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This paper investigates single-machine scheduling with a deteriorating maintenance activity, where the processing time of a job depends on whether it is handled before or after the maintenance activity. Under common and slack due date assignments, the aim is to find the optimal job schedule, position of the maintenance activity, and optimal value of the common due date (flow-allowance) so that the linear weighted sum of earliness, tardiness and common due date (flow-allowance) value is minimized, where the weights are location-dependent (position-dependent) weights. Through a series of optimal properties, a polynomial time algorithm is proposed and it is then proven that the problem is polynomially solvable.

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.

We study a single-machine scheduling model combining two competing agents and due-date assignment. The basic setting involves two agents who need to process their own sets of jobs, and compete on the use of a common processor. Our goal is to find the joint schedule that minimizes the value of the objective function of one agent, subject to an upper bound on the value of the objective function of the second agent. The scheduling measure considered in this paper is minimum total (earliness, tardiness and due-date) cost, based on common flow allowance, i.e., due-dates are defined as linear functions of the job processing times. We introduce a simple polynomial time solution for this problem (linear in the number of jobs), as well as to its extension to a multi-agent setting. We further extend the model to that of a due-window assignment based on common flow allowance.

This paper studies a due-window assignment problem on a single machine. The job-dependent due-windows are obtained by the common flow allowance criterion. We assume that the processing time of a job is a linear function of its starting time and decreasing function of the resource amount assigned to it. The objective is to find the optimal size and location of the due-windows, the sequence of jobs and resource allocation scheme to minimize a cost function based on the window size and location, the earliness and tardiness of jobs and resource cost. We propose an algorithm to solve the problem.

This paper studies a multiple common due-window assignment problem on a single machine. The job-dependent due-windows are obtained based on common flow allowance criteria. We assume that the processing time of a job is controllable by the resource amount assigned to it. The objective is to find the optimal size and location of the multiple common due-windows, the set of jobs assigned to each due window, the sequence of jobs and resource allocation scheme to minimize a cost function based on the window size and location, earliness and tardiness of jobs and resource cost. We propose an optimal algorithm to solve the problem.

This paper studies a multiple common due date assignment problem on a single machine. The job-dependent due dates are obtained based on common flow allowance criteria. We assume that the processing time of a job is controllable by the resource amount assigned to it. The objective is to find the optimal multiple common dues, the set of jobs assigned to each due date, the sequence of jobs and resource allocation scheme to minimize a total cost based on earliness and tardiness of jobs, the common dues and resource cost. We propose an optimal algorithm to solve the problem.

In due-date assignment problems with a common flow-allowance, the due-date of a given job is defined as the sum of its processing time and a job-independent constant. We study flow-allowance on a single machine, with an objective function of a minmax type. The total cost of a given job consists of its earliness/tardiness and its flow-allowance cost components. Thus, we seek the job schedule and flow-allowance value that minimize the largest cost among all the jobs. Three extensions are considered: the case of general position-dependent processing times, the model containing an explicit cost for the due-dates, and the setting of due-windows. Properties of optimal schedules are fully analysed in all cases, and all the problems are shown to have polynomial time solutions.

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.

In this paper, a set of jobs is scheduled using the SLK due-date determination method, according to which all the jobs are given the same flow allowance. The single machine case is considered. The objective function is a cost function including three components, namely flow allowance and weighted earliness and tardiness. An analytical solution is given and an algorithm, which provides optimal solutions, is presented. Finally, the parallel machines case is discussed.

The optimal due date determination and sequencing problem of n jobs, on a single machine, with deterministic processing times is reviewed. An algorithm, using the SLK method, has been previously described by the authors, by means of which one optimal sequence as well as all the alternative optima are determined without resorting to the Complementary Pair and Exchange Principle concepts. In this paper, a similar algorithm using the CON method is proposed, the optimization criterion being the minimization of the total lateness penalty. It is shown that both algorithms lead to the same minimum value of the objective function. It is also shown that all the alternative optima of either method may be determined, if those optima derived from the other method are known.