Part II:
Models
In Part I, we discussed the central role of descriptive and optimization models in supporting
supply chain decision making. In this part, we provide details about how these models are
constructed and solved. This part includes five chapters:
Chapter 3. Fundamentals of Optimization Models: Linear Programming
Chapter 4. Fundamentals of Optimization Models: Mixed-Integer Programming
Chapter 5. Unified Optimization Methodology for Operational Planning Problems
Chapter 6. Overview of Descriptive Models
Chapter 7. Supply Chain Decision Databases
In these chapters, greater attention is paid to optimization models and methods than descriptive
models and methods, although both are equally important. This emphasis is due to several
reasons. First, optimization models can provide managers with penetrating analysis of the
company’s decision options, goals, commitments, and resource constraints. Second, they can
provide a rich and robust framework for merging data, relationships, projections, and forecasts
from descriptive models.
Moreover, the fundamentals of optimization models for supply chain planning can be presented in
a compact manner. In particular, we explore linear programming (LP) models in Chapter 3 and
their extensions to mixed-integer programming (MIP) models in Chapter 4. In Chapter 5, we
extend the scope of MIP models for operational planning by presenting a unified optimization
methodology that combines model decomposition methods with heuristics. We note that the
same modeling techniques and algorithms discussed here have been applied to decision
problems arising in investment banking, engineering design, and many other areas.
By contrast, descriptive models are very broad in the methodologies they employ, which include
statistics, data mining, management accounting, deterministic and Monte Carlo simulation, and
others. It would not be possible to provide an in-depth presentation of all these methodologies in
one book. Instead we study an overview of important, illustrative descriptive models in Chapter 6,
including forecasting, simulation, and activity-based costing.
Finally, the focus on optimization models is motivated by the belief that decision makers should
possess knowledge about their form and function if they are to be used to their full advantage.
Much of this book could have been written from the perspective that the analytical engines of
optimization modeling systems are “black boxes,” which only specialists need to comprehend. We
reject such an approach because it fosters an unnecessary and sometimes dangerous lack of
understanding by managers seeking to use models to improve their decision making. If they have
little or no knowledge about how details of a model represent decision problems, managers might
be unwilling to trust its results or be too willing to blindly trust them.
Still, having committed us to study details of optimization model construction and solution, I wish
to reassure you that we are not about to embark on mathematical developments that require
graduate training in operations research. Rather, only mathematical constructions taught in high
school are used. Although this means that we are restricted to small models that do not convey
the richness of larger models for complex problems, a comprehensive knowledge of the
fundamentals can be conveyed. Moreover, without going into excessive detail, later chapters
describe how large-scale models are constructed by synthesizing smaller, simpler submodels of
the types discussed in this chapter and the next.
In Chapter 7, we examine the supply chain decision database that contains the inputs for supply
chain optimization models. The tables in this database serve as templates for populating
optimization models with data determined by descriptive models and other data input methods.
The supply chain decision database also contains optimization model outputs that are combined
with the inputs in creating managerial reports and graphical displays of supply chain decisions
determined by the models.
Chapter Three:
Fundamentals of
Optimization Models:
Linear Programming
In this chapter, we study linear programming (LP) models and their application to supply chain
planning. In Section 3.1, we present simple examples of LP models, but they are sufficiently
complicated to allow us to illustrate the underlying ideas. The examples are presented first in
standard algebraic form and then in the format of two spreadsheet optimizers, Solver and What’s
Best. We examine properties of LP models in Section 3.2, identifying weaknesses in their ability
to represent some features of supply chain–planning problems. This discussion serves as a
prelude to richer, more comprehensive mixed-integer programming models, extensions of LP
models that are discussed in the next chapter.
Section 3.3 provides an economic interpretation of the conditions establishing optimality used by
the simplex method of linear programming, which provides important insights into the optimization
process. Moreover, the marginal costs implicitly computed by the simplex method have practical
value to managers in resource and sales planning. Sensitivity and parametric analysis are also
discussed in that section.
LP methods can be adapted to measure trade-offs among conflicting objectives by tracing out the
efficient frontier of solutions. These methods are discussed and illustrated in Section 3.4. The
chapter continues with Section 3.5 where we discuss stochastic programming models, which are
generalizations of LP models that allow explicit treatment of planning uncertainties. Stochastic
programming is illustrated by its application to decisions about production and inventory planning
in the face of demand uncertainty. The chapter concludes with final thoughts in Section 3.6.
Appendix 3A presents the simplex method for optimizing LP models. The method is illustrated by
its application to the model of Example 3.1.