Single machine scheduling with general positional deterioration and rate-modifying maintenance

We present polynomial-time algorithms for single machine problems with generalized positional deterioration effects and machine maintenance. The decisions should be taken regarding possible sequences of jobs and on the number of maintenance activities to be included into a schedule in order to minimize the overall makespan. We deal with general non-decreasing functions to represent deterioration rates of job processing times. Another novel extension of existing models is our assumption that a maintenance activity does not necessarily fully restore the machine to its original perfect state. In the resulting schedules, the jobs are split into groups, a particular group to be sequenced after a particular maintenance period, and the actual processing time of a job is affected by the group that job is placed into and its position within the group

Approximation schemes for scheduling on a single machine subject to cumulative deterioration and maintenance

We consider a scheduling problem on a single machine to minimize the makespan. The processing conditions are subject to cumulative deterioration, but can be restored by a single maintenance. We link the problem to the Subset-sum problem (if the duration of maintenance is constant) and to the Half-Product Problem (if the duration of maintenance depends on its start time). For both versions of the problem, we adapt the existing fully polynomial-time approximation schemes to our problems by handling the additive constants

Scheduling Jobs with Variable Job Processing Times on Unrelated Parallel Machines

m unrelated parallel machines scheduling problems with variable job processing times are considered, where the processing time of a job is a function of its position in a sequence, its starting time, and its resource allocation. The objective is to determine the optimal resource allocation and the optimal schedule to minimize a total cost function that dependents on the total completion (waiting) time, the total machine load, the total absolute differences in completion (waiting) times on all machines, and total resource cost. If the number of machines is a given constant number, we propose a polynomial time algorithm to solve the problem

Order Acceptance and Scheduling: A Taxonomy and Review

Over the past 20 years, the topic of order acceptance has attracted considerable attention from those who study scheduling and those who practice it. In a firm that strives to align its functions so that profit is maximized, the coordination of capacity with demand may require that business sometimes be turned away. In particular, there is a trade-off between the revenue brought in by a particular order, and all of its associated costs of processing. The present study focuses on the body of research that approaches this trade-off by considering two decisions: which orders to accept for processing, and how to schedule them. This paper presents a taxonomy and a review of this literature, catalogs its contributions and suggests opportunities for future research in this area

A Note on Two-Agent Scheduling with Resource Dependent Release Times on a Single Machine

We consider a scheduling problem in which both resource dependent release times and two agents exist simultaneously. Two agents share a common single machine, and each agent wants to minimize a cost function dependent on its own jobs. The release time of each A-agent's job is related to the amount of resource consumed. The objective is to find a schedule for the problem of minimizing A-agent's total amount of resource consumption with a constraint on B-agent's makespan. The optimal properties and the optimal polynomial time algorithm are proposed to solve the scheduling problem

Serial-batch scheduling – the special case of laser-cutting machines

The dissertation deals with a problem in the field of short-term production planning, namely the scheduling of laser-cutting machines. The object of decision is the grouping of production orders (batching) and the sequencing of these order groups on one or more machines (scheduling). This problem is also known in the literature as "batch scheduling problem" and belongs to the class of combinatorial optimization problems due to the interdependencies between the batching and the scheduling decisions. The concepts and methods used are mainly from production planning, operations research and machine learning

Stochastic single machine scheduling problem as a multi-stage dynamic random decision process

In this work, we study a stochastic single machine scheduling problem in which the features of learning effect on processing times, sequence-dependent setup times, and machine configuration selection are considered simultaneously. More precisely, the machine works under a set of configurations and requires stochastic sequence-dependent setup times to switch from one configuration to another. Also, the stochastic processing time of a job is a function of its position and the machine configuration. The objective is to find the sequence of jobs and choose a configuration to process each job to minimize the makespan. We first show that the proposed problem can be formulated through two-stage and multi-stage Stochastic Programming models, which are challenging from the computational point of view. Then, by looking at the problem as a multi-stage dynamic random decision process, a new deterministic approximation-based formulation is developed. The method first derives a mixed-integer non-linear model based on the concept of accessibility to all possible and available alternatives at each stage of the decision-making process. Then, to efficiently solve the problem, a new accessibility measure is defined to convert the model into the search of a shortest path throughout the stages. Extensive computational experiments are carried out on various sets of instances. We discuss and compare the results found by the resolution of plain stochastic models with those obtained by the deterministic approximation approach. Our approximation shows excellent performances both in terms of solution accuracy and computational time

Controllable Processing Times in Project and Production Management: Analysing the Trade-Off between Processing Times and the Amount of Resources

The amount of resources assigned to a task highly influences its processing time. Traditionally, different functions have been used in the literature in order to map the processing time of the task with the amount of resources assigned to the task. Obviously, this relation depends on several factors such as the type of resource and/or decision problem under study. Although in the literature there are hundreds of papers using these relations in their models or methods, most of them do not justify the motivation for choosing a specific relation over another one. In some cases, even wrong justifications are given and, hence, infeasible or nonappropriated relations have been applied for the different problems, as we will show in this paper. Thus, our paper intends to fill this gap establishing the conditions where each relation can be applied by analysing the relations between the processing time of a task and the amount of resources assigned to that task commonly employed in the production and project management literature

Fuzzy Programming for Parallel Machines Scheduling: Minimizing Weighted Tardiness/Earliness and Flow Time through Genetic Algorithm

Appropriate scheduling and sequencing of tasks on machines is one of the basic and significant problems that a shop or a factory manager encounters; this is why in recent decades extensive studies have been done on scheduling issues. One type of scheduling problems is just-in-time (JIT) scheduling and in this area, motivated by JIT manufacturing, this study investigates a mathematical model for appraising a multi-objective programing that minimize total weighted tardiness, earliness and total flowtime with fuzzy parameters on parallel machines, simultaneously with respect to the impact of machine deterioration. Besides, in this paper attempted to present a defuzzification approach and a heuristic method based on genetic algorithm (GA) to solve the proposed model. Finally, several dominant properties of optimal solutions are demonstrated in comparison with the results of a state-of-the-art commercial solver and the simulated annealing method that is followed by illustrating some instances for indicating validity and efficiency of the method