Common Due Window Research Articles

Common due window assignment and single machine scheduling with delivery time, resource allocation, and job-dependent learning effect

Common due window assignment and single machine scheduling with delivery time, resource allocation, and job-dependent learning effect

Minmax Common Due-Window Assignment Scheduling with Deteriorating Jobs

Minmax Common Due-Window Assignment Scheduling with Deteriorating Jobs

Formulations and an adaptive large neighborhood search for just-in-time scheduling of unrelated parallel machines with a common due window

In this paper, we address an unrelated parallel machine scheduling problem inspired by aspects of semiconductor manufacturing and other production systems. The objective is to minimize the total sum of weighted earliness and tardiness penalties when jobs are subject to a common restrictive due window. We conceptualize the problem, present two mixed-integer linear programming (MILP) formulations, and give necessary but not sufficient conditions for an optimal schedule. Since optimal schedules do not necessarily start at time zero, we derive two constructive heuristics coupled with a shift-forward procedure that determines leading idle times based on the elimination of straddling jobs. We propose a novel earliness–tardiness extension of the adaptive large neighborhood search (ET-ALNS) with several ad hoc removal/insertion operators and an embedded procedure to accelerate the calculation of the objective function. We carry out extensive computational experiments on a new set of 600 benchmark instances and compare our methods against two modern solvers with an incorporated warm-start mechanism as well as other state-of-the-art algorithms designed for closely related problems. A careful statistical analysis is conducted and results show that ET-ALNS outperforms the remaining methods by a significant margin.

A property-based hybrid genetic algorithm and tabu search for solving order acceptance and scheduling problem with trapezoidal penalty membership function

To improve the profitability and customer satisfaction, in make-to-order environment, manufacturers need to simultaneously consider which orders should be accepted and how to arrange these accepted orders for production, i.e., order acceptance and scheduling (OAS) problem. In practice, orders are often expected to be completed in a certain time interval, but the existing OAS-related studies mainly focus on the hard due date. Therefore, this study is dedicated to solving a single-machine OAS problem that considers the earliness/tardiness penalty under the common due window to maximize the total net profit (TNP), and the main innovative works are described as follows: (1) a trapezoidal earliness/tardiness penalty membership function under the common due window is designed, and a mathematical model is established to characterize the concerned problem; (2) six problem-specific properties are derived for determining which orders to be accepted or rejected, arranging the processing sequence and deciding the start processing time for these accepted orders; and (3) an effective property-based hybrid algorithm (GATS-SSRIR) is designed to deal with the concerned problem, which hybridizes the genetic algorithm, tabu search and six problem-specific properties. In numerical experiments, Taguchi method is first employed to optimize the parameter setting of GATS-SSRIR under different initialization methods. Second, the effectiveness of the proposed problem-specific properties is verified by comparing with other strategies, and the average improvement is 45.3%. Next, the superiority of the proposed GATS-SSRIR algorithm is demonstrated by algorithm comparison, and the average improvement is 67.3%. Finally, a sensitivity analysis on the common due window is performed. To sum up, the proposed problem properties and GATS-SSRIR algorithm are efficient and benefit, and the length of due window has a significant impact on the TNP.

Resource Allocation Scheduling with Position-Dependent Weights and Generalized Earliness–Tardiness Cost

Under just-in-time production, this paper studies a single machine common due-window (denoted by CONW) assignment scheduling problem with position-dependent weights and resource allocations. A job’s actual processing time can be determined by the resource assigned to the job. A resource allocation model is divided into linear and convex resource allocations. Under the linear and convex resource allocation models, our goal is to find an optimal due-window location, job sequence and resource allocation. We prove that the weighted sum of scheduling cost (including general earliness–tardiness penalties with positional-dependent weights) and resource consumption cost minimization is polynomially solvable. In addition, under the convex resource allocation, we show that scheduling (resp. resource consumption) cost minimization is solvable in polynomial time subject to the resource consumption (resp. scheduling) cost being bounded.

The Due Window Assignment Problems with Deteriorating Job and Delivery Time

This paper considers the single machine scheduling problem with due window, delivery time and deteriorating job, whose goal is to minimize the window location, window size, earliness and tardiness. Common due window and slack due window are considered. The delivery time depends on the actual processing time of past sequences. The actual processing time of the job is an increasing function of the start time. Based on the small perturbations technique and adjacent exchange technique, we obtain the propositions of the problems. For common and slack due window assignment, we prove that the two objective functions are polynomial time solvable in O(nlogn) time. We propose the corresponding algorithms to obtain the optimal sequence, window location and window size.

Single machine scheduling with common assignable due date/due window to minimize total weighted early and late work

Traditional scheduling models assume that due dates are predefined and the aim is to find a schedule that minimizes a given scheduling criterion with respect to the given set of due dates. A more recent trend consists of models that focus on coordinating two sets of decisions: due date assignment to customers and determining a job schedule. We follow this trend by analyzing a single machine scheduling problem, where the scheduler is tasked with assigning a common due date to all jobs in order to minimize an objective function that includes job-dependent penalties due to early and late work. We show that the problem is solvable in linear time if the common due date value is unbounded, and in O(nlogn) time if it is bounded from above. We then extend the analysis to the case where a common due window has to be assigned to all jobs. We show that when the location of the due window is unbounded, the problem is solvable in O(nlogn) time (and further in linear time if the length of the due window is unbounded as well). However, it becomes NP-hard when it is bounded. We complement our analysis by (i) providing a pseudo-polynomial time algorithm to solve this hard variant of the problem, and (ii) study two special cases of this hard variant that are solvable in polynomial time.

A property-based genetic algorithm for order acceptance and scheduling with common due window

In a competitive make-to-order production environment, limited production capacity and strict delivery requirement prompt the manufacturer to make decisions of order acceptance and scheduling simultaneously with maximization of the total net profit (TNP). In this context, this paper studies an order acceptance and scheduling (OAS) problem in a single machine environment, and the earliness/tardiness penalties are exsiting when an order is not delivered on time under the common due window. To solve this problem, the membership function of earliness/tardiness penalties is designed and a mathematical model for maximizing the TNP is established. According to the characteristics of the problem, three properties that are related to rejecting orders, sequencing orders and determining the starting time of orders are derived separately. Based on these, a property-based genetic algorithm (P-GA) is designed to search for the optimal solution. In numerical experiments, the effectiveness and superiority of the proposed P-GA are demonstrated by comparing with the solutions that are obtained by other two heuristic algorithms.

Single-Machine Due-Window Assignment Scheduling with Resource Allocation and Generalized Earliness/Tardiness Penalties

In this study, the due-window assignment single-machine scheduling problem with resource allocation is considered, where the processing time of a job is controllable as a linear or convex function of amount of resource allocated to the job. Under common due-window and slack due-window assignments, our goal is to determine the optimal sequence of all jobs, the due-window start time, due-window size, and optimal resource allocation such that a sum of the scheduling cost (including weighted earliness/tardiness penalty, weighted number of early and tardy job, weighted due-window start time, and due-window size) and resource consumption cost is minimized. We analyze the optimality properties, and provide polynomial time solutions to solve the problem under four versions of due-window assignment and resource allocation function.

Common due-window assignment and minmax scheduling with resource allocation and group technology on a single machine

This article considers the minmax common due-window assignment in group scheduling with resource allocation on a single machine. In this problem, jobs are partitioned into groups. In a group, all jobs are processed contiguously, and a common due-window is assigned to them. First, a case with constant processing times is examined. The objective is to minimize the sum of the maximal costs arising from the common due-window among the jobs in each group. This problem is proved to be polynomially solvable. Next, the problem is extended to the case that includes resource allocation. The processing time of each job is considered as either a linear or a convex function of the quantity of resource allocation. The objective function considers the total resource-consumption cost and sum of the maximal costs. For the special case of group-position-dependent penalties, polynomial-time solutions are presented.

Multitasking scheduling problems with a common due-window

We study multitasking scheduling and due-window assignment problems in a single machine, which can be found in various application domains. In multitasking environment, unfinished job always interrupts in-processing job. In common due window assignment, the aim is to find optimal due window to minimise the value of the earliness and tardiness penalty. In this paper, we study two problems, where the objective of the first problem is minimise the earliness, tardiness, due-window starting time, and due-window size costs, the objective of the second problem is minmax common due-date with completion time penalty, then we obtain some analytical properties and provide polynomial time solutions. Finally, the experimental results show that the proposed methods are effective.

Minmax common flow-allowance problems with convex resource allocation and position-dependent workloads

We study minmax due-date based on common flow-allowance assignment and scheduling problems on a single machine, and extend known results in scheduling theory by considering convex resource allocation. The total cost function of a given job consists of its earliness, tardiness and flow-allowance cost components. Thus, the common flow-allowance and the actual jobs’ processing times are decision variables, implying that the due-dates and actual processing times can be controlled by allocating additional resource to the job operations. Consequently, our goal is to optimize a cost function by seeking the optimal job sequence, the optimal job-dependent due-dates along with the actual processing times. In all addressed problems we aim to minimize the maximal cost among all the jobs subject to a constraint on the resource consumption. We start by analyzing and solving the problem with position-independent workloads and then proceed to position-dependent workloads. Finally, the results are generalized to the method of common due-window. For all studied problems closed form solutions are provided, leading to polynomial time solutions.

Due-window assignment scheduling with learning and deterioration effects

<p style='text-indent:20px;'>This paper considers single machine due-window assignment scheduling problems with position-dependent weights. Under the learning and deterioration effects of jobs processing times, our goal is to minimize the weighted sum of earliness-tardiness, starting time of due-window, and due-window size, where the weights only depends on their position in a sequence (i.e., position-dependent weights). Under common due-window (CONW), slack due-window (SLKW) and different due-window (DIFW) assignments, we show that these problems remain polynomial-time solvable.</p>

A note on the single machine CON and CONW problems with lot scheduling

We study extensions of the classical single machine common due-date (CON) and common due-window (CONW) assignment problems to the setting of lot scheduling. In the CON problem, all the jobs share a common due-date, and jobs completed prior to or after the due-date are penalized according to their earliness/tardiness. In CONW, there exists a time interval, such that jobs completed within this interval are not penalized. In both cases the due-date/due-window are decision variables. In lot scheduling, a number of customer orders of different sizes may be processed in the same lot. We allow order splitting between consecutive lots. The objective is to find the order allocation to lots, such that the total cost of earliness, tardiness and due-date/due-window is minimized. Given $$n$$ orders, and under the very realistic assumption that the lot capacity is of the order of $$n$$ , we introduce polynomial time dynamic programming algorithms for both extensions. Our numerical tests indicate that both algorithms can easily solve medium-size problems.

Due-Window Assignment and Resource Allocation Scheduling with Truncated Learning Effect and Position-Dependent Weights

This paper studies single-machine due-window assignment scheduling problems with truncated learning effect and resource allocation simultaneously. Linear and convex resource allocation functions under common due-window (CONW) assignment are considered. The goal is to find the optimal due-window starting (finishing) time, resource allocations and job sequence that minimize a weighted sum function of earliness and tardiness, due window starting time, due window size, and total resource consumption cost, where the weight is position-dependent weight. Optimality properties and polynomial time algorithms are proposed to solve these problems.

Due-window assignment scheduling in the proportionate flow shop setting

In this paper, we consider due-window assignment scheduling in the proportionate flow shop setting with position-dependent weights where the weights depend on the position in which a job is scheduled. Under the common due-window (CONW) and slack due-window (SLKW) assignment methods, the location of the window and its properties are established. The objective is to determine the sequence of all jobs to minimize the total weighted cost function where the total weighted cost function must also consider the window start time and size. Based on these considerations, the corresponding algorithm and algorithm complexity are proposed.

An approximation algorithm for a supply-chain scheduling problem with an assignable common due window and holding time

This paper studies single machine scheduling with batch deliveries, where a common due window for all jobs has to be determined, not given in advance. The objective is to minimize the overall cost for the process and delivery. Concretely, it includes the penalty of a job being early or tardy, the cost for holding and delivering a job, and the cost incurred by a late starting or a long duration of the common due window. Observing the NP-hardness, we provide an optimal algorithm of the problem and convert it to a fully polynomial time approximation scheme for a special case.

Common due-window assignment for single-machine scheduling with generalized earliness/tardiness penalties and a rate-modifying activity

ABSTRACT This article investigates the single-machine common due-window assignment problem with generalized earliness/tardiness penalties and a rate-modifying activity. Job processing times include two cases: one with constant values and another with time-dependent processing times (deterioration effect). Considering the maintenance activity, the maintenance time is a fixed constant. The goal is to determine the position of the common due window and the optimal sequence such that the following objective function is minimized: the weighted penalties for the sum of earliness and tardiness, the weighted number of early and delayed, and the weighted due-window starting time and size. It is proved that the problem can be solved in time, where n is the number of jobs.

Common Due Window Assignment Scheduling with Proportional Linear Deterioration Effects

In this paper, single-machine scheduling problems with proportional linear deterioration effects and common due window assignment simultaneously are considered. Two different objective functions are studied, the first is to minimize the sum of the number of early jobs, number of tardy jobs and due window location and due window size, the second is to minimize the sum of the earliness cost, tardiness cost, due window location and due window size. Optimality properties for all problems are provided and polynomial time algorithms for solving these problems are given.

Research on common due window assignment flowshop scheduling with learning effect and resource allocation

ABSTRACTIn this article, the two-machine no-wait permutation flowshop scheduling problem with common due window assignment, learning effect and resource allocation is considered, wherein learning effect and resource allocation mean that the processing time of a job is a function of its position in a sequence and its amount of resource allocation. According to the common due window assignment method, each job is associated with a common due window, which is a decision variable. The goal is to determine the sequence of jobs, common due window starting time, due window size and resource allocation such that the linear weighted sum of job earliness, tardiness, due window size and resource cost is minimized. This article shows that the scheduling problem can be solved in polynomial time.