Inventory problems

A set of inventory examples

These examples are expressed by a piecewise linear program. A piecewise linear program can always be transformed into a mixed integer linear program and sometimes into a linear program.

The company Sailco must determine how many sailboats to produce over several time periods, while satisfying demand and minimizing costs. The demand for the periods is known and an inventory of boats is available initially. In each period, Sailco can produce boats inside at a fixed cost per boat. Additional boats can be produced outside at a higher cost per boat. There is an inventory cost per boat per period.

The examples are:

• A basic production model with inventory: examples/opl/sailco. This is accessed through the default run configuration Basic Configuration.

• Another version of the project with a piecewise linear cost function: examples/opl/sailco/sailcopw.mod. This is accessed through the run configuration Piecewise linear cost.

• Another version of the project with a generalized piecewise linear cost function: examples/opl/sailco/sailcopwg1.mod. This is accessed through the run configuration Generalized piecewise linear model - 2 pieces.

• Another version of the project with a generalized piecewise linear cost function: examples/opl/sailco/sailcopwg2.mod. This is accessed through the run configuration Generalized piecewise linear model - 3 pieces.

• Another version of the project with a generalized piecewise linear cost function: examples/opl/sailco/sailcopwg3.mod. This is accessed through the run configuration Generalized piecewise linear model - 4 pieces.

See Piecewise linear programming in the Language User’s Manual.