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.     

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.     

Resource-constrained scheduling with hard due windows and rejection penalties

This work studies a scheduling problem where each job must be either accepted and scheduled to complete within its specified due window, or rejected altogether. Each job has a certain processing time and contributes a certain profit if accepted or penalty cost if rejected. There is a set of renewable resources, and no resource limit can be exceeded at any time. Each job requires a certain amount of each resource when processed, and the objective is to maximize total profit. A mixed-integer programming formulation and three approximation algorithms are presented: a priority rule heuristic, an algorithm based on the metaheuristic for randomized priority search and an evolutionary algorithm. Computational experiments comparing these four solution methods were performed on a set of generated benchmark problems covering a wide range of problem characteristics. The evolutionary algorithm outperformed the other methods in most cases, often significantly, and never significantly underperformed any method.     

Convex resource allocation scheduling in the no-wait flowshop with common flow allowance and learning effect

We study the problem of two-machine no-wait flowshop scheduling with learning effect and convex resource-dependent processing times. Under the condition of the due-date assignment with common flow allowance (i.e. slack (SLK) due-date assignment), we provide a bi-criteria analysis where the first criterion is to minimise the scheduling criteria (i.e. the weighted sum of earliness, tardiness and flow allowance costs), and the second criterion is to minimise the resource consumption cost (i.e. the weighted sum of resource consumption cost). The objective is to determine the optimal job sequence, resource allocations and common (flow allowance) slack time that minimise the three different versions of the two criteria. We prove that these problems can be solved in polynomial time.     

Due-window assignment and scheduling with general position-dependent processing times involving a deteriorating and compressible maintenance activity

In this paper, we consider common due-window assignment and scheduling problems with general position-dependent processing times involving deteriorating and compressible maintenance activity on a single machine. Two models associated with maintenance activity are examined in this article, in which the maintenance length is assumed to be either time-dependent and compressible or position-dependent and compressible. The objective is to find jointly the location and size of due-window, position of maintenance as well as resource amount allocated to it, and job sequence to minimise a total cost function based on earliness, tardiness, window location, window size and resource cost. We show that the problem considered in each of the two models’ setting can be optimally solved with polynomial time algorithm by reducing to assignment problem. Finally, two examples are provided to illustrate the solution procedures.     

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 scheduling problems with generalised due-dates and job-rejection

We study single machine scheduling problems. Generalised due dates are assumed, i.e. job due dates are specified according to the positions of the jobs in the sequence, rather than their identity. Thus, assuming that due dates are numbered in a non-decreasing order, the jth due date refers to the job assigned to the jth position. In addition, we allow the option of job rejection, i.e. not all jobs must be processed. In this case, the scheduler is penalised for each rejected job, and the total rejection cost becomes part of the objective function. Two objective functions are considered: maximum tardiness plus rejection cost, and total tardiness plus rejection cost. Both problems are proved to be NP-hard. Pseudo-polynomial dynamic programmes and efficient heuristics are introduced and tested numerically.     

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.     

Due-date assignment and single-machine scheduling with generalised position-dependent deteriorating jobs and deteriorating multi-maintenance activities

This paper addresses a single-machine scheduling problem with simultaneous consideration of due-date assignment, generalised position-dependent deteriorating jobs, and deteriorating maintenance activities. It is assumed that the actual processing time of a job is a general non-decreasing function depending on the number of maintenance activities performed before it and its position in a sequence. Moreover, the machine may be subject to several maintenance activities up to a limit over the scheduling horizon. The maintenance activities do not necessarily restore the machine fully to its original perfect state and the duration of a maintenance activity depends on its start time. The objective is to find jointly the optimal job sequence, maintenance frequency and maintenance positions to minimise an objective function that includes the cost of due-date assignment, the cost of discarding jobs that cannot be completed by their due dates and the earliness of the scheduled jobs under the popular CON and SLK due-date assignment methods. We provide polynomial-time solution algorithms for various versions 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.     

A note on resource allocation scheduling with position-dependent workloads

In this note, single machine scheduling with concurrent resource allocation and position-dependent workloads is studied. The aim is to find jointly the optimal sequence and the optimal resource allocation. A bicriteria analysis of the problem is provided where the first criterion is to minimize the scheduling cost (i.e. makespan, total completion time, total absolute differences in completion times, total absolute differences in waiting times) and the second criterion is to minimize the total resource consumption cost. It is proved that four bicriteria problems can be solved efficiently.     

Due-date assignment scheduling involving job-dependent learning effects and convex resource allocation

ABSTRACT

This article addresses single machine resource allocation scheduling problems with learning effects, where learning effects mean job-dependent position-based learning effects. For the common due-date assignment (CON) and slack due-date assignment (SLK) methods, a bi-cost analysis of the scheduling cost and the total weighted resource consumption cost is provided. The objective is to determine the optimal job sequence and the resource allocation simultaneously, such that the scheduling cost (the total weighted resource consumption cost) is minimized subject to the total weighted resource consumption cost (the scheduling cost) being limited. Solution procedures are provided for the problems under consideration.     

Minimising makespan on a batch processing machine using heuristics improved by an enumeration scheme

Batch processing machines can process several job simultaneously and are encountered in many manufacturing environments. Jobs in a batch are processed together and have the same start and end processing time. Since jobs are non-identical in job sizes and job processing times, they should be reasonably scheduled to improve the machine utilisation and processing efficiency. Two well-known heuristics, first fit longest processing time and best fit longest processing time (BFLPT), are improved in this study by considering identical job sizes and then BFLPT is further improved by an enumeration scheme proposed. Computational experiments are conducted to evaluate the performance of the improvement and the results are compared with the existing heuristics.     

Single-machine common/slack due window assignment problems with linear decreasing processing times

This paper studies linear non-increasing processing times and the common/slack due window assignment problems on a single machine, where the actual processing time of a job is a linear non-increasing function of its starting time. The aim is to minimize the sum of the earliness cost, tardiness cost, due window location and due window size. Some optimality results are discussed for the common/slack due window assignment problems and two O(n log n) time algorithms are presented to solve the two problems. Finally, two examples are provided to illustrate the correctness of the corresponding algorithms.     

Scheduling with non-decreasing deterioration jobs and variable maintenance activities on a single machine

There is a situation found in many manufacturing systems, such as steel rolling mills, fire fighting or single-server cycle-queues, where a job that is processed later consumes more time than that same job when processed earlier. The research finds that machine maintenance can improve the worsening of processing conditions. After maintenance activity, the machine will be restored. The maintenance duration is a positive and non-decreasing differentiable convex function of the total processing times of the jobs between maintenance activities. Motivated by this observation, the makespan and the total completion time minimization problems in the scheduling of jobs with non-decreasing rates of job processing time on a single machine are considered in this article. It is shown that both the makespan and the total completion time minimization problems are NP-hard in the strong sense when the number of maintenance activities is arbitrary, while the makespan minimization problem is NP-hard in the ordinary sense when the number of maintenance activities is fixed. If the deterioration rates of the jobs are identical and the maintenance duration is a linear function of the total processing times of the jobs between maintenance activities, then this article shows that the group balance principle is satisfied for the makespan minimization problem. Furthermore, two polynomial-time algorithms are presented for solving the makespan problem and the total completion time problem under identical deterioration rates, respectively.     

Two Single Machine Sequencing Problems Involving Controllable Job Processing Times

This paper presents simple methods for solving two single machine sequencing problems when job processing times are themselves decision variables having their own associated linearly varying costs. These are the problems of minimizing the total processing cost plus either the average flow cost or the maximum tardiness cost. The paper treats only problems with zero ready times and no precedence constraints.     

Single CNC machine scheduling with controllable processing times and multiple due dates

In this study, we solve the single CNC machine scheduling problem with controllable processing times. Our objective is to maximize the total profit that is composed of the revenue generated by the set of scheduled jobs minus the sum of total weighted earliness and weighted tardiness, tooling and machining costs. Customers offer multiple due dates to the manufacturer, each coming with a distinct price for the order that is decreasing as the date gets later, and the manufacturer has the flexibility to accept or reject the orders. We propose a number of ranking rules and scheduling algorithms that we employ in a four-stage heuristic algorithm that determines the processing times for each job and a final schedule for the accepted jobs simultaneously, to maximize the overall profit.     

Single-machine scheduling with deteriorating effects and machine maintenance

In this paper, the single-machine scheduling problems with deteriorating effects and a machine maintenance are studied. In this circumstance, the deterioration rates of the jobs during the machining process are the same which reduces the production efficiency. The actual processing time of the job is a linearly increasing function of the starting time. In this process, the machine only performs a maintenance activity, and the maintenance time is a fixed value. After the maintenance work is completed, the machine will be restored to the initial state, and the deterioration of the job will be start again. The goal is to determine the optimal schedule in order to minimise the maximum completion time (i.e. the makespan) and the sum of job completion times. We prove that both problems are polynomial time solvable, and we also provide the corresponding algorithms.     

Rescheduling with controllable processing times for number of disrupted jobs and manufacturing cost objectives

We consider a machine rescheduling problem that arises when a disruption such as machine breakdown occurs to a given schedule. Machine unavailability due to a breakdown requires repairing the schedule as the original schedule becomes infeasible. When repairing a disrupted schedule a desirable goal is to complete each disrupted job on time, i.e. not later than the planned completion time in the original schedule. We consider the case where processing times of jobs are controllable and compressing the processing time of a job requires extra processing cost. Usually, there exists a nonlinear relation between the processing time and manufacturing cost. We solve a bicriteria rescheduling problem that trades off the number of on-time jobs and manufacturing cost objectives. We give a mixed-integer second-order cone programming formulation for the problem. We develop a heuristic search algorithm to generate efficient solutions for the problem. Heuristic algorithm searches solution space by moving and swapping jobs among machines. We develop cost change estimates for job moves and swaps so that the heuristic implements only promising moves and hence generates a set of efficient solutions in reasonably short CPU times.     

n jobs and m machines job-shop problems with sequence-dependent set-up times

This paper presents a mathematical model based on the branch-and-bound technique to solve static scheduling problems involving n jobs and m machines where the objective is to minimize the cost of setting up the machines. Set-up times are sequence dependent and not included in processing times. There is a finite non-zero cost associated with setting the machines which is different for each machine. It is further assumed that the routing may be different for different jobs and a job may return to a machine more than once.