IIT Madras is a public technical and research university located in Chennai, Tamil Nadu. Founded in 1959, it is recognised as an Institute of National Importance.

IIT Madras has been ranked as the top engineering institute in India for four years in a row by the National Institutional Ranking Framework of the MHRD

It currently offers undergraduate, postgraduate and research degrees across 16 disciplines in Engineering, Sciences, Humanities and Management. About 596 faculty belonging to science and engineering departments and centres of the Institute are engaged in teaching, research and industrial consultancy.

IIT Madras

For a service provider facing stochastic demand growth, expansion lead times and economies of scale complicate the expansion timing and sizing decisions. We formulate a model to minimize the infinite horizon expected discounted expansion cost under a service-level constraint. The service level is defined as the proportion of demand over an expansion cycle that is satisfied by available capacity. For demand that follows a geometric Brownian motion process, we impose a stationary policy under which expansions are triggered by a fixed ratio of demand to the capacity position, i.e., the capacity that will be available when any current expansion project is completed, and each expansion increases capacity by the same proportion. The risk of capacity shortage during a cycle is estimated analytically using the value of an up-and-out partial barrier call option. A cutting plane procedure identifies the optimal values of the two expansion policy parameters simultaneously. Numerical instances illustrate that if demand grows slowly with low volatility and the expansion lead times are short, then it is optimal to delay the start of expansion beyond when demand exceeds the capacity position. Delays in initiating expansions are coupled with larger expansion sizes. © 2009 Wiley Periodicals, Inc.

Department of Management Studies

Fulltext

Naval Research Logistics

Capacity expansion under a service-level constraint for uncertain demand with lead times

The geometric Brownian motion (GBM) process is frequently invoked as a model for such diverse quantities as stock prices, natural resource prices and the growth in demand for products or services. We discuss a process for checking whether a given time series follows the GBM process. Methods to remove seasonal variation from such a time series are also analyzed. Of four industries studied, the historical time series for usage of established services meet the criteria for a GBM; however, the data for growth of emergent services do not.&nbsp;

World University root node

The Engineering Economist

On The Validity of The Geometric Brownian Motion Assumption

Engineering economic decision problems encountered in practice are embedded in information-rich environments, where large volumes of data are available from multiple sources. However, the information that is most relevant to solving the problem may be unavailable, inaccessible, inaccurate, or uncertain. In contrast, typical engineering economy textbook problems present only the relevant information in a convenient format. To help bridge the gap between textbook and practice, we engage student teams in a series of ill-structured problems. Teams work in an online Problem Solving Learning Portal (PSLP) that provides access to a variety of information resources containing both relevant and irrelevant information. In one problem instance, some information relevant to the solution must be obtained from an external resource that is not available or mentioned in the PSLP. Student work in the PSLP is organized into successive stages of specifying decision criteria, stating assumptions, expressing their solution in a spreadsheet file and written rationale, and conducting a sensitivity analysis on a single variable they judge to be critical. In addition, they cut and paste information from the resources they see as relevant into a "working memory" repository. We explore different methods for assessing students' ability to select which information is relevant. Direct measures include simple counts of "hits" and "false alarms" in the working memory that are assessed as part of the grading rubric and analyzed using signal detection theory. Their choice of the parameter(s) on which to conduct the sensitivity analysis can be considered as an indirect measure because the most relevant information is that which provides the best prediction of the most critical parameter (i.e., the parameter that will have the greatest impact on the decision criterion). The online environment also tracks the information resources visited by the student teams and the time of visitation. Data collected from a large engineering economy course are used to evaluate the effectiveness of these assessment methods. © American Society for Engineering Education, 2007.

ASEE Annual Conference and Exposition, Conference Proceedings

Student selection of information relevant to solving ill-structured engineering economic decision problems

For a service provider, stochastic demand growth along with expansion lead times and economies of scale may encourage delaying the start of expansion until after some shortages have been accumulated. Assuming demand follows a geometric Brownian motion, we define the service level in terms of the proportion of demand satisfied, which is then analytically evaluated using financial option pricing theory. Under a stationary expansion policy, an infinite time horizon discounted expansion cost is minimized under the service level constraint, where the expansion timing and size parameters are the decision variables. With the current formulation, the problem seems to be unbounded.

2006 IIE Annual Conference and Exhibition

Optimal solution to a capacity expansion problem

For service providers, uncertain demand for capacity and expansion lead time may create unavoidable capacity shortages, which may be allowed to accumulate before initiating an expansion. For the demand following a geometric Brownian motion process, we assume a stationary expansion policy where the timing and size of expansion are determined as fixed proportions of the capacity position. We define the service level in terms of the capacity shortages, which can be evaluated by applying pricing formulae for barrier options in finance. We observe the relationship between the two policy parameters at different specified service levels and for other model parameters.