Tapan Sen

Static scheduling research to minimize weighted and unweighted tardiness:A state-of-the-art survey

Abstract This paper reviews research on the total tardiness (TT) and total weighted tardiness (TWT) problems. Heuristic methods and optimizing techniques are surveyed for both types of problems in the single-machine environment. Complexity theory related to these problems is also discussed. Some extensions of the TT and TWT problems are given for multi-machine environments.

Job lateness in a two-machine flowshop with setup times separated

Abstract This paper considers the two-machine flowshop problem of minimizing maximum lateness where setup times are separated from process times. Two sufficient conditions for optimality are presented. These conditions and a lower bound are used to develop a branch-and-bound solution procedure to arrive at an optimal solution. Computational results are also given. The computational results include comparison of the optimal solutions with the solutions obtained by two heuristic procedures based on the two sufficiency conditions mentioned earlier.

Minimizing a weighted quadratic function of job lateness in the single machine system

Abstract In many real world environments, early completion of a job is as undesirable as is late completion of the job. In such cases, minimizing the sum of squares of lateness of all the jobs may be an appropriate decision. Also, lateness (or earliness) of one job may be more or less expensive than lateness (or earliness) of another job. In those situations, different weights may be assigned to different jobs. Hence, the objective function to be minimized is the sum of weighted quadratic functions of job lateness. A similar problem has been attempted earlier where machine idle times are not acceptable. This paper relaxes this restriction and allows for idle time immediately prior to starting the first job on the machine. It presents a branch-and-bound methodology for the problem.

Minimizing a generalized quadratic penalty function of job completion times: An improved branch-and-bound approach

Abstract This paper considers the problem of minimizing a generalized quadratic penalty function of job completion times on a single machine. It presents some optimality conditions which, if satisfied for some jobs, build a-priori precedence relationships for those jobs, thus curtailing the enumeration effort at the branching stage. A branch-and-bound approach is presented to solve the problem. The computational results are also reported.

Bicriterion jobshop scheduling with total flowtime and sum of squared lateness

Abstract In this paper sufficient conditions for optimality for the single machine job scheduling problem with a linear combination of total flowtime and sum of squared lateness as the objective function are developed. Based on the sufficient conditions a lower bound for the objective function for a given schedule is derived. A branch-and-bound procedure incorporating the lower bound has also been developed. In addition, we also show how to fathom nodes in the branching tree using the a-priori precedence relationships among the jobs that can be determined using the sufficient conditions. Computational experiments for the branch-and-bound and its results are also presented.

Knowledge based scheduling systems: a framework

Scheduling is a complex problem which occurs often in a manufacturing environment. There are many possible variations within the context of a scheduling problem, enough to overwhelm anyone but an expert. A production manager, faced with the task of job scheduling for a particular process, might well benefit from the advice of a scheduling expert. Even though the scheduling literature is full of optimizing rules for a variety of manufacturing environments few, if any, of these rules have been used in practice. The bewildering variety of theoretical results, the lack of a mechanism to match theoretical results to practical problems and the difficulty in establishing the practical efficacy of the theoretical results are among the reasons for this gap between scheduling theory and practice. This paper describes a scheduling expert system framework which addresses these problems and helps bridge this gap. The solution techniques available in SCHEDEX produce a specific schedule for the problem according to a procedure which has been mathematically proven to provide a satisfactory and often optimal solution, given the criteria for the problem. A simulation model also tests for the effectiveness of a selected technique with respect to the chosen performance measure(s).

A Single Machine Bicriterion Scheduling Problem and an Optimizing Branch-and-Bound Procedure

Abstract This paper considers a bicritcrion scheduling problem with n jobs to be sequenced on a single machine. The objective function to be minimized is a linear Combination of range of lateness a...

An algorithm to minimize total flowtime and maximum job lateness in the two-machine flowshop system

Abstract This paper considers the dual criteria of minimizing flowtime and maximum lateness of jobs in the two-machine flowshop system. We discover the conditions that determine which of a pair of adjacent jobs in a sequence should precede the other to minimize either of the two objective functions. We also present a Branch-and-Bound procedure to arrive at an optimal solution.

Single machine jobshop scheduling problem with weighted quadratic function of job lateness: A branch-and-bound approach

Abstract This paper considers minimizing the sum of the weighted squares of lateness values for all jobs scheduled in a single machine system. In many real world jobshop scheduling situations, early completions of jobs are as undesirable as tardy completions. In such cases, minimization of the sum of squared lateness values of jobs may be an appropriate objective for the decision maker. Also, lateness of one job may be more or less expensive than the lateness of another job. In those situations, it is reasonable to consider different penalties for the lateness value of different jobs in the schedule. Therefore, this research considers minimizing the sum of the weighted squared lateness values of jobs in the schedule. A branch-and-bound technique is presented to find an optimal solution. Computational results are also reported.

Minimizing total flowtime and maximum job lateness in the twomachine flowshop system: a computerized algorithm

This paper is an improvement to an extension of a previously published paper which considered the dual criteria of minimizing flowtime and maximum lateness of jobs in the two-machine flowshop system. We discover the conditions that determine which of the pairs of adjacent jobs in a sequence should precede the other to minimize either of the two objective functions. We also present a Branch-and-Bound procedure to arrive at and optimal solution, along with a computerized example problem.