Jay B. Ghosh

The discrete time-cost tradeoff problem revisited

Abstract In the management of a project, the project duration can often be compressed by accelerating some of its activities at an additional expense. This is the so-called time-cost tradeoff problem which has been studied extensively in the project management literature. However, the discrete version of the problem, encountered frequently in practice and also useful in modeling general time-cost relationships, has received only scant and sporadic attention. Prompted by the present emphasis on time-based competition and recent developments concerning problem complexity and solution, we reexamine this important problem in this paper. We begin by formally describing the problem and discussing the difficulties associated with its solution. We then provide an overview of the past solution approaches, identify their shortcomings, and present a new solution approach. Next, we present network decomposition/reduction as a convenient basis for solving the problem and analyzing its difficulty. Finally, we point to several new directions for future research, where we highlight the need for developing and evaluating effective procedures for solving the general time-cost tradeoff problem. To the best of our knowledge, the popular project management software packages do not include provisions for time-cost tradeoff analyses. Our work, we hope, will provide the groundwork and an incentive for alleviating this deficiency.

Complexity of the Discrete Time-Cost Tradeoff Problem for Project Networks

This note addresses the discrete version of the well-known time-cost tradeoff problem for project networks, which has been studied previously in the standard project management literature as well as in the related literature on Decision-CPM. All the algorithms proposed thus far for the solution of the general problem exhibit exponential worst-case complexity, with the notable exception of the pseudo-polynomial dynamic program due to Hindelang and Muth. We first demonstrate that this algorithm is flawed, and that when we correct it, it no longer remains pseudo-polynomial. Continuing on in the main result of the note, we show that this is not at all surprising, since the problem is strongly NP-hard. Finally, we discuss the complexities of various network structures and validate an old conjecture that certain structures are necessarily more difficult to solve.

On the minimization of completion time variance with a bicriteria extension

We discuss a single-machine scheduling problem where the objective is to minimize the variance of job completion times. To date, the problem has not been solved in polynomial time. This paper presents a dynamic programming algorithm that is pseudopolynomial in complexity. We also propose a fully polynomial approximation scheme and derive a lower bound that is useful in its implementation. Furthermore, we show that the dynamic programming solution is easy to extend to a bicriteria version of the problem in which it is desired to simultaneously minimize the mean completion time.

Computational aspects of the maximum diversity problem

We address two variations of the maximum diversity problem which arises when m elements are to be selected from an n-element population based on inter-element distances. We study problem complexity and propose randomized greedy heuristics. Performance of the heuristics is tested on a limited basis.

Job selection in a heavily loaded shop

Recently, Slotnick and Morton address a job selection problem in a heavily loaded shop, where a tradeoff is sought between the reward obtained when a job is accepted for processing and the lateness penalty incurred when such a job is actually delivered. They provide a branch and bound algorithm and a couple of heuristics for the problems solution. They do not, however, resolve the issue of problem complexity. In this note, we first establish that the problem is NP-hard. We then go on to provide two pseudo-polynomial time algorithms which also show that the problem is solvable in polynomial time if either the job processing times or the job weights for the lateness penalty are equal. We further provide a fully polynomial time approximation scheme which always generates a solution within a specified percentage of the optimal.

ISO 9000 implementation in Turkish industry

Notes that it has become a competitive necessity for firms doing business globally to acquire the ISO 9000 certification, despite the misgivings many have with regard to its true effectiveness. Turkey, an emerging industrial economy, has a significant stake in the EU markets. At present, there is no systematic study documenting the status of ISO 9000 implementation in Turkey, the profile of the certified firms, their motivation, and their organizational experience during and after the certification process; whereas such studies have begun to emerge in other countries. Provides a background on the Turkish quality movement, and reports the results of a survey conducted among large Turkish companies that attempts to provide answers to the issues raised above. The findings are revealing and should help an international manager doing or planning to do business in Turkey, or his Turkish counterpart thinking about getting certification.

New heuristic for the dynamic layout problem

The dynamic layout problem addresses the situation where the traffic among the various units within a facility changes over time. Its objective is to determine a layout for each period in a planning horizon such that the total of the flow and the relocation costs is minimized. The problem is computationally very hard and has begun to receive attention only recently. In this paper, we present a new heuristic scheme, based on the idea of viable layouts, which is easy to operationalize. A limited computational study shows that, depending upon how it is implemented, this scheme can be reasonably fast and can yield results that are competitive with those from other available solution methods.

Scheduling with tool changes to minimize total completion time: Basic results and SPT performance

Abstract We consider a single machine sequencing problem subject to tool wear, where the objective is to minimize the total completion time. We briefly describe the problem and discuss its properties, complexity and solution. Mainly, however, we focus on the performance of the SPT list-scheduling heuristic. We provide theoretical worst-case bounds on SPT performance and also demonstrate its empirical behavior.

Batch scheduling to minimize maximum lateness

We address the single-machine batch scheduling problem which arises when there are job families and setup requirements exist between these families; our objective is to minimize the maximum lateness. As our main result, we give an improved dynamic program for the solution of the problem.

Batch scheduling to minimize total completion time

We address single and multiple machine versions of the batch scheduling problem which arises when there are job families and setup requirements between these families; our aim is to minimize the total of the completion or weighted completion times. The observations provided by us extend past results.