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Mathematical Programming is a powerful technique used to model and solve optimization problems. This training provides the necessary fundamentals of mathematical programming and useful tips for good modeling practice in order to construct simple optimization models.

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Module 1 – The Big Picture

Question: True or false? Constraint Programming is particularly useful for solving scheduling problems and certain combinatorial optimization problems.

• False
• True

Question: True or false? A feasible solution can be, but is not guaranteed to be, an optimal solution.

• False
• True

Question: True or false? Objective functions always start with the words “maximize” or “minimize”.

• False
• True

Module 2 – Linear Programming

Question: True or false? The following constraint is valid for a linear programming problem, where x and y are variables and z is a data item: 2x + 3y less than or equal to z²

• False
• True

Question: True or false? Hard constraints can be converted to soft constraints to help resolve infeasibilities.

• False
• True

Question: True or false? If a constraint is non-binding, its dual price will be zero.

• False
• True

Module 3 – Network Models

Question: True or false? In a transportation problem, if all the capacities and demands are integer, then you can declare the variables to be continuous even though they are integer.

• False
• True

Question: True or false? The critical path is the shortest path in the network.

• False
• True

Question: True or false? A sequence of arcs connecting two nodes is called a path.

• False
• True

Module 4 – Beyond Simple LP

Question: True or false? A piecewise linear function can be used to approximate convex nonlinear functions.

• False
• True

Question: True or false? The branch and bound method begins with LP relaxation.

• False
• True

Question: True or false? Mixed-integer programming is often used for investment planning.

• False
• True

Module 5 – Modelling Practice

Question: True or false? Data sparsity can be exploited to create only the essential variables and constraints, thus reducing memory requirements.

• False
• True

Question: True or false? It is important to always use integer variables when a model involves the production of whole items.

• False
• True

Question: True or false? It is important to use penalties only when absolutely necessary.

• False
• True

Final Exam

Question: What are the two types of objects used to describe network structures?

• Nodes and arcs
• Arcs and chains
• Nodes and chains

Question: What are the possible reasons for an infeasible model?

• Real-world conflict
• Incorrect data
• Incorrect formulation
• All of the above

Question: True or false? Mathematical programming and constraint programming are the techniques you can apply using CPLEX.

• False
• True

Question: True or false? Binary variables are also known as Boolean variables.

• False
• True

Question: What is the first step of a typical optimization model development cycle?

• The identification of objectives, variables, and constraints
• The scope definition
• The creation of a prototype

Question: True or false? Basic variables take zero values in an iteration or final solution of the Simplex method.

• False
• True

Question: True or false? An unbounded variable always influences the solvability of a model.

• False
• True

Question: True or false? Flow conservation constraints are typically used in network models.

• False
• True

Question: True or false? Nonlinear terms and absolute values are not permitted in linear programming.

• False
• True

Question: True or false? Piecewise linear programming is used when dealing with functions consisting of several nonlinear segments.

• False
• True

Question: True or false? Very large linear programming models are often non-sparse.

• False
• True

Question: What does an optimization-based solution involve?

• An optimization engine
• Data
• An optimization model
• All of the above

Question: True or false? When all arcs in a chain are directed in such a way that it is possible to traverse the chain following the directions of arcs, it is called a path.

• False
• True

Question: A region is convex if …

• A straight line connecting two points inside the region passes outside it to get from one point to the other
• Any straight line between two points inside the region remains entirely in the region
• All of the above

Question: True or false? The scale of numbers used in an LP problem can affect computational time.

• False
• True

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