Receding Horizon Control of Mixed Line Flow Shop Systems

Abstract

We consider reliable mixed line flow shop systems that are composed of controllable and uncontrollable machines. These systems are assumed to receive arrivals at random instants and process jobs deterministically in the order of arrival so as to depart them before their deadlines that are revealed at the time of arrival. We model these flow shops as serial networks of queues operating under a non-preemptive first-come-first-served policy. Defining completion-time costs for jobs and process costs at controllable machines, a stochastic convex optimization problem is formulated where the control variables are the constrained service times of jobs at the controllable machines. As an on-line solution method to determine these service times, we propose a receding horizon controller, which solves a deterministic problem at each decision instant. We quantify the available future information by the look-ahead window size. Numerical examples demonstrate the value of information and that the no-waiting property of the full-information case is not observed in the partial-information case.