Service time optimization of mixed-line flow shop systems,”

Abstract-We consider deterministic mixed-line flow shop systems that are composed of controllable and uncontrollable machines. Arrival times and completion deadlines of jobs are assumed to be known, and they are processed in the order they arrive at the machines. We model these flow shops as serial networks of queues operating under a non-preemptive first-come-first-served policy, and employ max-plus algebra to characterize the system dynamics. Defining completion-time costs for jobs and service costs at controllable machines, a non-convex optimization problem is formulated where the control variables are the constrained service times at the controllable machines. In order to simplify this optimization problem, under some cost assumptions, we show that no waiting is observed on the optimal sample path at the downstream of the first controllable machine. We also present a method to decompose the optimization problem into convex subproblems. A solution algorithm utilizing these findings is proposed, and a numerical study is presented to evaluate the performance improvement due to this algorithm

Optimal Switching Strategy between Admission Control and Pricing Control Policies with Two Types of Customers and Search Costs

This paper presents a switching strategy between the admission control and the pricing control policies in a queueing system with two types of customers. For an arriving first-type customer, the decision maker has an option on which policy to choose between the two control policies; that is, one determines whether or not to admit the customer’s request for the service (admission control) or decides a price of the customer’s request and offers it to the customer (pricing control). The second-type customers are only served when no first-type customers are present in the system in order to prevent the system from being idle. This would yield an extra income, which we refer to as the sideline profit. The so-called search cost, which is a cost paid to search for customers, creates the search option on whether to continue the search or not. We clarify the properties of the optimal switching strategy as well as the optimal search policy in relation to the sideline profit in order to maximize the total expected net profit. In particular, we show that when the sideline profit is sufficiently large, the two optimal switching thresholds exist with respect to the number of first-type customers in the system

Optimal admission control of discrete event systems with real-time constraints

The problem of optimally controlling the processing rate of tasks in Discrete Event Systems (DES) with hard real-time constraints has been solved i