Integer Programming Chapter 1

Integer Programming Overview

• Integer programming (IP) is a mathematical optimization method where some or all decision variables are restricted to integer values.
• Applications often involve yes-or-no decisions, making it suitable for problems with discrete choices.

Example: California Manufacturing Company

• The company is exploring expansion options by constructing a new factory in Los Angeles or San Francisco, with a possibility of building one warehouse at a factory site.
• The net present value (NPV), which considers profitability over time, is provided for each option.
• Total capital available for investment is set at $10 million.

Key Properties of the Problem

• Decisions involve mutually exclusive alternatives, meaning if one option is chosen, others cannot be.
• Constraints can require that the sum of binary variables (representing yes-or-no decisions) equals one (if exactly one decision must be selected) or is less than or equal to one (if at most one can be chosen).
• Contingent decisions may arise, where the choice is dependent on prior decisions.

Practical Applications

• Common scenarios in industries like manufacturing, logistics, and project management leverage integer programming for optimal resource allocation.
• IP can effectively handle complex decision-making processes with limited resources.

This quiz covers the foundational concepts of Integer Programming as discussed in Chapter 1. It includes formulating applications based on Integer Linear Programming (ILP) problems, with a focus on Binary Integer Problems. Ideal for engineering students looking to enhance their understanding of operational problems in manufacturing scenarios.