Technical Note - Analysis of a Heuristic for One Machine Sequencing with Release Dates and Delivery Times

EACH OF n jobs is to be processed without interruption on a single machine. The machine can process only one job at a time. Job i (i = 1, #t4, n) is available for processing at time ri, has a nonzero processing time pi and has a subsequent delivery time qi. We assume that all ri, pi and qi are integers. The objective is to find a sequence of jobs which minimizes the time by which all jobs are delivered. As the problem is stated above, it is in symmetric form because an equivalent inverse problem can be obtained from the original problem by interchanging ri and qi for all jobs i. For any constant K, we can define due dates for each job i by di = K qi. This produces a modified problem in which the due dates replace the delivery times. Minimizing the time by which all jobs are delivered in the symmetric form is equivalent to minimizing maximum lateness with respect to the due dates in the modified form. It has been shown by Lenstra et al. (1977) that the problem is NPhard, which implies that the existence of a polynomial bounded algorithm to solve the problem is unlikely. Implicit enumeration algorithms have been successfully applied to problems with up to 80 jobs by Baker and Su (1974), McMahon and Florian (1975) and Lageweg et al. (1976). Kise et al. (1978) has analyzed the performance of several heuristics, demonstrating that each heuristic can deviate by an amount arbitrarily close to 100% from the optimum. This analysis has since been extended by Kise and Uno (1978). In this note we shall concentrate on the analysis of some heuristics or approximation algorithms which never deviate by more than