Efficient algorithms for flexible job shop scheduling with parallel machines

Job shop scheduling with a bank of machines in parallel is important from both theoretical and practical points of view. Herein we focus on the scheduling problem of minimizing the makespan in a flexible two-center job shop. The first center consists of one machine and the second has k parallel machines. An easy-to-perform approximate algorithm for minimizing the makespan with one-unit-time operations in the first center and k-unit-time operations in the second center is proposed. The algorithm has the absolute worst-case error bound of k − 1 , and thus for k = 1 it is optimal. Importantly, it runs in linear time and its error bound is independent of the number of jobs to be processed. Moreover, the algorithm can be modified to give an optimal schedule for k = 2 .     

Workload distribution of discrete‐time parallel queues with two servers

We study discrete‐time, parallel queues with two identical servers. Customers arrive randomly at the system and join the queue with the shortest workload that is defined as the total service time required for the server to complete all the customers in the queue. The arrivals are assumed to follow a geometric distribution and the service times are assumed to have a general distribution. It is a no‐jockeying queue. The two‐dimensional state space is truncated into a banded array. The resulting modified queue is studied using the method of probability generating function (pgf) The workload distribution in steady state is obtained in form of pgf. A special case where the service time is a deterministic constant is further investigated. Numerical examples are illustrated. © 2000 John Wiley & Sons, Inc. Naval Research Logistics 47: 440–454, 2000     

Dynamic pricing and inventory control with learning

Optimal operating policies and corresponding managerial insight are developed for the decision problem of coordinating supply and demand when (i) both supply and demand can be influenced by the decision maker and (ii) learning is pursued. In particular, we determine optimal stocking and pricing policies over time when a given market parameter of the demand process, though fixed, initially is unknown. Because of the initially unknown market parameter, the decision maker begins the problem horizon with a subjective probability distribution associated with demand. Learning occurs as the firm monitors the market's response to its decisions and then updates its characterization of the demand function. Of primary interest is the effect of censored data since a firm's observations often are restricted to sales. We find that the first‐period optimal selling price increases with the length of the problem horizon. However, for a given problem horizon, prices can rise or fall over time, depending on how the scale parameter influences demand. Further results include the characterization of the optimal stocking quantity decision and a computationally viable algorithm. © 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 303–325, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/nav.10013     

A time dependent continuous review inventory model with compound poisson demand

We discuss a time dependent optimal ordering policy for a finite horizon inventory system for which the provision of service is essential and thus no stockout is allowed. It is assumed that the system can place an order at any point in time during the horizon when it cannot meet the customer's demand and that lead time is negligible. The demand is considered to be distributed as a compound Poisson process with known parameters and the functional equation approach of dynamic programming is used to formulate the objective function. An algorithm has been developed to obtain the solution for all the cases. In addition, analytical solutions of the basic equation under two limiting conditions are presented.     

A face search heuristic algorithm for optimizing over the efficient set

The problem of optimizing a linear function over the efficient set of a multiple objective linear program is an important but difficult problem in multiple criteria decision making. In this article we present a flexible face search heuristic algorithm for the problem. Preliminary computational experiments indicate that the algorithm gives very good estimates of the global optimum with relatively little computational effort. © 1993 John Wiley & Sons, Inc.     

A two-machine repair model with variable repair rate

A two-unit cold standby production system with one repairman is considered. After inspection of a failed unit the repairman chooses either a slow or a fast repair rate to carry out the corresponding amount of work. At system breakdown the repairman has an additional opportunity to switch to the fast rate. If there are no fixed costs associated with system breakdowns, then the policy which minimizes longrun average costs is shown to be a two-dimensional control limit rule. If fixed costs are incurred every time the system breaks down, then the optimal policy is not necessarily of control limit type. This is illustrated by a counterexample. Furthermore, we present several performance measures for this maintenance system controlled by a two-dimensional control limit rule. © 1993 John Wiley & Sons, Inc.