Deterministic OR Methods for Data Scientists

Learning Outcomes

Learning Outcomes

Having successfully completed this module you will be able to:

• derive (upper) bound on IP using LP relaxation (Section 5 (Integer Programming))
• apply these steps to the two examples in the handout (and similar problems) (Section 1 (Intro to MP))
• describe situations when sensitivity analysis is used (Section 4 (Sensitivity))
• define basic solution, basic feasible solution, optimal BSF of LP problems in standard form (Section 2 (Simplex Method))
• describe the dual Simplex method (using dictionary) (Section 3 (Duality))
• describe graphical method, simplex methods (primal and dual) and apply them to solve relatively small LP problems
• describe and prove week duality theorem (Section 3 (Duality))
• formulate various problems using LP, IP and NLP
• describe the motivation for using duality and formulate the dual problem given the primal
• apply the dictionary and full tableau Simplex method to solve LP problems in standard form given a starting BFS (Section 2 (Simplex Method))
• using duality and complementary slackness to verify optimality (Section 3 (Duality))
• interpret shadow price and primal-dual pair in terms of profit maximization vs. resource scarcity (Section 3 (Duality))
• derive the range of the RHS until the optimal basis start changing and the corresponding range of the optimal value (Section 4 (Sensitivity))
• describe the idea behind the Simplex method (Section 2 (Simplex Method))
• derive the range of the objective coefficient until the optimal basis start changing and the corresponding range of the optimal value (Section 4 (Sensitivity))
• write the general form of a mathematical programming problem (Section 1 (Intro to MP))
• formulate the knapsack problem using IP (Section 5 (Integer Programming))
• apply branch and bound to solve simple IP (e.g. with no more than 3 variables) (Section 5 (Integer Programming))
• solve LP problems with two variables using the graphical method (Section 1 (Intro to MP))
• distinguish between LP, IP, and NLP (Section 1 (Intro to MP))
• model either-or, set-up costs and other condition-based constraints using binary variables and constraints in the context of integer programming (Section 5 (Integer Programming))
• describe duality theorems and complementary slackness
• transform LP problems from general form to standard form and vice versa (Section 2 (Simplex Method))
• describe the motivation for using duality and formulate the dual problem given the primal (Section 3 (Duality))
• describe the method for finding initial BFS and to avoid cycling (Section 2 (Simplex Method))
• describe how dual simplex can be used in the case additional constraint leads to infeasibility (Section 4 (Sensitivity))
• describe relationships for primal-dual pair in terms of optimality, feasibility and boundedness (Section 3 (Duality))
• apply parametric programming to calculate the change of the objective value (and the optimal solutions) when more than one objective coefficient or the RHS are changed continuously (Section 4 (Sensitivity))
• describe 5 steps for formulating a mathematical programming problem (Section 1 (Intro to MP))
• describe branch and bound methods
• describe economic interpretation of shadow price and perform sensitivity analysis on LP
• describe complementary slackness conditions (Section 3 (Duality))
• obtain (lower) bound on IP using rounding (Section 5 (Integer Programming))
• write down general form and standard form of LP problems (Section 2 (Simplex Method))
• describe general branch and bound method (Section 5 (Integer Programming))
• state LP duality theorem (Section 3 (Duality))

Summative

This is how we’ll formally assess what you have learned in this module.

Referral

This is how we’ll assess you if you don’t meet the criteria to pass this module.

Repeat

An internal repeat is where you take all of your modules again, including any you passed. An external repeat is where you only re-take the modules you failed.