V-shape property for optimal schedules with monotone penalty functions

We study single-machine bicriteria scheduling problems with position-dependent weights. Due date costs and penalty costs can affect the decision-maker’s profit. Therefore, how to optimize the benefits and balance of these costs for decision-makers is the focus of this research. This paper discusses three models: weighted-sum scheduling problem, constrained scheduling problem, Pareto scheduling problem. It analyzes the properties of bicriteria schedule, determines the optimal due dates (usually referred to as different due dates: DIF), and gives the corresponding polynomial solvable algorithms.

An optimal procedure for minimizing total weighted resource tardiness penalty costs in the resource-constrained project scheduling problem

We study the scheduling of multiple tasks under varying processing costs and derive a priority rule for optimal scheduling policies. Each task has a due date, and a non‐completion penalty cost is incurred if the task is not completely processed before its due date. We assume that the task arrival process is stochastic and the processing rate is capacitated. Our work is motivated by both traditional and emerging application domains, such as construction industry and freelance consulting industry. We establish the optimality of Shorter Slack time and Longer remaining Processing time (SSLP) principle that determines the priority among active tasks. Based on the derived structural properties, we also propose an effective cost‐balancing heuristic policy and demonstrate the efficacy of the proposed policy through extensive numerical experiments. We believe our results provide operators/managers valuable insights on how to devise effective service scheduling policies under varying costs.

In this paper we consider a single machine preemptive scheduling problem to minimize the weighted number of late jobs. There are given n jobs and for each job we have a release date, a processing time and a due date. It is assumed that certain specified jobs have to be completed on time. The due dates for these jobs are considered as deadlines. while for the other jobs due dates may be violated. For the case of similarly ordered release and due dates (when there is no advantage to preemption) as well as for the case of embedded release and due date intervals and preemption allowed, we transform the initial problem into a reduced problem, where all jobs with deadlines are eliminated. It gives an opportunity to propose O(n log n) algorithms for some special cases of the considered problems.

We consider a single-machine job shop scheduling problem in which penalties occur for jobs that either commence before their target start times or are completed after their due dates. The objective is to minimize the maximum penalty, subject to restrictive assumptions on the target start times, the due dates, and the penalty functions. We present an algorithm for solving this problem, along with a method for generating alternative optima. The algorithm is generalized to cover the case in which the machine is available for only a limited time span.

This study applies permutation and combination techniques to optimize single machine job scheduling with precedence constraints and due dates. An R-based model was used to generate and evaluate all feasible job sequences, identifying the one that minimizes total completion time and penalty costs. Compared to traditional heuristics like SPT and EDD, the exhaustive combinatorial approach proved more effective in complex scheduling scenarios. The results highlight a data-driven method for improving scheduling efficiency, with practical relevance to manufacturing and project management.

We study a set of single-machine two-agent scheduling problems where the performance measure of the first agent, , is the weighted number of jobs completed exactly at the due date, i.e. completed in a just-in-time mode. The performance measure of the second agent, , is either the makespan, the total completion times or the weighted number of jobs completed exactly at the due date. For each combination of performance measures of the two agents, we study four different variations of the problem. We show that all four-problem variations are strongly -hard for when the performance measure of the second agent is either the makespan or the total completion time, even if all of the first agent’s weights are equal. We also study the special case of these problems where the job processing times of the second agent are all equal. For this special case, we prove that three variations of this problem are ordinary -hard with respect to the instance size, while all four problem variations are polynomial solvable with respect to the number of jobs. For the problem where the performance measure of both agents is the weighted number of jobs completed at the due date, we show that one problem variation is solvable in polynomial time, while all other three variations are ordinary -hard.

Single machine scheduling with due date assignment to minimize the total weighted lead time penalty and late work

In this paper, the problem of scheduling n jobs on a single machine is evaluated. We introduce a Modified Total Late Work function that allows a declining piecewise linear penalty over time. Multiple due dates for each job are identified and at each due date, the penalty is reassessed. Many instances occur when delivery urgency leads to progress metrics or dates being added to a contract. Over the life of the contract, a loss of incentives or a price decrease can occur at each of the negotiated due dates. After the final due date, the product is valueless and the penalty ceases to accrue. The number and placement of contract due dates are part of the initial negotiations. Two metaheuristics, Simulated Annealing and the Noising Method, are empirically evaluated to determine their performance when measured by this new loss function.

This paper considers a lot sizing and scheduling problem where jobs are processed on a batching machine, and then delivered to a customer by a capacitated transporter. Each job is associated with a due date and a volume. In order to guarantee customer service level, each job has to be delivered to customer before or on its due date. It is assumed that the job which is delivered to customer before its due date will occur an earliness penalty. The objective is to minimise the total logistics cost under two kinds of due-date conditions. We formulate the problem as a non-linear model, then develop a Tabu algorithm. To verify performance of this algorithm, we establish a dominance-related exact algorithm for the small-size problems and a lower bound for the large-size problems. Numerical experiments show that the proposed Tabu algorithm performs efficiently in terms of both solution quality and running time.

To make scheduling problems more realistic, we develop a new scheduling model with penalty functions for earliness and tardiness. Instead of a fixed due date, the scheduling problem is approached by taking the due date as a time period, which can handle flexible due dates and flexible customer requirements with penalty parameter modifications. We solve this optimization problem by the simulated annealing method and demonstrate its effectiveness with three examples.

An Optimal Static Priority Rule for Stochastic Scheduling with Impatience

Preemptive scheduling with variable profile, precedence constraints and due dates

A composite heuristic for the single machine early/tardy job scheduling problem

This paper addresses one-machine scheduling with maintenance restrictions. A maintenance operation is position dependent in a sequence of normal jobs if the maintenance has to be performed after at most some defined number of job changes on the machine. We show that several problems with objective functions Cmax and Lmax are still solvable in polynomial time if position-dependent maintenance is considered. We then consider the problem of preemptive scheduling with ready times and due dates on one machine with the Lmax criterion. We show that this problem is computationally hard and present the characteristics of this problem—for example, the fact that optimum schedules may be nonactive. After determining a set of dominance properties, branch-and-bound and local search algorithms are proposed. The performance of the algorithms is evaluated using a series of computational experiments.