Total Machine Load Research Articles

Optimization of multi-objective integrated process planning and scheduling problem using a priority based optimization algorithm

For increasing the overall performance of modern manufacturing systems, effective integration of process planning and scheduling functions has been an important area of consideration among researchers. Owing to the complexity of handling process planning and scheduling simultaneously, most of the research work has been limited to solving the integrated process planning and scheduling (IPPS) problem for a single objective function. As there are many conflicting objectives when dealing with process planning and scheduling, real world problems cannot be fully captured considering only a single objective for optimization. Therefore considering multi-objective IPPS (MOIPPS) problem is inevitable. Unfortunately, only a handful of research papers are available on solving MOIPPS problem. In this paper, an optimization algorithm for solving MOIPPS problem is presented. The proposed algorithm uses a set of dispatching rules coupled with priority assignment to optimize the IPPS problem for various objectives like makespan, total machine load, total tardiness, etc. A fixed sized external archive coupled with a crowding distance mechanism is used to store and maintain the non-dominated solutions. To compare the results with other algorithms, a C-matric based method has been used. Instances from four recent papers have been solved to demonstrate the effectiveness of the proposed algorithm. The experimental results show that the proposed method is an efficient approach for solving the MOIPPS problem.

Decision support for unrelated parallel machine scheduling with discrete controllable processing times

In a manufacturing or service system, the actual processing time of a job can be controlled by the amount of an indivisible resource allocated, such as workers or auxiliary facilities. In this paper, we consider unrelated parallel-machine scheduling problems with discrete controllable processing times. The processing time of a job is discretely controllable by the allocation of indivisible resources. The planner must make decisions on whether or how to allocate resources to jobs during the scheduling horizon to optimize the performance measures. The objective is to minimize the total cost including the cost measured by a standard criterion and the total processing cost. We first consider three scheduling criterions: the total completion time, the total machine load, and the total earliness and tardiness penalties. If the number of machines and the number of possible processing times are fixed, we develop polynomial time algorithms for the considered problems. We then consider the minimization problem of the makespan cost plus the total processing cost and present an integer programming method and a heuristic method to solve the studied problem.

The three-machine proportionate open shop and mixed shop minimum makespan problems

Abstract We first consider the ordinary NP-hard three-machine proportionate open shop minimum makespan O 3| prpt | C max problem and show that it is solvable in O ( n log n ) time when certain conditions on the total machine load are met. When these conditions are not met, we derive an approximate solution by implementing the optimal solution for the O 3| prpt | C max problem when the two longest jobs are of equal length. In that case, both absolute and ratio worst-case bounds are derived. We also consider the more general mixed shop problem M 3| prpt | C max in which a given job subset must be processed as in a flow shop while the remaining jobs can be processed as in the O 3| prpt | C max problem. We show that our open shop solution techniques can be implemented to derive exact and approximate solutions for the M 3| prpt | C max problem. Finally, we discuss the applicability of our open shop results to the proportionate open shop problem with unequal machine speeds.

SCHEDULING POSITION-BASED DETERIORATING JOBS WITH MULTIPLE RATE-MODIFYING ACTIVITIES AND PAST-SEQUENCE-DEPENDENT DELIVERY TIMES

In this paper, we consider a scheduling problem with position-based deteriorating jobs and past-sequence-dependent delivery times on a single machine or parallel machines. Each job's delivery time is dependent on its waiting time for processing. Because of the deteriorating effect, each machine will undergo multiple rate-modifying activities throughout the planning horizon to restore its processing rate. For the single-machine case, the objectives are to minimize the makespan and the total completion time. For the parallel-machine case, the objectives are to minimize the total completion time and the total machine load. We show that all these problems are solvable in polynomial time.

Scheduling deteriorating jobs with a learning effect on unrelated parallel machines

In this study we consider unrelated parallel machines scheduling problems with learning effect and deteriorating jobs, in which the actual processing time of a job is a function of joint time-dependent deterioration and position-dependent learning. The objective is to determine the jobs assigned to corresponding each machine and the corresponding optimal schedule to minimize a cost function containing total completion (waiting) time, total absolute differences in completion (waiting) times and total machine load. If the number of machines is a given constant, we show that the problems can be solved in polynomial time under the time-dependent deterioration and position-dependent learning model.

Scheduling jobs with variable job processing times on unrelated parallel machines.

m unrelated parallel machines scheduling problems with variable job processing times are considered, where the processing time of a job is a function of its position in a sequence, its starting time, and its resource allocation. The objective is to determine the optimal resource allocation and the optimal schedule to minimize a total cost function that dependents on the total completion (waiting) time, the total machine load, the total absolute differences in completion (waiting) times on all machines, and total resource cost. If the number of machines is a given constant number, we propose a polynomial time algorithm to solve the problem.

Multi-objective flexible job shop scheduling using hybrid differential evolution algorithm

The authors addressed multi objective flexible job shop scheduling problems using hybrid differential evolution algorithm for minimisation of makespan, total machine load and critical machine load. The differential evolution algorithm is a stochastic-based adaptive scheme used for global optimisation over continuous space and to apply it for flexible job shop scheduling problem a suitable encoding mechanism is required. In this work random keys encoding mechanism is used to generate schedules that deals with floating point vectors. A non-dominated sorting algorithm is used to find the set of non-dominated solutions for the given scheduling problem. The proposed approach is extensively tested on a set of standard flexible job shop scheduling instances reported in the literature and it is found that the proposed algorithm is performing well on all the test problems.

Unrelated parallel-machine scheduling problems with aging effects and deteriorating maintenance activities

This paper explores the problems of unrelated parallel-machine scheduling with aging effects and deteriorating maintenance activities. The jobs are non-resumable. Each machine has at most one maintenance activity which is allowed throughout the planning horizon. Assume that once the maintenance activity is completed, the functions of machine and the properties of jobs e.g. the temperature (hardness) of materials that processed by the machine will be restored to their initial conditions. The length of the maintenance activity is a linear function of its starting time. The objectives of this study are to minimize the total completion time and the total machine load. Three basic types of aging effect model are proposed. We show that all the proposed models can be solved optimally in polynomial time.

A particle swarm optimization for a fuzzy multi-objective unrelated parallel machines scheduling problem

This paper proposes a novel multi-objective model for an unrelated parallel machine scheduling problem considering inherent uncertainty in processing times and due dates. The problem is characterized by non-zero ready times, sequence and machine-dependent setup times, and secondary resource constraints for jobs. Each job can be processed only if its required machine and secondary resource (if any) are available at the same time. Finding optimal solution for this complex problem in a reasonable time using exact optimization tools is prohibitive. This paper presents an effective multi-objective particle swarm optimization (MOPSO) algorithm to find a good approximation of Pareto frontier where total weighted flow time, total weighted tardiness, and total machine load variation are to be minimized simultaneously. The proposed MOPSO exploits new selection regimes for preserving global as well as personal best solutions. Moreover, a generalized dominance concept in a fuzzy environment is employed to find locally Pareto-optimal frontier. Performance of the proposed MOPSO is compared against a conventional multi-objective particle swarm optimization (CMOPSO) algorithm over a number of randomly generated test problems. Statistical analyses based on the effect of each algorithm on each objective space show that the proposed MOPSO outperforms the CMOPSO in terms of quality, diversity and spacing metrics.

Unrelated parallel-machine scheduling problems with multiple rate-modifying activities

In this article we investigate scheduling problems with multiple rate-modifying activities on an unrelated parallel-machine setting. We assume that each machine may have multiple rate-modifying activities. The goal is to determine jointly the optimal rate-modifying activity frequencies, the optimal rate-modifying activity positions, and the optimal schedule to minimize the total completion time and the total machine load, respectively. If the number of machines is fixed, we propose two efficient polynomial time algorithms for solving both problems no matter what the processing time of a job scheduled after a rate-modifying activity is greater or less than its processing time scheduled before the rate-modifying activity.

Parallel machines scheduling with deterioration effects and resource allocations

This article studies multi-objective scheduling problems involving deterioration effects and resource allocations simultaneously on an unrelated parallel-machine setting. The linear and convex resource consumption models are examined, respectively. We aim to find the optimal resource allocation and the optimal job sequence to minimize the cost function including the total completion time, the total machine load, the total absolute differences in completion times and the resource allocation and the cost function including the total waiting time, the total absolute differences in waiting times, and the resource allocation, respectively. We develop polynomial time algorithms for all the problems studied.

Unrelated parallel-machine scheduling with aging effects and multi-maintenance activities

Machine maintenance is often performed in manufacturing to prevent premature machine failures with a view to sustaining production efficiency. In this paper we study the parallel-machine scheduling problem with aging effects and multi-maintenance activities simultaneously. We assume that each machine may be subject to several maintenance activities over the scheduling horizon. A machine reverts to its initial condition after maintenance and the aging effects start anew. The objective is to find jointly the optimal maintenance frequencies, the optimal positions of the maintenance activities, and the optimal job sequences such that the total machine load is minimized. We apply the group balance principle to obtain the optimal positions of the maintenance activities and the number of jobs in each group in the scheduling sequence on each machine. We provide an efficient algorithm to solve the problem when the maintenance frequencies on the machines are given.

Parallel machines scheduling with simultaneous considerations of position-dependent deterioration effects and maintenance activities

This article considers identical parallel-machine scheduling problems with simultaneous considerations of position-dependent deterioration effects and maintenance activities. To counteract the deterioration effects on the machines, we assume that each machine must be maintained exactly once during the planning horizon and the maintenance can be scheduled immediately after completing the processing of any job. We further assume that, after the maintenance on a machine, the machine reverts to its initial condition and the deterioration effect starts anew. The objective is to find jointly the optimal maintenance positions and the optimal job sequences to minimize the total machine load. We provide polynomial time solutions for all the problems studied. Furthermore, we also show that the problem under study remains polynomially solvable when each machine is subject to multiple maintenance activities.

Unrelated parallel-machine scheduling with deteriorating maintenance activities

We study the problem of unrelated parallel-machine scheduling with deteriorating maintenance activities. Each machine has at most one maintenance activity, which can be performed at any time throughout the planning horizon. The length of the maintenance activity increases linearly with its starting time. The objective is to minimize the total completion time or the total machine load. We show that both versions of the problem can be optimally solved in polynomial time.

Parallel-machine scheduling of simple linear deteriorating jobs

We consider parallel-machine scheduling problems in which the processing time of a job is a simple linear increasing function of its starting time. The objectives are to minimize the makespan, total machine load, and total completion time. We show that all the problems are strongly NP-hard with an arbitrary number of machines and NP-hard in the ordinary sense with a fixed number of machines. For the former two problems, we prove that there exists no polynomial time approximation algorithm with a constant worst-case bound when the number of machines is arbitrary unless P = N P . When the number of machines is fixed, we propose two similar fully polynomial-time approximation schemes for the former two problems.