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This paper addresses single-machine scheduling problems with past-sequence-dependent (denoted by $\widetilde{psd}$) delivery times, due-window assignments and deteriorating jobs simultaneously. The $\widetilde{psd}$ delivery time of a job is proportional to the job’s waiting time, and the deteriorating jobs mean that the processing time of a job is a proportional increasing function of its starting time. For common, slack and different due-window assignments, the goal is to minimize the weighted sum of earliness, tardiness, due-window starting time and size. Some optimal propositions of the problems are given, and by these propositions, polynomial time algorithms are proposed to optimally solve the above problems.

We consider a non-preemptive single machine scheduling problem with forbidden intervals. Associated with each job is a given processing time and a delivery time to its customer, when the processing of the job is complete. The objective is to minimize the time taken for all the jobs to be delivered to the customers. The problem is strongly NP-hard in general. In this study, we show that the case with a fixed number of forbidden intervals can be solved by a pseudo-polynomial time algorithm, while no polynomial time approximation algorithm with a fixed performance ratio exists for the case with two forbidden intervals. We also develop a polynomial time approximation scheme (PTAS) for the case with a single forbidden interval.

In this paper, we consider parallel-machine scheduling with past-sequence-dependent (p-s-d) delivery times and deteriorating maintenance. The delivery time of a job is proportional to its waiting time in the system. Each machine has a deteriorating maintenance activity, i.e., delaying the maintenance increases the time required to perform it. We consider three versions of the problem to minimize the total absolute deviation of job completion times, the total load on all the machines, and the total completion time. We develop polynomial-time algorithms to solve them.

Scheduling problems with variable processing times and past-sequence-dependent delivery times are considered on a single-machine. The delivery times of jobs depend on their waiting times of processing. A job’s actual processing time depends on its position in a sequence, its starting time and its allocation of non-renewable resources. Under the linear resource consumption function, the goal (version) is to determine the optimal sequence and optimal resource allocation such that the sum of scheduling cost and total resource consumption cost is minimized. Under the convex resource consumption function, three versions of the scheduling cost and total resource consumption cost are discussed. We prove that these four versions can be solved in polynomial time, respectively. Some applications are also given by using the scheduling cost, which involve the makespan, total completion time, total absolute differences in completion times (TADC), and total absolute differences in waiting times (TADW).

We consider the time-dependent scheduling with proportional and delivery times on a single machine. Three models of the processing times are addressed here, they are proportional deterioration, proportional-linear shortening and proportional-linear increasing. The objective is to minimize the time by which all jobs are delivered. For the first model, we prove that the problem is polynomial solvable when jobs have identical release dates. When jobs arrive dynamically, we first give the proof of the NP-hardness and present a two-approximation algorithm. Then we propose a fully polynomial time approximation scheme for the case where the number of distinct release dates is a constant by applying the “rounding-the-input-data” technique. For the second and third models, when jobs have identical release dates, we prove that they are polynomial solvable, when jobs have different release dates, we present two-approximation algorithms for each of them.