The single-machine earliness-tardiness scheduling problem with due date assignment and resource-dependent processing times

We study the earliness-tardiness scheduling problem on a single machine with due date assignment and controllable processing times. We analyze the problem with three different due date assignment methods and two different processing time functions. For each combination of these, we provide a polynomial-time algorithm to find the optimal job sequence, due date values and resource allocation minimizing an objective function which includes earliness, tardiness, due date assignment, makespan and total resource consumption costs.     

A due-window assignment problem with position-dependent processing times

We extend a classical single-machine due-window assignment problem to the case of position-dependent processing times. In addition to the standard job scheduling decisions, one has to assign a time interval (due-window), such that jobs completed within this interval are assumed to be on time and not penalized. The cost components are: total earliness, total tardiness and due-window location and size. We introduce an O(n³) solution algorithm, where n is the number of jobs. We also investigate several special cases, and examine numerically the sensitivity of the solution (schedule and due-window) to the different cost parameters.     

Single-machine scheduling with common due-window assignment for deteriorating jobs

In this paper, we consider a single-machine common due-window assignment scheduling problem with deteriorating jobs. Jobs’ processing times are defined by function of their starting times and job-dependent deterioration rates that are related to jobs and are not all equal. The objective is to determine an optimal combination of sequence and common due-window location so as to minimize the weighted sum of earliness, tardiness and due-window location penalties. We propose an O(n² log n) time algorithm to solve the problem and discuss several instances to illustrate it.     

Hybrid flowshop scheduling with machine and resource-dependent processing times

Most of research in production scheduling is concerned with the optimization of a single criterion. However the analysis of the performance of a schedule often involves more than one aspect and therefore requires a multi-objective treatment. In this research, with combination of two multiple objective decision-making methods, min–max and weighted techniques, a new solution presentation method and a robust hybrid metaheuristic, we solved sequence-dependent setup time hybrid flowshop scheduling problems. In this paper for reflecting real-world situation adequately, we assume the processing time of each job depends on the speed of machine and amount of resource allocated to each machine at the stage which is processed on it. In formulation of min–max type, the decision-maker can have the flexibility of mixed use of weights and distance parameter in expressing desired improvement on produced Pareto optimal solutions. To minimize makespan and total resource allocation costs, the proposed hybrid approach is robust, fast, and simply structured, and comprises two components: genetic algorithm and a variable neighborhood search. The comparison shows the proposal to be very efficient for different structure instances.     

Optimal due-date assignment problem with learning effect and resource-dependent processing times

In this paper, we consider a single-machine earliness-tardiness scheduling problem with due-date assignment, in which the processing time of a job is a function of its position in a sequence and its resource allocation. The due date assignment methods studied include the common due date, and the slack due date, which reflects equal waiting time allowance for the jobs. For each combination of due date assignment method and processing time function, we provide a polynomial-time algorithm to find the optimal job sequence, due date values, and resource allocations that minimize an integrated objective function, which includes earliness, tardiness, due date assignment, and total resource consumption costs.     

Some single-machine scheduling with sum-of-processing-time-based and job-position-based processing times

The single-machine scheduling problems with position and sum-of-processing-time based processing times are considered. The actual processing time of a job is defined by function of its scheduled position and total normal processing time of jobs in front of it in the sequence. We provide optimal solutions in polynomial time for some special cases of the makespan minimization and the total completion time minimization. We also show that an optimal schedule to be a V-shaped schedule in terms of the normal processing times of jobs for the total completion time minimization problem and the makespan minimization problem.     

Single machine common flow allowance scheduling with controllable processing times

In this paper, we consider single machine SLK due date assignment scheduling problem in which job processing times are controllable variables with linear costs. The objective is to determine the optimal sequence, the optimal common flow allowance and the optimal processing time compressions to minimize a total penalty function based on earliness, tardiness, common flow allowance and compressions. We solve the problem by formulating it as an assignment problem which is polynomially solvable. For some special cases, we present an O(n logn) algorithm to obtain the optimal solution respectively.     

Makespan minimization in single-machine scheduling with step-deterioration of processing times

This paper considers a single-machine scheduling problem of minimizing the maximum completion time for a set of independent jobs. The processing time of a job is a non-linear step function of its starting time and due date. The problem is already known to be ????-hard in the literature. In this paper, we first show this problem to be ????-hard in the ordinary sense by proposing a pseudo-polynomial time dynamic programming algorithm. Then, we develop two dominance rules and a lower bound to design a branch-and-bound algorithm for deriving optimal solutions. Numerical results indicate that the proposed properties can effectively reduce the time required for exploring the solution space.     

A note on single-machine scheduling with decreasing time-dependent job processing times

In this note we consider some single-machine scheduling problems with decreasing time-dependent job processing times. Decreasing time-dependent job processing times means that its processing time is a non-increasing function of its execution start time. We present polynomial solutions for the sum of squared completion times minimization problem, and the sum of earliness penalties minimization problem subject to no tardy jobs, respectively. We also study two resource constrained scheduling problems under the same decreasing time-dependent job processing times model and present algorithms to find their optimal solutions.     

Single-machine scheduling with learning effect and resource-dependent processing times in the serial-batching production

In this paper, we study a single machine scheduling problem by simultaneously considering the processing method of serial-batching, learning effect, resource-dependent processing times, and setup operations. We consider minimizing the makespan as the objective of the studied problem under the constraint that the total resource consumption does not exceed a given limit. For the special case where the resource allocation is given, we first propose the structural properties for job batching policies and batching sequencing, and an optimal batching policy is derived based on these properties. Then, we develop a novel hybrid GSA–TS algorithm which combines the Gravitational Search Algorithm (GSA) and the Tabu Search (TS) algorithm to solve the general case. Computational experiments with different scales show the effectiveness and efficiency of the proposed algorithm.     

Single-machine due window assignment and scheduling with a common flow allowance and controllable job processing time

In this paper, we consider single-machine due window assignment and scheduling with a common flow allowance and controllable job processing times, subject to unlimited or limited resource availability. Due window assignment with a common flow allowance means that each job has a job-dependent due window, the starting time and completion time of which are equal to its actual processing time plus the job-independent parameters q₁ and q₂, respectively, which are common to all the jobs. The processing time of each job is either a linear or a convex function of the amount of a common continuously divisible resource allocated to the job. We study five versions of the problem that differ in terms of the objective function and processing time function being used. We provide structural properties of the optimal schedules and polynomial-time solution algorithms for the considered problems.     

Single machine scheduling and due date assignment with positionally dependent processing times

We consider single machine scheduling and due date assignment problems in which the processing time of a job depends on its position in a processing 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, possibly, the total earliness of the scheduled jobs. We present polynomial-time dynamic programming algorithms in the case of two popular due date assignment methods: CON and SLK. The considered problems are related to mathematical models of cooperation between the manufacturer and the customer in supply chain scheduling.     

A branch-and-bound algorithm for single-machine scheduling with batch delivery minimizing flow times and delivery costs

This paper addresses scheduling a set of jobs on a single machine for delivery in batches to customers or to other machines for further processing. The problem is a natural extension of minimizing the sum of flow times by considering the possibility of delivering jobs in batches and introducing batch delivery costs. The scheduling objective adopted is that of minimizing the sum of flow times and delivery costs. The extended problem arises in the context of coordination between machine scheduling and a distribution system in a supply chain network. Structural properties of the problem are investigated and used to devise a branch-and-bound solution scheme. Computational experiments show significant improvements over an existing dynamic programming algorithm.     

A dynamic programming algorithm for the single-machine scheduling problem with release dates and deteriorating processing times

We consider a scheduling problem in which the processing time of each job deteriorates, i.e. it increases as time passes after the release date of the job. We present a dynamic programming algorithm coupled with upper bounding and lower bounding techniques to compute exact solutions. We report on problem instances of different size and we analyze the dependence between the ranges to which the data belong and the computing time.     

A unified analysis for the single-machine scheduling problem with controllable and non-controllable variable job processing times

We present a unified analysis for single-machine scheduling problems in which the actual job processing times are controlled by either a linear or a convex resource allocation function and also vary concurrently depending on either the job’s position in the sequence and/or on the total processing time of the already processed jobs. We show that the problem is solvable in O(nlogn)$O(n\log n)$ time by using a weight-matching approach when a convex resource allocation function is in effect. In the case of a linear resource allocation function, we show that the problem can be solved in O(n³)$O(n^3)$ time by using an assignment formulation. Our approach generalizes the solution approach for the corresponding problems with controllable job processing times to incorporate the variability of the job processing times stemming from either the job’s position in the sequence and/or the total processing time of the already processed jobs.     

Unrelated parallel-machine scheduling with position-dependent deteriorating jobs and resource-dependent processing time

This paper is to analyze unrelated parallel-machine scheduling resource allocation problems with position-dependent deteriorating jobs. Two general resource consumption functions, the linear and convex resource, are investigated. The objectives are to minimize the cost function that includes the weights of total load, total completion time, total absolute deviation of completion time, and total resource cost. Moreover, we try to minimize the cost function that includes the weights of total load, total waiting time, total absolute deviation of waiting time, and total resource cost. Although each job processing time can be compressed through incurring an additional cost, we show that the problems are polynomial time solvable when the number of machines is fixed.     

A note on due-date assignment and single-machine scheduling with deteriorating jobs

Journal of the Operational Research Society - In this note, we study a single-machine scheduling problem with deteriorating jobs whose processing times are an increasing function of their start...     

A two-machine flow shop scheduling problem with controllable job processing times

The paper deals with a two-machine flow shop scheduling problem in which both the sequence of jobs and their processing times are decision variables. It is assumed that the cost of performing a job is a linear function of its processing time, and the schedule cost to be minimized is the total processing cost plus maximum completion time cost. In is shown that the decision form of this problem is NP-complete, even when the processing times on one machine only are controllable and all the processing cost units are identical. Two heuristic methods for solving the problem are proposed and their worst-case analysis is presented.     

Single-machine scheduling with time-and-resource-dependent processing times

We consider single-machine scheduling problems in which the processing time of a job is a function of its starting time and its resource allocation. The objective is to find the optimal sequence of jobs and the optimal resource allocation separately. We concentrate on two goals separately, namely, minimizing a cost function containing makespan, total completion time, total absolute differences in completion times and total resource cost; minimizing a cost function containing makespan, total waiting time, total absolute differences in waiting times and total resource cost. We show that the problems remain polynomially solvable under the proposed model.     

A note on optimal assignment of slack due-dates in single-machine scheduling

This paper extends T.C.E. Cheng's approach for optimal assignment of slack due-dates and sequencing in the single-machine shop to the case when preemption is allowed and there are precedence constraints and ready times of jobs. It is shown that under special conditions the presented algorithm may be used when preemption is not allowed.