arXiv subjects

Michael Pinedo

Publications and source records attributed to Michael Pinedo.

3 recordsLinked to original sources

arXiv2026

Flow Shop Scheduling with Stochastic Reentry

We study flow shop scheduling with stochastic reentry, where jobs must complete multiple passes through the entire shop, and the number of passes that a job requires for completion is drawn from a discrete probability distribution. The goal is to find policies that minimize performance measures in expectation. Our main contribution is a reduction to a stochastic scheduling problem on identical parallel machines augmented by machine arrivals. This reduction preserves objective values and enables the transfer of structural results and performance guarantees from the auxiliary problems to the reentrant flow shop setting. We demonstrate the usefulness of this reduction by proving the optimality of simple priority policies for minimizing the makespan and the total completion time in expectation under geometric and, more generally, monotone hazard rate distributions. For minimizing the total weighted completion time, we derive an approximation guarantee for a simple priority policy that depends only on the squared coefficient of variation of the underlying distributions. Our results constitute the first optimality and approximation guarantees for flow shops with stochastic reentry and demonstrate that established scheduling policies naturally extend to this setting through the proposed reduction.

cs.DS↗

arXiv2024

Flow shops with reentry: The total weighted completion time objective

Flow shops are widely studied machine environments in which all jobs must visit all machines in the same order. While conventional flow shops assume that each job traverses the shop only once, many industrial environments require jobs to loop through the shop multiple times before completion. This means that after traversing the shop and completing its processing on the last machine, a job must return to the first machine and traverse the shop again until it has completed all its required loops. Such a setting, referred to as a flow shop with reentry, has numerous applications in industry, e.g., semiconductor manufacturing. The planning problem is to schedule all loops of all jobs while minimizing the total weighted completion time. In this paper, we consider reentrant flow shops with unit processing times. We show that this problem is strongly NP-hard if the number of machines is part of the input. We propose the Least Remaining Loops First (LRL) priority rule and show that it minimizes the total unweighted completion time. Then, we analyze the Weighted Least Remaining Loops First (WLRL) priority rule and show that it has a worst-case performance ratio of $(1+\sqrt{2})/2$ (about 1.2). Additionally, we present a fully polynomial time approximation scheme (FPTAS) and a pseudo-polynomial time algorithm if the number of machines in the flow shop is fixed.

math.OC↗

arXiv2024

Fairness in Repetitive Scheduling

Recent research found that fairness plays a key role in customer satisfaction. Therefore, many manufacturing and services industries have become aware of the need to treat customers fairly. Still, there is a huge lack of models that enable industries to make operational decisions fairly, such as a fair scheduling of the customers' jobs. Our main aim in this research is to provide a unified framework to enable schedulers making fair decisions in repetitive scheduling environments. For doing so, we consider a set of repetitive scheduling problems involving a set of $n$ clients. In each out of $q$ consecutive operational periods (e.g. days), each one of the customers submits a job for processing by an operational system. The scheduler's aim is to provide a schedule for each of the $q$ periods such that the quality of service (QoS) received by each of the clients will meet a certain predefined threshold. The QoS of a client may take several different forms, e.g., the number of days that the customer receives its job later than a given due-date, the number of times the customer receive his preferred time slot for service, or the sum of waiting times for service. We analyze the single machine variant of the problem for several different definitions of QoS, and classify the complexity of the corresponding problems using the theories of classical and parameterized complexity. We also study the price of fairness, i.e., the loss in the system's efficiency that results from the need to provide fair solutions.

cs.DS↗