Tsung-Chyan Lai

Schedule execution for two-machine flow-shop with interval processing times

This paper addresses the issue of how to best execute the schedule in a two-phase scheduling decision framework by considering a two-machine flow-shop scheduling problem in which each uncertain processing time of a job on a machine may take any value between a lower and upper bound. The scheduling objective is to minimize the makespan. There are two phases in the scheduling process: the off-line phase (the schedule planning phase) and the on-line phase (the schedule execution phase). The information of the lower and upper bound for each uncertain processing time is available at the beginning of the off-line phase while the local information on the realization (the actual value) of each uncertain processing time is available once the corresponding operation (of a job on a machine) is completed. In the off-line phase, a scheduler prepares a minimal set of dominant schedules, which is derived based on a set of sufficient conditions for schedule domination that we develop in this paper. This set of dominant schedules enables a scheduler to quickly make an on-line scheduling decision whenever additional local information on realization of an uncertain processing time is available. This set of dominant schedules can also optimally cover all feasible realizations of the uncertain processing times in the sense that for any feasible realizations of the uncertain processing times there exists at least one schedule in this dominant set which is optimal. Our approach enables a scheduler to best execute a schedule and may end up with executing the schedule optimally in many instances according to our extensive computational experiments which are based on randomly generated data up to 1000 jobs. The algorithm for testing the set of sufficient conditions of schedule domination is not only theoretically appealing (i.e., polynomial in the number of jobs) but also empirically fast, as our extensive computational experiments indicate.

Flowshop scheduling problem to minimize total completion time with random and bounded processing times

The flowshop scheduling problems with n jobs processed on two or three machines, and with two jobs processed on k machines are addressed where jobs have random and bounded processing times. The probability distributions of random processing times are unknown, and only the lower and upper bounds of processing times are given before scheduling. In such cases, there may not exist a unique schedule that remains optimal for all feasible realizations of the processing times, and therefore, a set of schedules has to be considered which dominates all other schedules for the given criterion. We obtain sufficient conditions when transposition of two jobs minimizes total completion time for the cases of two and three machines. The geometrical approach is utilized for flowshop problem with two jobs and k machines.

Mean flow time minimization with given bounds of processing times

Abstract We consider a job shop scheduling problem under uncertain processing times and fixed precedence and capacity constraints. Each of the random processing times can take any real value between given lower and upper bounds. The goal is to find a set of schedules which contains at least one optimal schedule (with mean flow time criterion) for any admissible realization of the random processing times. In order to compute such a set of schedules efficiently and keep it as small as possible, we develop several exact and heuristic algorithms and report computational experience based on randomly generated instances.

Measures of problem uncertainty for scheduling with interval processing times

The paper deals with scheduling under uncertainty of the job processing times. The actual value of the processing time of a job becomes known only when the schedule is executed and may be equal to any value from the given interval. We propose an approach which consists of calculating measures of problem uncertainty to choose an appropriate method for solving an uncertain scheduling problem. These measures are based on the concept of a minimal dominant set containing at least one optimal schedule for each realization of the job processing times. For minimizing the sum of weighted completion times of the

The optimality box in uncertain data for minimising the sum of the weighted job completion times

n

The stability radius of an optimal line balance with maximum efficiency for a simple assembly line

jobs to be processed on a single machine, it is shown that a minimal dominant set may be uniquely determined. We demonstrate how to use an uncertainty measure for selecting a method for finding an effective heuristic solution of the uncertain scheduling problem. The efficiency of the heuristic

Minimizing total weighted flow time under uncertainty using dominance and a stability box

O(n\log n)