Sushil Gupta

Single facility scheduling with nonlinear processing times

Abstract This paper considers the static single facility scheduling problem where the processing times of jobs are a monotonically increasing function of their starting (waiting) times and the objective is to minimize the total elapsed time (called the makespan) in which all jobs complete their processing. Based on the combinatorial analysis of the problem, an exact optimization algorithm is developed for the general processing time function which is then specialized for the linear case. In view of the excessive computational burden of the exact optimization algorithm for the nonlinear processing time functions, heuristic algorithms are proposed. The effectiveness of these proposed alogrithms is empirically evaluated and found to indicate that these heuristic algorithms yield optimal or near optimal schedules in many cases.

Minimizing the makespan with late start penalties added to processing times in a single facility scheduling problem

Abstract This paper considers the following scheduling problem: Minimize the makespan in a single facility problem where the processing time of a job consists of a fixed and a variable part. The variable part depends on the start time of the job. The objective is to minimize makespan. Two optimizing algorithms based on dynamic programming and branch-and-bound techniques and five heuristic rules have been proposed. The heuristic solutions have been compared with the optimal solution for upto 7 jobs to identify the best heuristic. The detailed computational results for the branch-and-bound and the best heuristic rule are then obtained for problems with up to 15 jobs.

Single machine scheduling research

This paper reviews static scheduling research on single machine for the last three decades. One hundred seventy one papers were found on this topic after an extensive search in the English language periodicals. These papers are classified on the basis of the objective functions and constraints. Contribution of each paper is analyzed in terms of its theoretical and computational results. An analysis of the literature on the basis of number of articles published in each year, in each category, in different journals and by different authors has also been provided. This reveals several interesting facts about the developments in single machine scheduling (SMS) research and its future.

A state-of-art survey of static scheduling research involving due dates

This paper provides a guided tour of those scheduling techniques in which the performance measures bear in one way or the other on job due dates. The classification is based on scheduling objectives. Within each category the theoretical developments and computational experiences have been reviewed.

A categorized bibliographic survey of goal programming

A total of 240 goal programming articles that have so far appeared in over 60 English journal publications are compiled and classified according to technique and application areas. Analysis of these data provides interesting insights regarding goal programming article characteristics, literature trends and future needs.

A Review of Program Evaluation and Fund Allocation Methods Within the Service and Government Sectors

A detailed analysis of existing published research on project/program evaluation, selection and fund allocation within service and government sectors is presented. This analysis is based on a survey of 306 articles from 93 journals. Different methods for measuring intangibles are briefly presented and contrasted along with typical non-industrial applications. It is concluded that few publications deal with both evaluation and allocation as an integrated process, and that a systematic classification of prevailing research does not exist. A scheme is developed for categorizing published research in terms of modeling methodology, objectives, scope and areas of application. Additionally, trends and new areas of research are identified.

Modeling of financial supply chain

The research work on supply-chain management has primarily focused on the study of materials flow and very little work has been done on the study of upstream flow of money. In this paper we study the flow of money in a supply chain from the viewpoint of a supply chain partner who receives money from the downstream partners and makes payments to the upstream partners. The objective is to schedule all payments within the constraints of the receipt of the money. A penalty is to be paid if payments are not made within the specified time. Any unused money in a given period can be invested to earn an interest. The problem is computationally complex and non-intuitive because of its dynamic nature. The incoming and outgoing monetary flows never stop and are sometimes unpredictable. For tractability purposes we first develop an integer programming model to represent the static problem, where monetary in-flows and out-flows are known before hand. We demonstrate that even the static problem is NP-Complete. First we develop a heuristic to solve this static problem. Next, the insights derived from the static problem analysis are used to develop two heuristics to solve the various level of dynamism of the problem. The performances of all these heuristics are measured and presented.

Optimal repayment policies for multiple loans

This paper extends the applications of scheduling theory to certain problems in the area of finance. Specifically, a branch and bound algorithm to identify optimal repayment policies for multiple loans (credit purchases) has been developed. Each loan qualifies for a discount if it is paid on or before a certain date and a penalty is imposed if it is paid after its due date. These two dates are different in general. It is assumed that the cash for repayment is generated at a constant rate per day and it can be invested so that it continues to earn money until used for repayment. The objective is to minimize the present value of all future cash outflows.

Project selection with discounted returns and multiple constraints

Abstract This paper considers the problem of selecting a subset of N projects subject to multiple resource constraints. The objective is to maximize the net present value of the total return, where the return from each project depends on its completion time and the previously implemented projects. It is observed that the optimal order (sequence) of projects does not depend on the particular subset of selected projects and hence the overall problem reduces to a multiconstraint nonlinear integer (0–1) problem. This problem can be solved optimally in pseudo-polynomial time using a dynamic programming method but the method is impractical except when the number of constraints, K , is very small. We therefore propose two heuristic methods which require O( N 3 K ) and O( N 4 K ) computations, respectively, and evaluate them computationally on 640 problems with up to 100 projects and up to 8 constraints. The results show that the best heuristic is on the average within 0.08% of the optimum for the single-constraint case and within 2.61% of the optimum for the multiconstraint case.

Supply chain scheduling: Just-in-time environment

Abstract We study the benefits of coordinated decision making in a supply chain consisting of a manufacturer, a distributor, and several retailers. The distributor bundles finished goods produced by the manufacturer and delivers them to the retailers to meet their demands. The distributor is responsible for managing finished goods inventory. An optimal production schedule of the manufacturer, if imposed on the distributor, may result in an increased inventory holding cost for the distributor. On the other hand, an optimal distribution schedule of the distributor, if imposed on the manufacturer, may result in an increased production cost for the manufacturer. In this paper we develop mathematical models for individual optimization goals of the two partners and compare the results of these models with the results obtained for a joint optimization model at the system level. We investigate the computational complexities of these scheduling problems. The experimental results indicate that substantial cost savings can be achieved at the system level by joint optimization. We also study conflict and cooperation issues in the supply chain. The cost of conflict of a supply chain partner is a measure of the amount by which the unconstrained optimal cost increases when a decision is to be made under the scheduling constraint imposed by the other partner. We quantify these conflicts and show that the cost of conflicts are significant. We also show that a cooperative decision will generate a positive surplus in the system which can be shared by the two partners to make cooperation and coordination strategy more attractive.