Multiple Rate-modifying Activities Research Articles

An exact solution method for seru scheduling problems with multiple rate-modifying activities and learning effect

An exact solution method for seru scheduling problems with multiple rate-modifying activities and learning effect

Single machine scheduling problem with batch setups involving positional deterioration effects and multiple rate-modifying activities

ABSTRACTThis article considers a single machine scheduling problem with batch setups, positional deterioration effects, and multiple optional rate-modifying activities to minimize the total completion time. This problem is formulated as an integer quadratic programming problem. In view of the complexity of optimally solving this problem, a two-phase heuristic algorithm is proposed where an optimal but non-integer solution is obtained in the first phase by solving a continuous relaxed version of the problem. This solution serves as a lower bound for the optimal value of the total completion time. The second phase of the algorithm generates an integer solution using a simple rounding scheme that is optimum or very close to optimum for this problem. Empirical evaluation and comparison with an existing heuristic algorithm show that the proposed heuristic algorithm is substantially more effective in solving large-size problem instances.

Matheuristic approaches for parallel machine scheduling problem with time-dependent deterioration and multiple rate-modifying activities

The study considers a parallel machine scheduling (PMS) problem with time-dependent deterioration and multiple rate-modifying activities (RMAs). The objective of the problem is to simultaneously determine the number and positions of RMAs and a schedule of jobs on parallel machines to minimize the makespan. In order to determine an optimal solution, a mixed integer linear programming (MILP) model for the PMS problem is introduced. Subsequently, novel metaheuristic algorithms embedding a mathematical model are developed based on matheuristic approaches to effectively handle large-sized problems. The matheuristic approaches decompose the original problem into sub-problems by determining partial decision variables from each iteration in simulated annealing (SA) and genetic algorithm (GA). Subsequently, the rest of the decision variables are optimally determined by using a mathematical model for the sub-problems with partial decision variables predetermined. In order to enhance the performance of SA and GA, an adjustment heuristic is proposed based on an optimality property for the problem. The performance of the proposed algorithms is evaluated by conducting numerical experiments based on randomly generated examples, and subsequently the behavior of the algorithms is discussed.

A rule-based genetic algorithm with an improvement heuristic for unrelated parallel machine scheduling problem with time-dependent deterioration and multiple rate-modifying activities

In this article, we consider an unrelated parallel machine scheduling (UPMS) problem with time-dependent deterioration and multiple rate-modifying activities (RMAs). The actual processing time of a job is defined by a linear function of a gap between starting time of the job and ending time of the recent RMA. The starting rate of the actual processing time of jobs is restored to the original processing time through the application of RMAs. In the UPMS problem, we simultaneously determine the schedule of jobs and the number and positions of RMAs to minimize the makespan. To solve the problem, a mixed integer linear programming (MILP) model for the problem is developed to find the optimal solution. Then, we propose a novel rule-based genetic algorithm (GA) with a chromosome representing job assigning sequence to one of the machines and the schedule of jobs and the number and positions of RMAs in each machine are determined by a completion time rule-based dispatching heuristic during the decoding process of the chromosome. To enhance the solution effectiveness, an improvement heuristic is implemented to the GA. Extensive computational experiments are conducted through randomly generated examples to evaluate the performance of the proposed algorithms.

Multitasking scheduling with multiple rate‐modifying activities

AbstractThis paper considers scheduling problems with human operators having the option to perform multiple rate‐modifying activities (MRMAs) while they are carrying out multitasking. Thus, the processing of a selected task suffers jointly from interruptions by other available but unfinished tasks and MRMAs. Two types of objective functions are studied: single‐criterion minimizing the total completion time, and multicriteria minimizing a weighted combination of the total completion time, the total absolute differences in completion times, and a weighted combination of the total waiting time and the total absolute differences in waiting times. We propose optimal solution algorithms for all the studied problems and also analyze some special cases of them.

A hybrid genetic algorithm with two-stage dispatching heuristic for a machine scheduling problem with step-deteriorating jobs and rate-modifying activities

This article is concerned with a single machine scheduling problems that integrate by step-deterioration along with multiple rate-modifying activities (RMAs). The actual processing time of a job is defined by a step function of its starting time and a specific deterioration threshold. The starting rate of the actual processing time of jobs is restored through the application of RMAs, which recover the original processing time. In this scheduling environment, we simultaneously determine the schedule of step-deteriorating jobs and the number and positions of RMAs to minimize the makespan. We derive a mixed integer programming model to obtain the optimal solution and propose a hybrid genetic algorithm with a two-stage dispatching heuristic represented by a simple chromosome. The performance of the proposed genetic algorithm (GA) is compared with GAs with two types of chromosome representations using randomly generated test instances.

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.

An optimal single-machine scheduling with linear deterioration rate and rate-modifying activities

This paper considers a single-machine scheduling with linear deterioration rate of processing speed and multiple rate-modifying activities simultaneously. A rate-modifying activity can change the processing rate of machine under consideration, which means after each rate-modifying activity the speed of the machine is fully recovered. The integration of these two concept is motivated by human operators and semi-automatic systems that experience performance degradation over time and require rate-modifying activities for recovery. The objective is to minimize the makespan. We need to decide the sequence of jobs and when to schedule the rate-modifying activities. An optimal schedule is proposed, which can solve the problem in $$O(n\log n)$$O(nlogn) time where $$n$$n is the number of jobs.

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.

Single-Machine Total Completion Time Scheduling with Position-Based Deterioration and Multiple Rate-Modifying Activities

In this paper, we study a single-machine scheduling problem with deteriorating processing time of jobs and multiple rate-modifying activities which reset deteriorated processing time to the original processing time. In this situation, the objective function is to minimize total completion time. First, we formulate an integer programming model. Since the model is difficult to solve as the size of real problem being very large, we design an improved genetic algorithm called adaptive genetic algorithm (AGA) with spontaneously adjusting crossover and mutation rate depending upon the status of current population. Finally, we conduct some computational experiments to evaluate the performance of AGA with the conventional GAs with various combinations of crossover and mutation rates.

Due-Window Assignment and Scheduling with Multiple Rate-Modifying Activities under the Effects of Deterioration and Learning

This paper discusses due-window assignment and scheduling with multiple rate-modifying activities. Multiple types of rate-modifying activities are allowed to perform on a single machine. The learning effect and job deterioration are also integrated concurrently into the problem which makes the problem more realistic. The objective is to find jointly the optimal location to perform multiple rate-modifying activities, the optimal job sequence, and the optimal location and size of the due window to minimize the total earliness, tardiness, and due-window-related costs. We propose polynomial time algorithms for all the cases of the problem under study.

Scheduling with job-dependent learning effects and multiple rate-modifying activities

We consider a scheduling problem with job-dependent learning effects and multiple rate-modifying activities. The learning effects manifest such that the processing time of a job is a decreasing function of its position in a sequence. By job-dependent learning effects, we mean that the learning of the jobs is different. A rate-modifying activity is an activity that changes the production rate of a machine. So the actual processing time of a job in our problem is a variable, which depends not only on its position in a sequence but also on whether it is scheduled before or after a rate-modifying activity. We assume that each machine may have multiple rate-modifying activities. The objective is to minimize the total completion time. We show that all the cases of the problem are polynomially solvable.