Single-machine earliness–tardiness scheduling with two competing agents and idle time

Two-agent scheduling has gained a lot of research attention recently. Two competing agents who have their own objective functions have to perform their respective set of jobs on one or more shared machines. This study considers a two-agent single-machine earliness and tardiness scheduling problem where jobs have distinct due dates and unforced idleness in between any two consecutive jobs is allowed. The objective is to minimize the total earliness and tardiness of jobs from one agent given that the maximum earliness–tardiness of jobs from the other agent cannot exceed an upper bound. In other words, each job from the second agent has a hard due window, whereas each job from the first agent will incur a penalty if completed either before or after its due date. Two mathematical models of the problem are presented, and several necessary optimality conditions are derived. By exploiting the established dominance properties, heuristic algorithms are developed for the problem. Finally, computational experiments are conducted to assess the models and heuristic procedures.     

Permutation flow shop scheduling with earliness and tardiness penalties

We consider the permutation flow shop scheduling problem with earliness and tardiness penalties (E/T) and common due date for jobs. We show that the problem can be sub-divided into three cases: (i) the due date is such that all jobs are necessarily tardy; (ii) the due date is unrestricted; and (iii) the due date is between the two. Based on analytical results we provide partial characterisation of the optimal solution and develop a comprehensive approach for solving the problem over the entire range of due dates. Our approach, which draws upon the existing literature and results for the single machine problem, successfully exploits the properties of the optimal solution. Limited computational results indicate that the performance of the heuristic is reasonable and has the potential to significantly improve performance. This approach has been incorporated as part of the scheduling module of the production planning and scheduling system we developed for a medium-sized bulk drug manufacturer.     

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.     

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.     

Heuristic methods for the single machine scheduling problem with different ready times and a common due date

The single machine scheduling problem with a common due date and non-identical ready times for the jobs is examined in this work. Performance is measured by the minimization of the weighted sum of earliness and tardiness penalties of the jobs. Since this problem is NP-hard, the application of constructive heuristics that exploit specific characteristics of the problem to improve their performance is investigated. The proposed approaches are examined through a computational comparative study on a set of 280 benchmark test problems with up to 1000 jobs.     

Error bound for common due date assignment and job scheduling on parallel machines

We consider a heuristic which has been applied to assign a common due date to a set of n jobs and schedule them on a set of m parallel and identical machines so that the weighted sum of the due date, earliness and tardiness is approximately minimized. We alter the heuristic slightly and show that the revised version is asymptotically optimal as n→∞.     

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.     

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 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.     

A Meta-RaPS for the early/tardy single machine scheduling problem

This paper investigates a meta-heuristic solution approach to the early/tardy single machine scheduling problem with common due date and sequence-dependent setup times. The objective of this problem is to minimise the total amount of earliness and tardiness of jobs that are assigned to a single machine. The popularity of just-in-time (JIT) and lean manufacturing scheduling approaches makes the minimisation of earliness and tardiness important and relevant. In this research the early/tardy problem is solved by Meta-RaPS (meta-heuristic for randomised priority search). Meta-RaPS is an iterative meta-heuristic which is a generic, high level strategy used to modify greedy algorithms based on the insertion of a random element. In this case a greedy heuristic, the shortest adjusted processing time, is modified by Meta-RaPS and the good solutions are improved by a local search algorithm. A comparison with the existing ETP solution procedures using well-known test problems shows Meta-RaPS produces better solutions in terms of percent difference from optimal. The results provide high quality solutions in reasonable computation time, demonstrating the effectiveness of the simple and practical framework of Meta-RaPS.     

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.     

Simulated annealing for parallel machine scheduling with earliness-tardiness penalties and sequence-dependent set-up times

Scheduling problems with earliness and tardiness penalties are commonly encountered in today's manufacturing environment due to the current emphasis on the just-in-time (JIT) production philosophy. The problem studied in this work is the parallel machine earliness-tardiness non-common due date sequence-dependent set-up time scheduling problem (PETNDDSP) for jobs with varying processing times, where the objective is to minimize the sum of the absolute deviations of job completion times from their corresponding due dates. The research presented provides a first step towards obtaining near optimal solutions for this problem using local search heuristics in the framework of a meta-heuristic technique known as simulated annealing (SA). The computational study shows that, using the SA methodology, significant improvements to the local search heuristic solutions can be achieved for problems of this type.     

Minimizing earliness–tardiness on a single burn-in oven with a common due date and maximum allowable tardiness constraint

This paper considers a scheduling problem for a single burn-in oven in the semiconductor manufacturing industry where the oven is a batch processing machine with restricted capacity. The batch processing time is set by the longest processing time among those of all the jobs contained in the batch. All jobs are assumed to have the same due date. The objective is to minimize the sum of the absolute deviations of completion times from the due date (earliness–tardiness) of all jobs under the constraint that the maximum tardiness should be less than or equal to the maximum allowable time value. We suggest several two-phase heuristic algorithms for this problem. In the first phase, some heuristic algorithms are developed without maximum allowable tardiness constraint. If the schedule from the first phase violates the maximum tardiness constraint, then the schedule is changed to satisfy maximum allowable tardiness constraint in the second phase. The suggested heuristics are based on genetic algorithms and dominance properties of optimal schedules. We present the results of computational experiments that clearly show the solution quality obtained by the suggested heuristics.     

A canned food scheduling problem with batch due date

This article considers a canned food scheduling problem where jobs are grouped into several batches. Jobs can be sent to the next operation only when all the jobs in the same batch have finished their processing, i.e. jobs in a batch, have a common due date. This batch due date problem is quite common in canned food factories, but there is no efficient heuristic to solve the problem. The problem can be formulated as an identical parallel machine problem with batch due date to minimize the total tardiness. Since the problem is NP hard, two heuristics are proposed to find the near-optimal solution. Computational results comparing the effectiveness and efficiency of the two proposed heuristics with an existing heuristic are reported and discussed.     

Scheduling on uniform parallel machines with periodic unavailability constraints

Scheduling problems under unavailability constraints has become a popular research topic in the last few years. Despite it’s important application in the real world, the uniform parallel machine scheduling problem was the least studied due to its complexity. In this paper, we investigated the uniform parallel machine scheduling problem under deterministic availability constraints. Each machine is subject to one unavailability period. Different versions of the problem regarding the type of jobs (identical and non-identical) and the performance measures (the total completion times and the makespan) were studied. For the case of identical jobs and for both performance measures, we developed linear programming models and optimal algorithms to provide a solution to the problem. For the case of non-identical jobs, we proved that the problem is NP-hard and propose a quadratic program. Because, this later cannot solve problems with very large number of jobs and machines, a heuristic was developed to find near optimal solutions to the problem especially with very large number of jobs and machines. The computational results showed that the heuristic’s performance is very high regardless the dimensions of problem instances.     

Jobs and tool sequencing in an automated manufacturing environment

A practical approach is presented for determining the sequence of jobs and tools in the magazine that would be required to process the jobs in an automated manufacturing environment. Each job has to be completed before a given due date. The magazine has a limited capacity necessitating setups which increase the lead times, Processing jobs also requires an appropriate fixture. Setting up a fixture also contributes to the setup times. A heuristic procedure is developed which determines the above sequences while minimizing the total setup and processing times. The performance of the heuristic is checked against optimal solutions for small-size problems while bounds are obtained (based on statistical lower bounding procedures) on the optimal solution for large-size problems. Computational results are provided for 155 test problems.     

Machine scheduling in the presence of sequence-dependent setup times and a rate-modifying activity

Rate modifying activity (RM) is a type of maintenance after which the processing rate of the machine increases. RM is a very new topic in academic studies. However, it is very common in real world situations. In this paper, we study the integrated problem of assigning a common due-date to all jobs, scheduling the jobs and making decisions about the position of RM in a single machine environment in which the setup times are sequence dependent. The objective is minimising the summation of earliness costs, tardiness costs and due date related costs. This problem has never been studied in the literature with any arbitrary criterion. We construct a time-dependent travelling salesman problem (TDTSP) formulation for this problem. The position of the optimal common due date and some dominance properties for the position of RM are presented. A branch and bound (B&B) procedure is developed to solve the problem optimally. Numerical results justify the effectiveness of the B&B method for small problems. For larger problems, two robust metaheuristics are proposed.     

API-based two-dimensional dispatching decision-making approach for semiconductor wafer fabrication with operation due date–related objectives

This paper presents an adjacent pairwise interchanges (API)-based two-dimensional dispatching decision-making approach for semiconductor wafer fabrication with operation due date-related objectives. Each time when a machine becomes idle, the proposed dispatcher chooses a target processing job from the competing jobs and assigns it a start time. Giving the operation due date information of each competing job, we formulate this dispatcher as the mean absolute deviation problem to keep the jobs finished around their operation due dates in a proactive way. Dominance properties of this problem are established using proof by APIs. Then, a heuristic comprised of job selection within candidate set, movement of job cluster and local search is designed to solve this problem more efficiently. Numerical experiments validate the efficiency of the proposed heuristic in a single-machine environment as well as in a simulated wafer fab abstracted from practice. In comparison with four most referenced due date-related dispatching rules, the simulation study reveals the benefits brought by the two-dimensional dispatching decision with different due date tightness taken into account.     

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 comparison of metaheuristic procedures to schedule jobs in a permutation flow shop to minimise total earliness and tardiness

This paper considers the problem of scheduling jobs in a permutation flow shop with the objective of minimising total earliness and tardiness. A genetic algorithm is proposed for the problem. This procedure and five other procedures were tested on problem sets that varied in terms of number of jobs, machines and the tightness and range of due dates. It was found that the genetic algorithm procedure was consistently effective in generating good solutions relative to the other procedures.