Solving coupled task assignment and capacity planning problems for a job shop by using a concurrent genetic algorithm

The problems of task assignment and capacity planning of manufacturing systems have been researched for many years. However, in the existing literature, these two types of problems are researched independently. Namely, when solving the task assignment problem, it is usually assumed that the production capacity of the manufacturing systems has been determined. On the other hand, when solving the capacity planning problem, the production tasks assigned to the workstations in the manufacturing system have also been determined. Actually, the task assignment problem and the capacity planning problem are coupled with each other. When we assign production tasks to workstations, production capacities of these workstations should be regulated so that they are enough for completing the tasks. At the same time, when planning the production capacity, we must know what production tasks are assigned to what workstations. This research focuses on the coupling relations between the two problems for a closed job shop, in which the total work-in-process (WIP) is assumed to be constant. The objective of the task assignment problem is to balance the workloads of the workstations and the objectives of the capacity planning problem are maximising the throughput and minimising total costs of machine purchasing and WIP inventory. We construct the fundamental system architecture for controlling the two coupled optimisation processes, and propose a concurrent genetic algorithm (CGA) to solve the two coupled optimisation problems. The influences of the decision variables of one problem on the objective function of the other problem are taken into consideration when the fitness functions of the CGA are constructed. Numerical experiments are done to verify the effectiveness of the algorithm.     

JOB ASSIGNMENT ALGORITHMS ON UNIFORM PARALLEL MACHINES

Uniform parallel machine scheduling problems with a makespan measure cannot generally be solved within polynomial time complexity. This paper considers special problems with a single type of job on the uniform parallel machines, where each machine is available at a given ready time. Also the machine can be restricted on the number of jobs to be processed. The objective is to develop job assignment or batching algorithms which minimize makespan. When all the machines are available at time zero and have no restriction on the number of assignable jobs, a lower bound and optimal solution properties are derived. Based upon these properties, a polynomial algorithm is suggested to find the optimal job assignment on each machine. Three generalized problems are considered under the following situations: (1) some machines have capacity restrictions on the production batch, (2) each machine has its ready time, and (3) the jobs require series-parallel operations. The generalized problems arc also characterized and polynomial algorithms are developed for the same aim of optimal job assignment, except for the case of series-parallel operations. A heuristic algorithm is suggested with numerical tests for the series-parallel operations problem     

A computational study of heuristics for two-stage flexible flowshops

We consider the scheduling of two-stage flexible flowshops. This manufacturing environment involves two machine centres representing two consecutive stages of production. Each machine centre is composed of multiple parallel machines. Each job has to be processed serially through the two machine centres. In each machine centre, a job may be processed on any of the machines. There are n independent jobs to be scheduled without preemption. The jobs can wait in between the two machine centres and the intermediate storage is unlimited. Our objective will be to minimize the maximum completion time of the jobs. We formulate the problem as a mixed integer program. Given this problem class is NP-hard in the strong sense, we present three lower bounds to estimate the optimal solution. We then propose a sequence-first, allocate-second heuristic approach for its solution. We heuristically decompose the problem by first creating a priority list to order the jobs and then assign the jobs to the available machines in each machine centre based on this order. We describe seven rules for the sequencing phase. The assignment phase consists of a heuristic which attempts to minimize each partial schedule length while looking ahead at the future assignment of the currently unscheduled jobs. The computational performance of the heuristic approach was evaluated by comparing the value of each heuristic variant to the best among the three lower bounds. Its effectiveness was tested on scenarios pertinent to flexible flowshop environments, such as cellular manufacturing, by conducting a computational study of over 3400 problems. Our computational results indicate that the most effective approach used Johnson's rule to provide the priority list for job assignment. This provided integrality gaps which on the average were less than 0·73%.     

On scheduling models for the frequency interval assignment problem with cumulative interferences

In this article, models and methods for solving a real-life frequency assignment problem based on scheduling theory are investigated. A realistic frequency assignment problem involving cumulative interference constraints in which the aim is to maximize the number of assigned users is considered. If interferences are assumed to be binary, a multiple carrier frequency assignment problem can be treated as a disjunctive scheduling problem since a user requesting a number of contiguous frequencies can be considered as a non-preemptive task with a processing time, and two interfering users can be modelled through a disjunctive constraint on the corresponding tasks. A binary interference version of the problem is constructed and a disjunctive scheduling model is derived. Based on the binary representation, two models are proposed. The first one relies on an interference matrix and the second one considers maximal cliques. A third, cumulative, model that yields a new class of scheduling problems is also proposed. Computational experiments show that the case-study frequency assignment problem can be solved efficiently with disjunctive scheduling techniques.     

Balancing two-sided assembly lines with sequence-dependent setup times

Two-sided assembly lines are often designed to produce large-sized products, such as automobiles, trucks and buses. In this type of production line, both left-side and right-side of the line are used in parallel. In all studies on two-sided assembly lines, sequence-dependent setup times have not yet been considered. However, in real life applications, setups may exist between tasks. Performing a task directly before another task may influence the latter task inside the same station, because a setup for performing the latter task may be required. Furthermore, if a task is assigned to a station as the last one, then it may cause a setup for performing the first task assigned to that station since the tasks are performed cyclically. In this paper, the problem of balancing two-sided assembly lines with setups (TALBPS) is considered. A mixed integer program (MIP) is proposed to model and solve the problem. The proposed MIP minimises the number of mated-stations (i.e., the line length) as the primary objective and it minimises the number of stations (i.e., the number of operators) as a secondary objective for a given cycle time. A heuristic approach (2-COMSOAL/S) for especially solving large-size problems based on COMSOAL (computer method of sequencing operations for assembly lines) method is also presented. An illustrative example problem is solved using 2-COMSOAL/S. To assess the effectiveness of MIP and 2-COMSOAL/S, a set of test problems are solved. The computational results show that 2-COMSOAL/S is very effective for the problem.     

Solving vehicle assignment problems by process-network synthesis to minimize cost and environmental impact of transportation

A method and software are proposed for optimal assignment of vehicles to transportation tasks in terms of total cost and emission. The assignment problem is transformed into a process-network synthesis problem that can be algorithmically handled by the P-graph framework. In the proposed method, each task is given by a set of attributes to be taken account in the assignment; this is also the case for each vehicle. The overall mileage is calculated as the sum of the lengths of all the routes to be travelled during, before, after, and between the tasks (Desaulniers et al. 1998; Baita et al. 2000). Cost and emission are assigned to the mileages of each vehicle type. In addition to the globally optimal solution of the assignment problem, the P-graph framework provides the n-best suboptimal solutions that can be ranked according to multiple criteria. The viability of the proposed method is illustrated by an example.     

Integrated project task and manpower scheduling

The objective of project task scheduling is to determine task start dates and durations to complete a project on time with the minimum cost of performing tasks plus overhead. By altering task start dates and durations, the daily labor-demand profile can be changed. The objective of personnel scheduling is to determine how many workers must be assigned to each feasible days-off tour to satisfy a given labor-demand profile with minimum labor cost. Integrating these two problems permits the simultaneous determination of start dates, durations, labor levels and required tours for a minimum-cost and on-time schedule. Both integer programming and heuristic solution procedures to solve the integrated problem are presented. In a series of 20 test problems, the heuristic procedure outperformed the traditional two-step scheduling procedure by reducing the cost of labor and overhead by 8.6%.     

Job shop scheduling with a non-regular objective: A comparison of neighbourhood structures based on a sequencing/timing decomposition

Commercial software packages for production management are characterized by a gap between MRP logic, based on a backward scheduling approach, and finite capacity scheduling, usually based on forward scheduling. In order to partially bridge that gap, we need scheduling algorithms able to meet due dates while keeping WIP and inventory costs low. This leads us to consider job shop scheduling problems characterized by non-regular objective functions; such problems are even more difficult than classical job shop scheduling, and suitable heuristics are needed. One possibility is to consider local search strategies based on the decomposition of the overall problem into sequencing and timing sub-problems. For given job sequences, the optimal timing problem can be solved as a node potential problem on a graph. Since solving the timing problem is a relatively time-consuming task, we need to define a suitable neighbourhood structure to explore the space of job sequences; this can be done by generalizing well-known results for the minimum makespan problem. A related issue is if solving timing problems exactly is really necessary, or if an approximate solution is sufficient; hence, we also consider solving the timing problem approximately by a fast heuristic. We compare different neighbourhood structures, by embedding them within a pure local improvement strategy. Computational experiments show that the overall approach performs better than release/dispatch rules, although the performance improvement depends on the problem characteristics, and that the fast heuristic is quite competitive with the optimal timing approach. On the one hand, these results pave the way to the development of better local search algorithms (based e.g. on tabu search); on the other hand, it is worth noting that the heuristic timing approach, unlike the optimal one, can be extended to cope with the complicating features typical of practical scheduling problems.     

A heuristic for assigning facilities to locations to minimize WIP travel distance in a linear facility

Many manufacturing systems require an assignment of machines to locations along a straight track, so as to optimize material flow. This paper uses a cut approach to the corresponding quadratic assignment problem, and derives a heuristic which generates a good solution. In addition, a modified lower bound to the assignment problem is also developed, which is always better than the classical lower bound. Results showing the performance of the heuristic are demonstrated, along with a comparison of the modified and classical lower bound. In almost all the test problems, the solution generated by the heuristic was either optimal or better than any solution obtained by other methods. Extension of the heuristic to more general cases also is considered.     

Operator assignment with cell loading and product sequencing in labour-intensive assembly cells – a case study of a bicycle assembly company

This research deals with an operator assignment problem in which cell loading and product sequencing are taken into account in labour-intensive assembly cells. In each cell the number of assembly tasks is more than the number of operators, so multi-assembly tasks are assigned to each operator. Because the assembly procedure and time required for each assembly task are quite different for different products, some tasks will be transferred when the product changes. Reducing the number of task transfers can smooth the process of product change. A four-phase methodology is proposed to minimise the total manpower required and task transfers at the same time. The four phases are manpower configuration design, calculating the number of task transfers, manpower requirement minimization and cell loading and product sequencing optimization. A case study from a bicycle assembly company is introduced. For comparison, two methodologies are applied. The results show that the proposed four phase methodology can provided the solution with fewer task transfers based on the same total manpower requirement. However, when the number of products increases, the computation time of the proposed four-phase methodology increases rapidly.     

A heuristic for setting up a flexible assembly system

We consider setup problems in flexible assembly systems (FASs) with an objective involving job priorities and station workloads. Because of the difficulty in solving the FAS setup problem, it is partitioned into two subproblems: the part type selection problem and the loading problem. We suggest a solution procedure in which branch-and-bound methods and heuristic methods are used for solving the subproblems. Part types are tentatively selected first without explicitly considering the system's restrictions, such as precedence relationships among tasks. As a result, the alternative for part type selection may not always be feasible for the loading problem. For a feasibility check and for a use in assigning tasks of selected part types, we develop an algorithm for finding a feasible sequence of the tasks. In the loading problem, tasks are assigned to stations using LPT-type rules with improvements tried through interchanging tasks. Results of computational tests on randomly generated problems are reported.     

A priority rule-based constructive heuristic and an improvement method for balancing assembly lines with parallel multi-manned workstations

Assembly lines of big-size products such as buses, trucks and helicopters are very different from the lines studied in the literature. These products’ manufacturing processes have a lot of tasks most of which have long task times. Since traditional assembly line models including only one worker in each station (i.e. simple assembly lines) or at most two workers (two-sided assembly lines) may not be suitable for manufacturing these type of products, they need much larger shop floor for a number of stations and long product flow times. In this study, an assembly line balancing problem (ALBP) with parallel multi-manned stations is considered. Following the problem definition, a mixed integer programming formulation is developed. A detailed study of priority rules for simple ALBPs is also presented, and a new efficient constructive heuristic algorithm based on priority rules is proposed. In order to improve solutions found by the constructive heuristic, a genetic algorithm-based solution procedure is also presented. Benchmark instances in the literature are solved by using the proposed mathematical programming formulation. It has been seen that only some of the small-size instances can be solved optimally by this way. So the efficiency of the proposed heuristic method is verified in small-size instances whose optimal solutions are found. For medium- and big-size instances, heuristics’ results and CPU times are demonstrated. A comparative evaluation with a branch and bound algorithm that can be found in the literature is also carried out, and results are presented.     

Task assignment problems in distributed computing systems by simulated annealing

Abstract

The stochastic, heuristic search algorithm called simulated annealing is considered for the problems of static task assignment in distributed computing systems. The purposes of task assignment problems are to assign modules of programs over a set of interconnected processors in order to both maximize the utilization of processors and minimize interprocessor communication costs. This problem has been proven to be NP‐hard. Although simulated annealing has been applied to a broad class of combinatorial optimization problems, but it requires a long computation time in order to converge to the globally optimal solution. In this paper, we design a very efficient annealing schedule with good move generation strategies and use the concept of specific heat and the frozen condition to obtain near‐optimal solutions for task assignment problems with a significantly large reduction in the number of iterations.     

Robotic U-shaped assembly line balancing using particle swarm optimization

Automation in an assembly line can be achieved using robots. In robotic U-shaped assembly line balancing (RUALB), robots are assigned to workstations to perform the assembly tasks on a U-shaped assembly line. The robots are expected to perform multiple tasks, because of their capabilities. U-shaped assembly line problems are derived from traditional assembly line problems and are relatively new. Tasks are assigned to the workstations when either all of their predecessors or all of their successors have already been assigned to workstations. The objective function considered in this article is to maximize the cycle time of the assembly line, which in turn helps to maximize the production rate of the assembly line. RUALB aims at the optimal assignment of tasks to the workstations and selection of the best fit robot to the workstations in a manner such that the cycle time is minimized. To solve this problem, a particle swarm optimization algorithm embedded with a heuristic allocation (consecutive) procedure is proposed. The consecutive heuristic is used to allocate the tasks to the workstation and to assign a best fit robot to that workstation. The proposed algorithm is evaluated using a wide variety of data sets. The results indicate that robotic U-shaped assembly lines perform better than robotic straight assembly lines in terms of cycle time.     

Pattern-set generation algorithm for the one-dimensional multiple stock sizes cutting stock problem

A pattern-set generation algorithm (PSG) for the one-dimensional multiple stock sizes cutting stock problem (1DMSSCSP) is presented. The solution process contains two stages. In the first stage, the PSG solves the residual problems repeatedly to generate the patterns in the pattern set, where each residual problem is solved by the column-generation approach, and each pattern is generated by solving a single large object placement problem. In the second stage, the integer linear programming model of the 1DMSSCSP is solved using a commercial solver, where only the patterns in the pattern set are considered. The computational results of benchmark instances indicate that the PSG outperforms existing heuristic algorithms and rivals the exact algorithm in solution quality.     

An efficient heuristic approach for parallel machine scheduling with job splitting and sequence-dependent setup times

In this paper, we consider a simplified real-life identical parallel machine scheduling problem with sequence-dependent setup times and job splitting to minimize makespan. We propose a heuristic to solve this problem. Our method is composed of two parts. The problem is first reduced into a single machine scheduling problem with sequence-dependent setup times. This reduced problem can be transformed into a Traveling Salesman Problem (TSP), which can be efficiently solved using Little's method. In the second part, a feasible initial solution to the original problem is obtained by exploiting the results of the first part. This initial solution is then improved in a step by step manner, taking into account the setup times and job splitting. We develop a lower bound and evaluate the performances of our heuristic on a large number of randomly generated instances. The solution given by our heuristic is less than 4.88% from the lower bound.     

A genetic algorithm for the multi-stage and parallel-machine scheduling problem with job splitting – A case study for the solar cell industry

This paper studies a multi-stage and parallel-machine scheduling problem with job splitting which is similar to the traditional hybrid flow shop scheduling (HFS) in the solar cell industry. The HFS has one common hypothesis, one job on one machine, among the research. Under the hypothesis, one order cannot be executed by numerous machines simultaneously. Therefore, multiprocessor task scheduling has been advocated by scholars. The machine allocation of each order should be scheduled in advance and then the optimal multiprocessor task scheduling in each stage is determined. However, machine allocation and production sequence decisions are highly interactive. As a result, this study, motivated from the solar cell industry, is going to explore these issues. The multi-stage and parallel-machine scheduling problem with job splitting simultaneously determines the optimal production sequence, multiprocessor task scheduling and machine configurations through dynamically splitting a job into several sublots to be processed on multiple machines. We formulate this problem as a mixed integer linear programming model considering practical characteristics and constraints. A hybrid-coded genetic algorithm is developed to find a near-optimal solution. A preliminary computational study indicates that the developed algorithm not only provides good quality solutions but outperforms the classic branch and bound method and the current heuristic in practice.     

Expert judgments in the cost-effectiveness analysis of resource allocations: a case study in military planning

We consider resource allocation problems in which agents are assigned to tasks with the aim of (1) minimizing the costs of assigning the agents and (2) maximizing the overall value resulting from the completion of tasks. Often, such assignment problems are challenging, because it may not be known to what extent the agents can complete tasks or what the value of either full or partial task completion is. Furthermore, it may be difficult to determine how important the tasks are relative to each other. In this paper, we therefore develop an optimization framework that helps determine for a range of levels of resource expenditure (1) which combinations of agents are cost-effective and (2) to which tasks these agents should be assigned. The parameters for the optimization problem can be derived, for instance, by eliciting evaluation judgments from experts. We also provide tools for analyzing which combinations of agents outperform others in view of the judgments of all experts, and which ones are cost-ineffective based on the judgments of some or all experts. A computational algorithm is presented, and the framework is illustrated by reporting a real application in military planning.     

Algorithms for the joint multitasking scheduling and common due date assignment problem

In this paper, we investigate a joint multitasking scheduling and common due date assignment problem on a single machine, for which examples can be found in product delivery process in logistics. Multitasking allows the machine to perform multiple tasks. The multitasking phenomenon has been observed in various practical domains, including manufacturing and administration. In multitasking settings, each waiting job interrupts a currently in-processing job, causing an interruption time and a switching time. In common due date assignment problems, the objective is to determine the optimal value of this due date with the purpose of minimising a total penalty function, which is associated with service quality. For the problem with general interruption functions, analytical properties are obtained to reduce the search space of the optimal solutions. For the cases with linear interruption functions, we develop a polynomial-time algorithm. Numerical experiments have been conducted to validate the efficiency of our proposed algorithm. Computational results also demonstrate an interesting phenomenon that in some cases, the optimal solutions under multitasking are superior to the counterparts without multitasking. Besides, we also devise a mixed integer programme for the cases with linear interruption function.     

A constructive heuristic algorithm for concurrently selecting and sequencing jobs in an FMS environment

This paper deals with the concurrent solution of the loading and scheduling problems in a flexible manufacturing system ( FMS) environment. It is assumed that the FMS environment has production planned periodically and each job in the system has a number of operations to be processed on flexible machines. A heuristic approach using a constructive scheduling method is developed to solve the FMS loading and scheduling problems concurrently. The computational results are compared to an existing procedure that considers a hierarchical approach with a similar problem environment. The comparison study shows a significant improvement over the existing hierarchical procedure. This experiment indicates that a concurrent solution approach can solve the FMS loading and scheduling problems very effectively.