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54 August 31, 2006 2:55 Fortifying Six Sigma with OR/MS Tools
Table 5.2 A summary of OR/MS techniques integrated into Six Sigma phases.
OR/MS tools
Define Mathematical programming techniques for resource allocation
and project selection
Decision analysis
Project management tools
Analysis Forecasting
Basic queuing systems
Simulation and modeling
Improve Optimization and control of queues
Mathematical programming techniques
Heuristics

techniques, sometimes in conjunction with sensitivity analysis, can be exploited to
solve such problems. These techniques have been predominantly used in production
planning and operations management. They can be deployed in Six Sigma projects for
project selection and planning during the Define phase of the Six Sigma deployment
for selecting an optimal number of projects or to achieve profit maximization or cost
minimization goals in general. Problems such as Six Sigma resources allocation, Six
Sigma facilities layout and location, and production and service planning can also be
solved using mathematical programming techniques. These applications may take a
wide variety of forms depending on the particular problem situation and the various
objectives involved. For example, given some limited capital budget, the decision of
how to select a subset of proposed Six Sigma projects to invest in can be readily mod-
eled as a single or multiobjective knapsack problem. Solution techniques for problems
9
of this type are discussed by Martello and Toth, and by Zhang and Ong, 10 among
others.
Besides the Define phase, applications of mathematical programming techniques
are interspersed in all subsequent phases. In particular, as the objective of mathemat-
ical programming techniques is optimization, various techniques can naturally be
weaved into the Improve phase to solve various optimization problems. For example,
a general framework for dual response problem can be cast using multiobjective math-
ematical programming. 11,12 Nonlinear optimization techniques can be applied, for
example, to optimize mechanical design tolerance 13 and product design capability, 14
as well as to estimate various statistical parameters. In the Control phase, nonlinear
optimization techniques have been applied to optimize the design of control charts,
including economic design, economic-statistical design and robust design, design of
sampling schemes and control plans. Examples of these applications can be found in
many papers 15−29 . Some of these techniques are included in the proposed Six Sigma
roadmap discussed in Section 5.3.2.
In addition, heuristics, the most popular ones of which include the classical meta-
heuristics of simulated annealing, genetic algorithms and tabu search, are a class
of effective solution techniques for solving various mathematical programming and
combinatorial optimization problems, among others. It is thus proposed that a brief
introduction to heuristics should also be included in the training of Six Sigma BBs and