Anand Paul

Analysis of the Effects of Uncertainty, Risk-Pooling, and Subcontracting Mechanisms on Project Performance

The problem of designing a contract mechanism to allocate the component subprojects of a large project to a pool of contractors has important implications for project success. Our research analytically addresses issues involved in diversifying risk for the project owner by partitioning the project and assigning the subprojects to multiple contractors whose performance characteristics are imperfectly known. We begin by giving a precise analytical treatment of the effect of activity variance on expected project duration, characterizing the cases when an increase in activity variance pushes up the expected project duration. In the case of a homogeneous project consisting of serial subprojects, we show that disaggregating the project and assigning the subprojects to the contractors on a piecemeal basis reduces variance of project duration while leaving the mean unchanged. On the other hand, in the case of a homogeneous project consisting of parallel subprojects, aggregating the subprojects and assigning the aggregated project to one of the contractors reduces mean project duration.

A Note on Closure Properties of Failure Rate Distributions

Increasing generalized failure rate (IGFR) distributions were introduced as a tool in the study of contracting mechanisms in supply chains. In this note, we compare and contrast the closure-and the lack thereof-of IGFR and increasing failure rate (IFR) distributions with respect to standard operations on random variables. Some implications of these results for the use of IGFR distributions in supply chain models are noted.

Equilibrium Returns Policies in the Presence of Supplier Competition

The pioneering Pasternack returns-policy model analyzed channel coordination with a single supplier catering to a retailer facing stochastic demand for a perishable product with a fixed price, and the model showed that giving partial returns of unsold stock to the retailer is the optimal policy for the entire supply chain. The result thus begs the question as to why manufacturers of perishable commodities widely accept full returns of unsold stock as the norm. We model the environment as one where two capacity-constrained manufacturers compete for shelf space with the same retailer, and we show that a complete-credit returns policy is in fact the only possible equilibrium of the game. Our results obviate the need for knowing the exact functional form of the demand distribution in order to compute the returns credit, as Pasternacks results would require. From a retailers standpoint, we establish a simple procurement strategy and show that it is optimal. The same game with price-only contracting has a pure-strategy equilibrium when the supplier capacities are below a threshold value and a mixed-strategy equilibrium when the supplier capacities cross this threshold but are still so limited that no single supplier can with certainty supply all the quantity demanded.

Minimizing makespan on a single machine subject to random breakdowns

We investigate optimal sequencing policies for the expected makespan problem with an unreliable machine, where jobs have to be reprocessed in their entirety if preemptions occur because of breakdowns. We identify a class of uptime distributions under which LPT minimizes expected makespan.

Mean sample spacings, sample size and variability in an auction-theoretic framework

In terms of a standard model for English auctions and sealed-bid auctions, we study the impact of an increase in bidding competition and in variance of the distribution of valuations on the winners expected rent using tools from order statistics and stochastic ordering.

Average fill rate and horizon length

Given a sequence of independent and identically distributed demands and an order up to replenishment policy with negligible lead time, we prove that average fill rate is monotonically decreasing in the number of periods in the planning horizon. This was conjectured to be true in a recent issue of this journal.

A Generalized Model of Operations Reversal for Fashion Goods

Operations reversal is a process design principle that involves switching two consecutive stages of the manufacturing process to improve process performance. In this paper we investigate conditions under which operations reversal can be used to reduce the variability--as measured by the variance and standard deviation--of production volumes at the intermediate stage of the manufacturing process. We generalize the operations reversal model of Lee and Tang (1998) to explicitly incorporate two important characteristics of fashion goods markets: heterogeneity among customers and unpredictability of customer preferences. We also present a new approach to modeling the operations reversal problem.

Projects with sequential iteration: Models and complexity

Many New Product Development (NPD) projects are inherently complex, making effective management of the tasks, resources, and teams necessary to bring new products to market problematic. Frequently, managers of NPD projects are overwhelmed by complicating factors such as stochastic task times, ill-defined specifications, complex interrelationships between tasks, and information dependencies. Recently, an alternative project management tool called the Design Structure Matrix (DSM) that explicitly takes into account the iterative nature of NPD projects has been proposed. In this paper, we first introduce a mixed-integer linear programming formulation for the numerical DSM. Then, we analyze the numerical DSM and establish the complexity of this class of problems. Finally, numerical analysis of the DSM problem and heuristic approaches is presented that shows that relatively good solutions can be easily obtained, thereby offering managers an efficient alternative solution approach to the original DSM problem.

On path correlation and PERT bias

Most studies of project time estimation assume that (a) activity times are mutually independent random variables; many also assume that (b) path completion times are mutually independent. In this paper, we subject the impact of both these assumptions to close scrutiny. Using tools from multivariate analysis, we make a theoretical study of the direction of the error in the classical PERT method of estimating mean project completion time when correlation is ignored. We also investigate the effect of activity dependence on the normality of path length via simulation.

Robustness to Variability in Project Networks

Our aim in this paper is to highlight the relative impact of activity variability on the completion time of different project configurations. We show that there is, in general no categorical connection between the stage of a project in its life-cycle and the impact of increased activity variability on the expected remaining project duration. Thus investing resources to decrease activity variability is, in general, as important in the early stages of the project life-cycle as it is in the later stages. However, our analysis suggests that in projects with dominant critical paths, it pays to invest resources to reduce activity variability at an early stage rather than at a later stage in the project. We apply some of our analytical results to gain insights into the issue of structuring project activities into work packets and assigning the work packets to project teams. We extend our framework to examine different modes of subcontracting projects.