Common Due Window Research Articles

Algorithms for Minimizing Resource Consumption Over Multiple Machines With a Common Due Window

Algorithms for Minimizing Resource Consumption Over Multiple Machines With a Common Due Window

Single Machine Job Sequencing With a Restricted Common Due Window

This article deals with the problem of sequencing $N$ jobs on a single machine with a restrictive common due window. The objective is to minimize the total weighted earliness-tardiness penalties, which conform to just-in-time (JIT) manufacturing. A novel backtracking simulated annealing (BSA) algorithm with a backtracking mechanism and an effective coding scheme is proposed herein to solve this problem. The performance of the proposed BSA algorithm is compared with that of the best available algorithm and the simulated annealing (SA) algorithm using four benchmark problem sets. The computational results reveal that the backtracking mechanism can improve the performance of the SA algorithm and make the proposed BSA algorithm outperform the state-of-the-art algorithm. The proposed BSA algorithm is sufficiently efficient to satisfy the real-world scheduling requirements of the JIT manufacturing system.

Bicriterion scheduling with a negotiable common due window and resource-dependent processing times

We investigate scheduling problems with a negotiable common due window where the job processing times are controllable by allocating extra resources to process the jobs and the resource amounts can be either discrete or continuous. We adopt a bicriterion analysis, where one criterion is a cost function consisting of the weighted numbers of early and late jobs, and due window assignment cost (DWAC), whereas the other criterion is the total resource consumption cost (TRSC). We investigate four problems resulting from different treatments of the two criteria as follows: P1, which minimizes the sum of the two criteria; P2 and P3, which minimize one of the two criteria subject to a constraint on the value of the other criterion, respectively; and P4, which identifies the set of Pareto-optimal points of the two criteria. We show that P1 is polynomially solvable, while P2–P4 with both resource types are all NP-hard. With the discrete resource type, we propose pseudo-polynomial-time algorithms for P4, establishing that P2–P4 are all binary NP-hard. With the continuous resource type, we provide an optimal algorithm for P2–P4 by solving a series of mixed integer linear programming (MILP) models. We also provide a two-dimensional fully polynomial-time approximation scheme (FPTAS) to approximate the Pareto set. Finally, we perform computational experiments to verify the effectiveness of the developed solution procedures.

Single-machine minmax common due-window assignment and scheduling problems with convex resource allocation

ABSTRACTIn this article, the common due-window (CON DW) assignment and scheduling problem on a single machine is studied. The minmax CON DW problem is extended by considering convex resource allocation. In extended problems, the scheduler needs to find, in addition to the optimal job sequence, the start time and size of the due window, as well as the actual processing time of each job that optimizes a cost function. First, the focus is on minimizing the maximum scheduling criteria subject to maximal resource consumption. Next, the complementary problem of minimizing resource consumption subject to an upper bound on the scheduling measure is solved. For these problems, a closed form solution is provided, with computational complexity of , where is the number of jobs. An extension to the first problem is offered by assuming general position-dependent workloads, proving that the problem remains polynomially solvable.

Two-stage medical supply chain scheduling with an assignable common due window and shelf life

This paper considers a two-stage medical supply chain scheduling problem from the perspective of the medicine manufacturer in which jobs have an assignable common due window and shelf life. Each job will incur an early (tardy) penalty if it is early (tardy) with respect to the common due window under a given schedule. The job’s holding time, which is the time interval that passes from the completion time of the job to the delivery date of the job in the batch, must be no more than its shelf life. The objective is to minimize the total cost comprising earliness, weighted number of tardy jobs, holding time, due window starting time, window size, and batch delivery. We first show that the problem is NP-hard and then provide a pseudo-polynomial-time algorithm. We also prove that a special case of the problem can be optimally solved in polynomial time.

Single machine due window assignment resource allocation scheduling with job-dependent learning effect

This paper deals with a single machine common due window assignment resource allocation scheduling problem with job-dependent learning effect. The objective is to find the due window starting time, a due window size, resource allocation and a job schedule such that total resource consumption cost is minimized subject to a cost function associated with the window location, window size, earliness, tardiness and makespan is less than or equal to a fixed constant number. We show that the problem can be solved in polynomial time. Some extensions of the problem are also given.

Single machine due window assignment and resource allocation scheduling problems with learning and general positional effects

This paper considers single machine scheduling problems which determine the optimal job schedule, due window location and resource allocation simultaneously. The optimized criteria consist of makespan, earliness, tardiness, due window starting time and size, and the allocated resource cost, to conform with just-in-time (JIT) manufacturing. The job's actual processing time is a general function of its position, starting time, and the resource quantity allocated for the job. Specifically, both the linear and convex resource consumption scenarios are considered. In the context of the linear and convex resource consumption, we present four research problems and prove that all of them are polynomially solvable under CON due window (all jobs share a common due window), SLK due window (each job is assigned an individual due window based on a common flow allowance) and DIF due window (each job has a different due window with no restrictions) assignment assumptions, respectively.

带有退化维修和交货期窗口的加工时间分别可控的单机排序问题

本文讨论了带有退化维修和交货期窗口的加工时间分别可控的单机排序问题。每个工件有多个可能的加工时间，不同的加工时间会产生不同的费用。为了提高机器的生产效率，进行一次退化维修。考虑了两个不同的问题：所有工件有一个共同的交货期窗口；每个工件有属于自己的交货期窗口。目标是确定最优的工件加工顺序、维修活动位置、交货期窗口位置以及极小化总费用函数，给出了多项式时间算法，证明了该问题是多项式时间可解。 In this paper, we consider single-machine due-window assignment and scheduling with discretely controllable job processing times and a deteriorating rate-modifying activity. Each job has multiple processing times to be selected and different processing times are associated with different costs. In addition, we can schedule a deteriorating rate-modifying activity in order to reduce the total cost. We consider two versions of the problem, in the first version, all the jobs share a common due-window and in the second version, each job has their own due-window. The objective is to determine the optimal job sequence, schedule the deteriorating rate-modifying activity and the due-window, so as to minimize the total cost. We provide polynomial-time algorithms for the considered problems.

Effective dynamic dispatching rule and constructive heuristic for solving single-machine scheduling problems with a common due window

This study addresses the single-machine scheduling problem with a common due window (CDW) that has a constant size and position. The objective is to minimise the total weighted earliness–tardiness penalties for jobs completed out of the CDW. To determine a schedule as close to optimum as possible, this study develops a dynamic dispatching rule and an effective constructive heuristic. The better performance of the proposed heuristic is demonstrated by comparing the results of it with those of a state-of-the-art greedy heuristic on a well-known benchmark problem set. In addition, we incorporate the constructive heuristic into a best-so-far meta-heuristic to examine the benefit of the proposed heuristic. The results show that the best known solutions in 144 out of the 250 benchmark instances are improved.

Common Due-Window Assignment and Group Scheduling with Position-Dependent Processing Times

This paper investigates a single-machine scheduling problem involving both the due-window assignment and position-dependent processing times under a group technology environment. By position-dependent processing times, we mean that the processing time of a job is dependent of its processing position in the job sequence within the group it belongs to. A setup time is incurred whenever the single machine transfers job processing from a group to another group. Each group is assigned an assignable common due-window. A job completed earlier (respectively, later) than the common due-window of the group it belongs to will incur an earliness (respectively, tardiness) penalty. The objective is to determine the optimal group sequence, the optimal job sequence, and the optimal due-window assignment so as to minimize the total cost including the earliness and tardiness (or weighted number of tardy jobs) penalties, black and the due-window starting time and due-window size costs. We show that both the problems can be solved in polynomial times.

Single machine due-window assignment scheduling with resource-dependent processing times to minimise total resource consumption cost

This paper considers a single-machine scheduling problem involving convex resource-dependent processing times and due-window assignment simultaneously. The goal is to minimise the total resource consumption cost under the constraint that the schedule cost involving earliness, tardiness, window location, window size and makespan does not exceed a given limit for two popular due window assignment methods: the common flow allowance (slack) due window assignment method (referred to SLKW) and the common due window assignment method (referred to CONW). We show that the problem can be solved in polynomial time. Some extensions of the problem are also given.

Improved algorithms for single-machine common due window assignment and scheduling with batch deliveries

We consider a single-machine due window assignment and scheduling problem with batch deliveries, where all jobs have a common due window, and the start time and size of the due window are decision variables. Finished jobs are delivered in batches with unlimited batch capacity. The objective is to determine the due window, a job sequence, and the delivery times, so as to minimize the total cost which comprises earliness of delivery, job holding, start time of due window, size of due window, number of delivery batches, and tardiness penalty. We consider three different variants of the problem corresponding to different measurements of tardiness penalty. We present polynomial-time solution procedures for these variants with significantly lower computational complexities than those of known algorithms in the literature.

Multiple Common Due-Window Assignment Based on Common Flow Allowance and Resource-Dependent Processing Times

This paper studies a multiple common due-window assignment problem on a single machine. The job-dependent due-windows are obtained based on common flow allowance criteria. We assume that the processing time of a job is controllable by the resource amount assigned to it. The objective is to find the optimal size and location of the multiple common due-windows, the set of jobs assigned to each due window, the sequence of jobs and resource allocation scheme to minimize a cost function based on the window size and location, earliness and tardiness of jobs and resource cost. We propose an optimal algorithm to solve the problem.

Single Machine Due Window Assignment and Scheduling with an Optional Maintenance Activity

This paper considers single machine scheduling with general position-dependent and job-dependent aging effect. All jobs share a common due window, and an optional maintenance activity (OMA) is taken into consideration. The processing time of a job is a non-decreasing function in its position. Such category of maintenance activity is called the OMA since one can determine the position and the actual duration of it. The objective is to determine the optimal due window position, the optimal location and duration of the OMA, and the optimal job sequence so as to minimize the total of earliness, tardiness, due window starting time, due window size, and the OMA duration related costs. We show that the considered problem can be solved in polynomial time.

Scheduling with Multiple Common Due Windows Assignment and General Position-Dependent and Resource-Dependent Processing Times

In this paper we consider multiple common due windows assignment and single-machine scheduling problems with general position-dependent and resource-dependent processing times simultaneously. Multiple common due windows, an extension of single common due window, allow a job to fit one from multiple common due windows. We assume that the number of common due windows to be assigned to the jobs is given. Two resource allocation models are examined, namely the linear resource consumption model and the convex re-source consumption model. The actual processing time of a job is a function of its scheduled position in a sequence and its resource allocation. We aim to determine jointly the optimal common due window positions and sizes, the set of jobs assigned to each common due window, the optimal resource allocations, and the optimal schedule for minimizing an objective function which includes earliness, tardiness, common due windows assignment, makespan, and resource consumption costs. We provide some properties of the optimal schedule for the problem and propose polynomial time algorithms for all the problems considered.

Single-machine due-window assignment and scheduling with resource allocation, aging effect, and a deteriorating rate-modifying activity

We consider single-machine scheduling with a common due-window and a deteriorating rate-modifying activity. We assume that the processing time of a job is a function of the amount of a resource allocated to it, its position in the processing sequence, and its aging effect. The objective is to minimize the total cost, which is a function of earliness, tardiness, due-window starting time, due-window size, and resource consumption. We consider two models of the job processing time function and provide polynomial-time solution algorithms for the corresponding problems. We also give a more efficient solution algorithm for a special case of the second problem.

Optimal Common Due-Window Assignment with Linear Deteriorating and Resource-Dependent Processing Times under a Deteriorating Maintenance Activitiy

This paper studies single-machine scheduling problems with a due-window assignment under a deteriorating maintenance and time-and-resource-dependent processing times. Jobs completed within the due-window incur no penalties, other jobs incur either earliness or tardiness penalties. The maintenance activity can be scheduled immediately after any of the completed jobs. We assume that once the maintenance activity has been completed, the machine efficiency will be improved and the machine maintenance duration depends on its starting time. The objective is to find the maintenance position, the size and location of the due-window, and the sequence of jobs and resource allocation scheme to minimize a cost function based on the window size and location and the earliness and tardiness of jobs and resource. We propose an algorithm to solve the problem.

Scheduling problems with a common due window assignment: A survey

In this article a survey of studies on scheduling problems with a common due window assignment and earliness/tardiness penalty functions is presented. A due window is a generalization of the classical due date and describes a time interval in which a job should be finished. If a job is completed before or after the due window, it incurs an earliness or a tardiness penalty, respectively. In this survey we separately analyse the classical models with job-independent and job-dependent earliness/tardiness penalty functions and some other more complicated models. We describe the computational complexity of the problems and the main features of the approaches developed to solve them. Particular attention is paid to practical applications of the analysed models. As turns out, some complicated models combining classical scheduling problems with, e.g., learning and aging effects have no reasonable practical justification in the literature.

Multiprocessor Flow Shop Scheduling Problem with Common due Window

The objective of scheduling is to maximize capacity utilization, minimize work-in-process inventory and ensure timely delivery. The due windows problem proposes that jobs should only be finished within the time interval that meets customer needs. This research applies integer programming (IP) and ant colony optimization (ACO) to solve due window problems in a flow shop with multiprocessors (FSMP). To improve the performance of jobs within due windows, this research splits them into different numbers of processing lots so they can be processed on more than one machine simultaneously. This shortens the total weighted earliness and tardiness of the jobs. The ACO is applied as a heuristic tool for solving the scheduling problems, and the solution results show that ACO has good validity, robustness and effectiveness.

Due-window assignment with identical jobs on parallel uniform machines

A scheduling problem with a common due-window, earliness and tardiness costs, and identical processing time jobs is studied. We focus on the setting of both (i) job-dependent earliness/tardiness job weights and (ii) parallel uniform machines. The objective is to find the job allocation to the machines and the job schedule, such that the total weighted earliness and tardiness cost is minimized. We study both cases of a non-restrictive (i.e. sufficiently late), and a restrictive due-window. For a given number of machines, the solutions of the problems studied here are obtained in polynomial time in the number of jobs.