Manufacturing and service organizations routinely face the challenge of scheduling jobs, orders, or individual customers in a schedule that optimizes either (i) an aggregate efficiency measure, (ii) a measure of performance balance, or (iii) some combination of these two objectives. We address these questions for single-machine job scheduling systems with fixed or controllable due dates. We show that a large class of such problems can be optimized by solving either a single instance or a finite sequence of instances of the so-called (SQC) problem, in which the sum of general quasiconvex functions of the jobs' completion times is to be minimized. To solve a single instance of (SQC), we develop an efficient, though pseudopolynomial algorithm, based on dynamic programming. The algorithm generates a solution that is optimal among all schedules whose starting time is restricted to the points of a prespecified (arbitrary) grid. The algorithm is embedded in an iterative procedure, where in each iteration a specific instance of (SQC) is solved. Special attention is given to the simultaneous minimization of the mean and variance of completion times.

Awi Federgruen and Gur Mosheiov
Journal Article
Publication Date
Naval Research Logistics

Full Citation

Federgruen, Awi and Gur Mosheiov
. “Simultaneous optimization of efficiency and performance balance measures in single-machine scheduling problems.”
Naval Research Logistics
, (January 01, 1993):