This Article Full Text (PDF) References Alert me when this article is cited Alert me if a correction is posted Services Email this article to a friend Similar articles in this journal Alert me to new issues of the journal Download to citation manager Citing Articles Citing Articles via HighWire Citing Articles via Google Scholar Google Scholar Articles by Bar-Noy, A. Articles by Schieber, B. Search for Related Content

Minimizing Service and Operation Costs of Periodic Scheduling

Computer and Information Science Department, Brooklyn College, 2900 Bedford Avenue, Brooklyn, New York 11210
Bell Labs, Lucent Technologies, Murray Hill, New Jersey 07974
Computer Science Department, Technion, Haifa 32000, Israel
IBM T. J. Watson Research Center, PO Box 218, Yorktown Heights, New York 10598
amotz{at}sci.brooklyn.cuny.edu
randeep{at}research.bell-labs.com
naor{at}cs.technion.ac.il
sbar{at}watson.ibm.com

We study the problem of scheduling activities of several types under the constraint that, at most, a fixed number of activities can be scheduled in any single time slot. Any given activity type is associated with a service cost and an operating cost that increases linearly with the number of time slots since the last service of this type. The problem is to find an optimal schedule that minimizes the long-run average cost per time slot. Applications of such a model are the scheduling of maintenance service to machines, multi-item replenishment of stock, and minimizing the mean response time in Broadcast Disks. Broadcast Disks recently gained a lot of attention because they were used to model backbone communications in wireless systems, Teletext systems, and Web caching in satellite systems.

The first contribution of this paper is the definition of a general model that combines into one several important previous models. We prove that an optimal cyclic schedule for the general problem exists, and we establish the NP-hardness of the problem. Next, we formulate a nonlinear program that relaxes the optimal schedule and serves as a lower bound on the cost of an optimal schedule. We present an efficient algorithm for finding a near-optimal solution to the nonlinear program. We use this solution to obtain several approximation algorithms.

(1) A 9/8 approximation for a variant of the problem that models the Broadcast Disks application. The algorithm uses some properties of "Fibonacci sequences." Using this sequence, we present a 1.57-approximation algorithm for the general problem.

A simple randomized algorithm and a simple deterministic greedy algorithm for the problem. We prove that both achieve approximation factor of 2. To the best of our knowledge this is the first worst-case analysis of a widely used greedy heuristic for this problem.

Key Words: scheduling; maintenance service; broadcast disk; cyclic schedule; approximation algorithm
History: Received: August 8, 1997; revision received: June 22, 1999;revision received: November 2, 2000;revision received: July 12, 2001;

This article has been cited by other articles:

				M. A. Kubzin and V. A. Strusevich Planning Machine Maintenance in Two-Machine Shop Scheduling Operations Research, July 1, 2006; 54(4): 789 - 800. [Abstract] [PDF]

				D. van der Laan Routing Jobs to Servers with Deterministic Service Times Mathematics of Operations Research, February 1, 2005; 30(1): 195 - 224. [Abstract] [PDF]