GA for block erection scheduling problem in a shipyard is illustrated by using the real data from a local shipyard.Findings – The proposed GA produces lesser values of makespan against the random heuristic algorithm for the collected real instances.Research limitations/implications – The proposed GA can solve other similar parallel machine‐scheduling problems with PCME to minimize makespan.Practical implications – Based on the proposed GA, the developed sched...

Scheduling of AGVs and machines in FMS with makespan criteria using sheep flock heredity algorithm

This paper addresses the problem of simultaneous scheduling of machines and two identical automated guided vehicles (AGVs) in a flexible manufacturing system (FMS) so as to minimize makespan and mean tardiness. For solving this problem, a sheep flock heredity algorithm is proposed. An increase in the performance of the FMS under consideration would be expected as a result of making the scheduling of AGVs an integral part of the overall scheduling activity. For this particular problem, coding has been developed, which gives optimum sequence with makespan value and AGV’S schedule for ten job sets and four layouts. Most of the time, results of sheep flock algorithm are better than other algorithm and traditional methods. Key words: Scheduling, AGVs, FMS.

A novel parallel quantum genetic algorithm for stochastic job shop scheduling

In this paper, a Novel Parallel Quantum Genetic Algorithm (NPQGA) is proposed for the stochastic Job Shop Scheduling Problem with the objective of minimizing the expected value of makespan, where the processing times are subjected to independent normal distributions. Based on the parallel evolutionary idea and some concepts of quantum theory, we simulate a model of parallel quantum computation. In this frame, there are some demes (sub-populations) and some universes (groups of populations), which are structured in super star-shaped topologies. A new migration scheme based on penetration theory is developed to control migration rate and direction adaptively between demes, and a novel quantum crossover strategy is devised among universes. The quantum evolution is executed in every deme by applying some improvement operators (the coding mechanism aiming at job shop, the new quantum rotation angle and the catastrophe operator). Experiment results show NPQGA's effectiveness and applicability.

Heuristic procedures and mathematical models for cell loading and scheduling in a shoe manufacturing company

This paper focuses on cell loading and scheduling issues in a shoe manufacturing company. It involves a three-phase solution methodology where first number of cells is determined, then cells are loaded and finally detailed scheduling is performed. Three different family definitions are used (subfamilies, families and superfamilies) during the cell loading process. Three cell loading heuristic procedures (H1, H2, and H3), a simple cell scheduling heuristic and two-level mathematical models are proposed and then compared with respect to makespan. An important observation is that better post-loading schedules did not lead to better post-scheduling results. As a result, the best schedule can only be known after both cell loading and cell scheduling functions are performed. The results showed that H1 led to the best post-scheduling makespan values and they were on the average within 3% of the optimal solution. The execution time for H1 was less than four seconds for the problems tested in the experimentation and this can be considered negligible for a manufacturing setting.

An Application Of Effective Genetic Algorithms For Solving Hybrid Flow Shop Scheduling Problems

This paper addresses the Hybrid Flow Shop (HFS) scheduling problems to minimize the makespan value. In recent years, much attention is given to heuristic and search techniques. Genetic algorithms (GAs) are also known as efficient heuristic and search techniques. This paper proposes an efficient genetic algorithm for hybrid flow shop scheduling problems. The proposed algorithm is tested by Carlier and Neron's (2000) benchmark problem from the literature. The computational results indicate that the proposed efficient genetic algorithm approach is effective in terms of reduced total completion time or makespan (Cmax) for HFS problems.

Allocation of work to the stations of an assembly line with buffers between stations and three general learning patterns

This paper addresses the problem of allocating work to the stations of an assembly line for minimising the makespan required to process a lot of products with a low overall demand. This environment is characterised by different learning slopes in the various stations (due to the nature of work). We assume small (e.g. a laser pen) to medium size products (e.g. a pilot helmet) so buffer space, for temporary purposes, is typically not a problem. Three general patterns of stations' learning are considered, namely, decreasing, increasing and constant. Methodologies are presented for the optimal allocation of work to the stations for each of these cases. Some numerical results are also presented to show a significant impact of buffer capacity on makespan reduction as well as to reveal significant improvement in the makespan value due to unequal (but optimal) work allocation.

AN EXPERIMENTAL STUDY ON GENETIC ALGORITHMS FOR RESOURCE ALLOCATION ON GRID SYSTEMS

Computational Grid (CG) is an emerging paradigm in which geographically distributed resources are logically unified as a computational unit. A challenging problem in such systems is the allocation of jobs to resources that minimizes both makespan and flowtime parameters. In this paper, we present an experimental study on Genetic Algorithms (GAs) for scheduling independents jobs to Grid resources based on two replacement strategies: Steady-State GA (SSGA) and Struggle GA (SGA). SSGA distinguishes for its accentuated convergence of the population that rapidly reaches good solutions though it is soon stagnated. The SGA is based on struggle replacement and adaptively maintains diverse population, reducing thus convergence rapidity. The experimental results, based on a benchmark simulation model, showed that SGA outperforms SSGA for moderate size instances. On the other hand, the time needed by the SGA to reach makespan values obtained by the SSGA rapidly increases as more jobs and machines are added to the Grid. Thus, for larger size instances, SGA is not able to improve the results of the SSGA. Finally, we also report and analyze flowtime values for the considered benchmark.

Investigation of Ant System parameter interactions by using design of experiments for job-shop scheduling problems

In recent years, one of the most important and promising research fields has been metaheuristics to find optimal or near-optimal solutions for NP-hard combinatorial optimization problems. Improving the quality of the solution or the solution time is basic research area on metaheuristics. Modifications of the existing ones or creation of hybrid approaches are the focus of these efforts. Another area of improving the solution quality of metaheuristics is finding the optimal combination of algorithm control parameters. This is usually done by design of experiments or one-at-a-time approach in genetic algorithms, simulated annealing and similar metaheuristics. We observe that, in studies which use Ant Colonies Optimization (ACO) as an optimization technique; the levels of control parameters are determined by some non-systematic initial experiments and the interactions of the parameters are not studied yet. In this study, the parameters of Ant System have been investigated on different sized and randomly generated job-shop scheduling problems by using design of experiments. The effects and interactions of the parameters have been interpreted with the outputs of the experiments. Referring to the statistical analysis it is observed that none of the interactions between the Ant System parameters has a significant effect on makespan value. A specific fractional experimental design is suggested instead of the full factorial design. Depending on the findings from the benchmark problems it will be a reliable approach to use the suggested design for saving time and effort in experiments without sacrificing the solution quality.

Optimal allocation of work in assembly lines for lots with homogenous learning

This paper deals with the problem of allocating work to the stations of an assembly line to minimize the makespan of a lot of products with a low overall demand. There is no buffer permitted in between the stations, and the line operates under homogeneous learning (i.e., under the same learning rate for all stations). We show that in the presence of learning, the optimal makespan requires imbalanced allocation of work to stations. The level of savings in the optimal makespan value due to the imbalanced loading of work over the balanced loading case are demonstrated as a function of the value of the learning constant, number of stations on the line as well as lot size. These savings can be quite significant under the case of low overall demand.

Solving job shop scheduling problems using artificial immune system

The n-job, m-machine job shop scheduling (JSS) problem is one of the general production scheduling problems. Many existing heuristics give solutions for small size problems with near optimal solutions. This paper deals with the criterion of makespan minimization for the job shop scheduling of different size problems. The proposed computational method of artificial immune system algorithm (AIS) is used for finding optimal makespan values of different size problems. The artificial immune system algorithm is tested with 130 benchmark problems [10 (ORB1-ORB5 & ARZ5-ARZ9), 40 (LA01-LA40) and 80 (TA01-TA80)]. The results show that the AIS algorithm is an efficient and effective algorithm which gives better results than the Tabu search shifting bottleneck procedure (TSSB) as well as the best solution of shifting bottleneck procedure ( SB-GLS1 ) of Balas and Vazacopoulos.

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.

Maximization of solution flexibility for robust shop scheduling

We consider the problem of introducing flexibility in the schedule determination phase, for shop scheduling problems with release dates and deadlines. The flexibility is provided by generating a family of schedules, instead of a unique one. We represent a family of schedules by an ordered group assignment defining for each machine a sequence of groups where the operations within a group are totally permutable. We propose a polynomial time algorithm to evaluate the worst case completion time of operations in an ordered group assignment. We then consider the single machine problem with heads and deadlines associated to operations, as a sub-problem of the job shop problem. We propose polynomial time dynamic programming algorithms for minimizing the number of groups and for maximizing the number of characterized sequences, under specific constraints. Finally, computational experiences on job shop benchmarks, show the impact of grouping operations on the solution makespan value.

Scheduling Malleable Tasks on Parallel Processors to Minimize the Makespan

The problem of optimal scheduling n tasks in a parallel processor system is studied. The tasks are malleable, i.e., a task may be executed by several processors simultaneously and the processing speed of a task is a nonlinear function of the number of processors allocated to it. The total number of processors is m and it is an upper bound on the number of processors that can be used by all the tasks simultaneously. It is assumed that the number of processors is sufficient to process all the tasks simultaneously, i.e. n≤m. The objective is to find a task schedule and a processor allocation such that the overall task completion time, i.e. the makespan, is minimized. The problem is motivated by real-life applications of parallel computer systems in scientific computing of highly parallelizable tasks. An O(n) algorithm is presented to solve this problem when all the processing speed functions are convex. If these functions are all concave and the number of tasks is a constant, the problem can be solved in polynomial time. A relaxed problem, in which the number of processors allocated to each task is not required to be integer, can be solved in O(nmax {m,nlog 2 m}) time. It is proved that the minimum makespan values for the original and relaxed problems coincide. For n=2 or n=3, an optimal solution for the relaxed problem can be converted into an optimal solution for the original problem in a constant time.

A bi-criteria optimization: minimizing the integral value and spread of the fuzzy makespan of job shop scheduling problems

The processing times in reality are often uncertain and this uncertainty is critical for the scheduling procedures. This article presents bi-criteria genetic algorithm approach to solve fuzzy job shop scheduling problems (JSSPs), in which the integral value and the uncertainty of the fuzzy makespan (FM), which are conflicting objectives, are minimized. In this approach, imprecise processing times are modeled as triangular fuzzy numbers (TFNs), which results in a makespan that is a triangular fuzzy number. Therefore, it is practically important to pay attention to the uncertainty of the FM. Fuzzified benchmark problems; FT 6×6, La12, La13, and La14 were used to show the effectiveness of the proposed approach compared with optimizing fuzzy JSSPs with respect to either the FM or the uncertainty separately. A sensitivity analysis is also presented that shows the effect of the vagueness (uncertainty) of the processing times on the uncertainty of the FM.

Three stage no-idle flow-shops

The three stage no-idle flow-shop configuration, where machines work continuously without idle intervals, is an interesting manufacturing environment in many industries. Few researches have investigated this type of systems. The idle characteristic is a very strong constraint and it affects seriously the value of makespan (C max) criterion. We treat here the scheduling problem of three stage permutation flow-shop configuration with no-idle machines in order to minimise the makespan F3/no-idle/C max. An easily implementing heuristic is proposed to solve this problem with O(n log n) complexity. It finds optimal solutions for several cases. A computational study shows the result quality.

Scheduling a flowline manufacturing cell with sequence dependent family setup times

This paper considers the problem of scheduling part families and jobs within each part family in a flowline manufacturing cell where the setup times for each family are sequence dependent and it is desired to minimize the makespan while processing parts (jobs) in each family together. Lower bounds on the optimal makespan value and efficient heuristic algorithms for finding permutation schedules are proposed and empirically evaluated as to their effectiveness in finding optimal permutation schedules.

Minimizing makespan subject to minimum total flow-time on identical parallel machines

This paper considers the identical parallel-machine scheduling problem of minimizing makespan subject to minimum total flow-time. In view of the NP-hard nature of the problem, lower bounds on the optimal makespan value and efficient heuristic algorithms for finding optimal schedules are described and empirically evaluated as to their effectiveness in finding optimal schedules.

An improved part grouping model for minimizing makespan in FMS

In some flexible manufacturing systems (FMSs), limited tool magazine capacity requires grouping of parts into subsets for production. Although several studies have addressed the part grouping issue, research comparing the performance of models is scanty. Moreover, there is no congruency in the objectives of the present part grouping models and subsequent loading models. Traditionally, part grouping is addressed before machine loading. In this study, we overcome the drawbacks by proposing two models: model LM, which does not require part grouping, and model PGLRM (part grouping, loading and routing model), which requires part grouping. The performance of model LM serves as a benchmark. These two models also address machine loading and part routing issues concurrently. Model PGLRM's performance is then compared with the performance of model LM and few other existing part grouping models in terms of makespan and routing flexibility. Our analysis shows that model PGLRM not only results in a lower value of makespan but also imparts higher routing flexibility as compared to existing part grouping models.

Analysis of antithetic sequences in flowshop scheduling to minimize makespan

The antithetic properties of flowshop sequences are investigated to improve the classical Monte Carlo method for solving the n -job, m -machine problem with minimization of makespan. The major issues considered are (1) establishing a negative correlation of the makespan values of forward and reverse sequences; (2) developing the Antithetical Monte Carlo (AMC) method, which can be used to quickly estimate the mean of the makespan distribution by exploiting the antithetic property of sequences; (3) using AMC to find low makespan values; (4) determining a threshold value of makespan beyond which it would be likely to find an optimal or near optimal makespan when reversing a sequence. Statistical tests indicate that the performance of AMC is superior to that of the classical Monte Carlo method. Possible applications of this concept are discussed including extensions to other mathematical problems with antithetic properties.

A Hybrid Bounding Procedure for the Workload Allocation Problem on Parallel Unrelated Machines with Setups

A nonpreemptive single stage manufacturing process with parallel, unrelated machines and multiple job types with setups (PUMS) is considered. We propose a hybrid approximation procedure where a Lagrangean relaxation dual and a Lagrangean decomposition dual are solved one after the other to generate a good lower bound on the optimal makespan value. Computational results are reported.