Abstract: Cost Estimation as a Linear Programming Problem
We tend to think of cost estimating as a non-linear, non-integer problem in which the quantities of items we will buy are known, but the costs of each item are unknown. But what happens when the reverse is true? In other words, what happens when every item procured is commercial off the shelf (COTS), with a known unit price.
We still have significant uncertainty in such a situation. This is because we don’t know how many of each item we will need from each COTS vendor, and each vendor charges a potentially difference price for the same item. We cannot simply order each item from the vendor that charges the lowest price, because that vendor might not produce a sufficient quantity to satisfy our demand. Further complicating matters, there may be political or contractual constraints obligating us to give a certain percentage of sales to certain types of businesses (for example, small business set-asides).
The author proposes a method for viewing cost estimating as a linear or integer programming problem. In this framework, we have a nonlinear objective function (cost), but we have linear constraints, and all of our decision variables (such as how much of each item to buy from each vendor) must be nonnegative integers.
The author discusses similarities and differences between integer programming and traditional cost estimation, including advantages and disadvantages of each. The mathematics behind integer programming problems are briefly explored.
Finally, the author examines the impact of risk, or uncertainty, on an integer programming-derived cost estimate. The counterintuitive result that an integer programming-produced cost estimate may actually lie at the 0th percentile of the distribution of possible costs is explored, and reconciled with our common sense intuition that point estimates represent most likely costs.
Kevin Cincotta is a Research Fellow at LMI, formerly the Logistics Management Institute. His primary areas of expertise are cost analysis, database creation and management, and statistics. Mr. Cincotta has led numerous cost analysis tasks for the Departments of the Army and Air Force since joining LMI in September, 2003, as well as several joint capability area (JCA)-related tasks for the Office of the Secretary of Defense, Program Analysis and Evaluation (OSD PA&E). Notably, he led the creation of an integer programming-based pricing model for the General Services Administration
From 2001 to 2003, Mr. Cincotta served as a Senior Cost Analyst at MCR, LLC. He worked closely with government clients at the Missile Defense Agency (MDA) to develop a radar cost model, which was presented by MCR at the 2004 Society of Cost Estimating and Analysis (SCEA) conference.
Mr. Cincotta also led several cost analysis-related tasks at the New Vectors (formerly Vector Research, Incorporated and the Altarum Institute) from 1997 to 2001. As a Senior Cost Analyst and Systems Developer, he assisted in creating life cycle cost estimates (LCCEs) for myriad DOD projects, including the Standard Procurement System (SPS), the Defense Occupational Health Readiness System (DOHRS), and the Simplified Tax and Wage Reporting System (STAWRS). He is a frequent presenter at both the Department of Defense Cost Analysis Symposium (DODCAS) and SCEA conferences. Mr. Cincotta is a (SCEA)-Certified Cost Estimator/Analyst (C/CEA). He now serves on the committees that create and review exam questions for the updated C/CEA exam, and has created several model questions for the new exam. He holds a master’s degree in economics and philosophy from the London School of Economics and Political Science, and a bachelor’s in the same fields from the University of Virginia.
Andrew Busick is a Research Fellow at LMI, formerly the Logistics Management Institute. His primary areas of expertise are cost analysis, cost estimation, and modeling and simulation. Mr. Busick has supported several cost analysis tasks for the Departments of the Army, Air Force and Coast Guard since joining LMI in October, 2007. Notably, he designed an integer programming-based pricing model for the General Services Administration (GSA). He holds a bachelor’s degree in economics and mathematics from the University of Virginia.