Question

The Milton Lumber Company sells boards of various lengths (2-foot, 3-foot, and 7-foot wood boards). This company’s customers demand 30 2-foot boards, 35 3-foot boards, and 40 7-foot per week. Milton Lumber cuts up boards of 10 feet in length to meet this demand and wants to determine how to satisfy its customers’ demands with a minimal amount of waste. Assume that all boards share the same width and thickness. Formulate and solve an IP model.

a) Define decision variables

b) define objective function

c) define constraints for only 2 ft board

Answer 1

Decision variables

A decision variable is a quantity that the decision-maker controls. For example, in an optimization model for labor scheduling, the number of nurses to employ during the morning shift in an emergency room may be a decision variable. The OptQuest Engine manipulates decision variables in search of their optimal values.

Decision variables are added to an optimization problem by instantiating a decision variable and adding the instance to the optimization using the COptQuestOptimization::AddVariable() method.

Objective Function

An equation to be optimized given certain constraints and with variables that need to be minimized or maximized using nonlinear programming techniques. An objective function can be the result of an attempt to express a business goal in mathematical terms for use in decision analysis, operations research or optimization studies.