Due date assignment in single machine with stochastic processing times

This paper considers two different due date assignment and sequencing problems in single machine where the processing times of jobs are random variables. The first problem is to minimise the maximum due date so that all jobs are stochastically on time. It is shown that sequencing the jobs in decreasing service level (DSL) order optimally solves the problem. The results are then extended for two special cases of flow shop problem. The other problem is to minimise a total cost function which is a linear combination of three penalties: penalty on job earliness, penalty on job tardiness, and penalty associated with long due date assignment. The assignment of a common due date and distinct due dates are investigated for this problem. It is shown that the optimal sequence for the case of common due date is V-shaped.     

Multitasking parallel-machine scheduling with machine-dependent slack due-window assignment

We consider the problem of parallel-machine scheduling with machine-dependent slack (SLK) due-window assignment in the multitasking environment, which exists in various application domains such as Internet services, project management, and manufacturing. Motivated by practical observations, we extend the original model of multitasking to a more general model where each job’s interruption proportion depends on the job itself and its processing position. In the light of individualised service, we consider SLK due-window assignment. Our objective is to minimise the total cost that comprises the earliness, tardiness, and due-window-related costs. Finding that an optimal schedule exists when each machine is occupied by at least one job, we show that the problem is polynomially solvable. We provide a more efficient solution algorithm for a special case of the problem. Finally, we present numerical examples to illustrate the application of the theoretical results and working of the solution algorithms.     

Single-machine scheduling and common due date assignment with potential machine disruption

This paper studies a single-machine due date assignment and scheduling problem in a disruptive environment, where a machine disruption may occur at a particular time that will last for a period of time with a certain probability, and the job due dates are determined by the decision-maker using the popular common due date assignment method. The goal is to determine jointly the optimal job sequence and the common due date so as to minimise the expected value of an integrated cost function that includes the earliness, tardiness and due date assignment costs. We analyse the computational complexity status of various cases of the problem, and develop pseudo-polynomial-time solution algorithms, randomised adaptive search algorithms, and fully polynomial-time approximation schemes for them, if viable. Finally, we conduct extensive numerical testing to assess the performance of the proposed algorithms.     

Research on scheduling with job-dependent learning effect and convex resource-dependent processing times

We study resource allocation scheduling with job-dependent learning effect on a single machine with or without due date assignment considerations. For a convex resource processing time function, we provide a polynomial time algorithm to find the optimal job sequence, and resource allocations that minimise the schedule criterion (the total compression cost) subject to the constraint that the total compression cost (the schedule criterion) is less than or equal to a fixed amount.     

Single-machine due-window assignment scheduling based on common flow allowance,learning effect and resource allocation

This article considers a single-machine due-window assignment scheduling problem based on a common flow allowance (i.e. all jobs have slack due window (SLKW)). We assume that the actual processing time of a job is a function of its position in a sequence (learning effect) and its continuously divisible and non-renewable resource allocation. The problem is to determine the optimal due windows, the optimal resource allocation and the processing sequence simultaneously to minimise costs for earliness, tardiness, the window location, window size, makespan and resource consumption. For a linear or a convex function of the amount of a resource allocated to the job, we provide a polynomial time algorithm, respectively. Some extensions of the problem are also shown.     

Determination of an optimal common due date and optimal sequence in a single machine job shop

In this paper we consider an n jobs one machine sequencing problem in which all jobs have a common due date and a deviation in its completion time occurs when a job is completed before or after the common due date. The objective is to find an optimal value of this common due date and a corresponding optimal sequence such that the mean absolute deviation of the completion times of the jobs in the optimal sequence from the corresponding optimal common due date is at its global minimum. Starting with an arbitrary sequence we relate the problem to a generalized linear goal program from which some basic results are proved using elementary properties of linear equations and a linear goal programming problem. Using these results and the idea of sensitivity analysis in linear programming, an algorithm is developed that determines the optimal due date and the corresponding optimal sequence yielding the global minimum value of the mean absolute deviation of the completion times of the jobs in the optimal sequence from the corresponding optimal common due date. In the end a numerical example to explain the algorithm is provided.     

Multiple machine JIT scheduling: a tabu search approach

This paper presents an approach to solving the multiple machine, non-preemptive, earliness-tardiness scheduling problem with unequal due dates in a flow shop with machine tiers (FMT). In this variant of the flow shop problem, machines are arranged in tiers or groups, and the jobs must visit one machine in each tier. The processing times, machine assignments, and due dates are deterministic and known in advance. The objective is to find a permutation schedule that minimizes the total deviation of each job from its due date. A tabu search (TS) meta-heuristic combined with an LP evaluation function is applied to solve this problem and results are compared to optimal permutation solutions for small problems and the earliest due date schedule for large problems. Several neighborhood generation methods and two diversification strategies are examined to determine their effect on solution quality. Results show that the TS method works well for this problem. TS found the optimal solution in all but one of the small problem instances and improved the earliest due date solutions for larger instances where no optimal solutions could be found.     

Common due date assignment scheduling for a no-wait flowshop with convex resource allocation and learning effect

This article addresses the no-wait flowshop scheduling problem with simultaneous consideration of common due date assignment, convex resource allocation and learning effect in a two machine setting. The processing time of each job can be controlled by its position in a sequence and also by allocating extra resource, which is a convex function of the amount of a common continuously divisible resource allocated to the job. The objective is to determine the optimal common due date, the resource allocation and the schedule of jobs such that the total earliness, tardiness and common due date cost (the total resource consumption cost) are minimized under the constraint condition that the total resource consumption cost (the total earliness, tardiness and common due date cost) is limited. Polynomial time algorithms are developed for two versions of the problem.     

No-wait two-machine permutation flow shop scheduling problem with learning effect,common due date and controllable job processing times

We consider a two-machine no-wait permutation flow shop common due date assignment scheduling problem where the processing time of a job is given as a function of its position in the sequence and its amount of resource allocated to this job. The common due date (CON) assignment method means that all the jobs are given a common due date. We need to make a decision on the common due date, resource allocation and the sequence of jobs to minimise total earliness, tardiness, common due date cost and total resource cost. We show that the problem remains polynomially solvable under the proposed model.     

Single-machine batch delivery scheduling and common due-date assignment with a rate-modifying activity

We consider batch delivery scheduling on a single machine, where a common due-date is assigned to all the jobs and a rate-modifying activity on the machine may be scheduled, which can change the processing rate of the machine. Thus the actual processing time of a job is variable depending on whether it is processed before or after the rate-modifying activity. The objective is to determine the optimal job sequence, the optimal partition of the job sequence into batches, the optimal assigned common due-date, and the optimal location of the rate-modifying activity simultaneously to minimize the total cost of earliness, job holding, weighted number of tardy jobs, due-date assignment, and batch delivery. We derive some structural properties of the problem, based on which we design polynomial-time algorithms to solve some special cases of the problem.     

A note on single machine scheduling and due date assignment with general position-dependent processing times

This note considers single machine scheduling and due date assignment in which a job’s processing time depends on its position in a sequence. The objective functions include the cost of changing the due dates, the total cost of discarded jobs that cannot be completed by their due dates and the total earliness of the scheduled jobs. We analyse these problems with three different due date assignment methods. We provide a generic polynomial-time dynamic programming algorithm to solve the problems.     

SINGLE-MACHINE SCHEDULING WITH CONTROLLABLE PROCESSING TIMES AND EARLINESS,TARDINESS AND COMPLETION TIME PENALTIES

The paper considers the problem of scheduling nindependent and simultaneously available jobs on a single machine, where the job processing times are compressible as a linear cost function. The objective is to find an optimal permutation of the jobs, an optimal due date and the optimal processing times which jointly minimize a cost function consisting of the earliness, tardiness, completion time and compressing costs. It shows that the problem can be solved as an assignment problem.     

ON THE DUALITY APPROACH TO OPTIMAL DUE DATE DETERMINATION AND SEQUENCING IN A JOB SHOP

This paper considers the problem of finding an optimal CON due date and sequencing of n independent jobs to be processed on a single machine by minimizing the total value of lateness. A linear programming model is developed to find an optimal CON due date which is solved by considering its dual. A procedure to find the optimal job sequence is then presented and elaborated by a numerical example.     

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.     

A two‐phase approach for single machine scheduling problems: Minimizing the total absolute deviation

Abstract

This paper presents a heuristic for solving a single machine scheduling problem with the objective of minimizing the total absolute deviation. The job to be scheduled on the machine has a processing time, p_i , and a preferred due date, d_i . The total absolute deviation is defined as the sum of the earliness or tardiness of each job on a schedule 5. This problem is proved to be NP‐complete by Garey et al. [8]. As a result, we developed a two‐phase procedure to provide a near‐optimal solution to this problem. The two‐phase procedure includes the following steps: First, a greedy heuristic is applied to the set of jobs, N, to generate a “good” initial sequence. According to this initial sequence, we run Garey's local optimization algorithm to provide an initial schedule. Then, a pairwise switching algorithm is adopted to further reduce the total deviation of the schedule. The effectiveness of the two‐phase procedure is empirically evaluated and has been found to indicate that the solutions obtained from this heuristic procedure are often better than other heuristic approaches.     

A Review of: “PRACTICAL OPTIMIZATION”

We consider a generalized optimal common due-date assignment problem and derive the optimality conditions for finding the optimal solution in this paper. We show that some versions of the common due-date determination problem can be treated as special cases of this generalized problem. For these special cases, we show that closed-form optimal solutions can be obtained from the optimality conditions. As for the solution of the generalized problem, we suggest an iterative solution procedure to help determine the optimal solution. Finally, we discuss the limiting behaviour of the optimal solution in a special situation and derive the asymptotic result     

Genetic algorithms for job shop scheduling problems with alternative routings

The purpose of this research is to solve a general job shop problem with alternative machine routings. We consider four performance measures: mean flow time, makespan, maximum lateness, and total absolute deviation from the due dates. We first develop mixed-integer linear programming (MILP) formulations for the problems. The MILP formulations can be used either to compute optimal solutions for small-sized problems or to test the performance of existing heuristic algorithms. In addition, we have developed a genetic algorithm that can be used to generate relatively good solutions quickly. Further, computational experiments have been performed to compare the solution of the MILP formulations with that of existing algorithms.     

Parallel-machine scheduling with controllable processing times and rate-modifying activities to minimise total cost involving total completion time and job compressions

In this paper, we consider unrelated parallel-machine scheduling involving controllable processing times and rate-modifying activities simultaneously. We assume that the actual processing time of a job can be compressed by allocating a greater amount of a common resource to process the job. We further assume that each machine may require a rate-modifying activity during the scheduling horizon. The objective is to determine the optimal job compressions, the optimal positions of the rate-modifying activities and the optimal schedule to minimise a total cost function that depends on the total completion time and total job compressions. If the number of machines is a given constant, we propose an efficient polynomial time algorithm to solve the problem.