Abstract
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.
Highlights
Single machine scheduling is a decision-making process that plays a critical role in all manufacturing and service systems
We present the results of the computational experiments carried out to evaluate the effectiveness of the Extreme Value Theory-based Deterministic Approximation (EVTDA) approach in comparison with the twostage and multi-stage recourse models to address the proposed problem
We have addressed the stochastic single machine scheduling problem where learning effect on processing time, sequence-dependent setup times, and machine configuration selection are considered simultaneously
Summary
Single machine scheduling is a decision-making process that plays a critical role in all manufacturing and service systems. This problem has been extensively investigated for a long time because of its practical importance in developing scheduling theory in more complex job shops and integrated processes. The same machine can be used for different jobs, but the efficiency of processing them depends on the configuration used. The setup times are considered either sequenceindependent or sequence-dependent. Sequence-dependent setup time between two different activities is encountered in many industries such as the printing industry, paper industry, automotive industry, chemical processing, and plastic manufacturing industry. Dudek et al (1974) reported that 70% of industrial activities include sequence-dependent setup times
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