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This paper considers a single-machine scheduling problem where jobs have multiple slack due-date assignments, i.e., some jobs have a common flow allowance and all jobs have m (m > 0 is a given constant) common flow allowances. The objective is to determine the multiple common flow allowances and optimal job sequence that minimizes the weighted sum of earliness-tardiness penalty and slack due-date assignment cost, where the weights only depend on their positions in a sequence, i.e., the position-dependent weights. Optimal properties are given for this problem, and then the problem is shown to be polynomially solvable when the number of multiple slack due-date assignments is a given constant. The model with multiple slack due-date assignments can also be extended to position (time)-dependent scheduling. [ABSTRACT FROM AUTHOR]

Single-machine due-window assignment scheduling with delivery times and variable processing times is investigated, where the variable processing time of a job means that the processing time is a function of its position in a sequence and its resource allocation. Currently, there are multiple optimization objectives for the due-window assignment problem, and there is a small amount of research on optimization problems where the window starting time, the rejected cost and the optimal scheduling are jointly required. The goal of this paper is to minimize the weighed sum of scheduling cost, resource consumption cost and outsourcing measure under the optional job outsourcing (rejection). Under two resource allocation models (i.e., linear and convex resource allocation models), the scheduling cost is the weighted sum of the number of early–tardy jobs, earliness–tardiness penalties and due-window starting time and size, where the weights are positional-dependent. The main contributions of this paper include the study and data simulation of single-machine scheduling with learning effects, delivery times and outsourcing cost. For the weighed sum of scheduling cost, resource consumption cost and outsourcing measure, we prove the polynomial solvability of the problem. Under the common and slack due-window assignments, through the theoretical analysis of the optimal solution, we reveal that four problems can be solved in O (n 6) time, where n is the number of jobs. [ABSTRACT FROM AUTHOR]

This paper studies the single-machine scheduling problem with truncated learning effect, time-dependent processing time, and past-sequence-dependent delivery time. The delivery time is the time that the job is delivered to the customer after processing is complete. The goal is to determine an optimal job schedule to minimize the total weighted completion time and maximum tardiness. In order to solve the general situation of the problem, we propose a branch-and-bound algorithm and other heuristic algorithms. Computational experiments also prove the effectiveness of the given algorithms. [ABSTRACT FROM AUTHOR]

In this paper, we consider two single-machine scheduling problems with deteriorating jobs and controllable processing time. The job processing time is a function of its starting time and resource allocation. For the convex resource function, a bicriteria analysis is provided, where the first (respectively, second) criteria is to minimize total weighted completion time (respectively, total resource consumption cost). The first problem is to minimize the weighted sum of the total weighted completion time and the total resource consumption cost. The second problem is to minimize the total weighted completion time subject to the total resource consumption cost is bound. These both problems are NP-hard, we propose some heuristic algorithms and a branch-and-bound algorithm to solve the problems. [ABSTRACT FROM AUTHOR]

In this paper, we address single-machine scheduling with sum of logarithm processing times-based learning effect. Under exponential past-sequence-dependent delivery times, we proved that the makespan and total completion time minimizations can be solved by the smallest processing time (SPT) first rule. Under the agreeable weight condition and agreeable due date condition, we show that the total weighted completion time minimization and maximum tardiness minimization can be solved in polynomial time, respectively. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the minmax single-machine scheduling problem with the slack due window, where the actual processing time of a job is the deterioration function of its starting time. The goal is to obtain the optimal schedule of the job and the related decision variables of the slack due window to minimize the linear combination cost function of the maximum earliness (tardiness) of the job and the due window. We show that this problem is solvable in O(n) time, and we carry out the numerical analysis, where $ n $ is the number of jobs. [ABSTRACT FROM AUTHOR]

This paper concentrates on the single-machine scheduling problem with past-sequence-dependent setup times and general truncated learning effects, where the job processing times are non-increasing function of their positions in a sequence. Under common, slack and different (unrestricted) due-date assignments, our goal is to minimize the weighted sum of number of early/tardy jobs and due-date assignment cost, where the weight is not related to the job but to a position, i.e., the position-dependent weight. Under the three due-date assignments, some optimal properties and three optimal solution algorithms are proposed to solve these problems, respectively. [ABSTRACT FROM AUTHOR]