D2 Curriculum Map
Transportation problems
Terminology used in describing and modelling the transportation problem
Finding an initial solution to the transportation problem
Adapting the algorithm to deal with unbalanced transportation problems
Knowing what is meant by a degenerate solution and how to manage such solutions
Finding shadow costs
Finding improvement indices and using these to find entering cells
Using the stepping-stone method to obtain an improved solution
Formulating a transport problem as a linear programming problem
Allocation (assignment) problems
Reducing the cost matrices
Using the Hungarian algorithm to find a least: cost allocation
Adapting the algorithm to use a dummy location
Adapting the algorithm to manage incomplete data
Modifying the algorithm to deal with a maximum profit allocation
Formulating allocation problems as linear programming problems
The travelling salesman problem
Understanding the terminology used
Knowing the difference between the classical and practical problems
Converting a network into a complete network of least distances
Using a minimum spanning tree method to find an upper bound
Using a minimum spanning tree method to find a lower bound
Using the nearest neighbour algorithm to find an upper bound
Further linear programming
Formulating problems as linear programming problems
Formulating problems as linear programming problems, using slack variables
Understanding the simplex algorithm to solve maximising linear programming problems
Solving maximising linear programming problems using simplex tableaux
Using the simplex tableau method to solve maximising linear programming problems requiring integer solutions
Game theory
Knowing about two-person games and pay-off matrices
Understanding what is meant by play safe strategies
Understanding what is meant by a zero-sum game
Determining the play safe strategy for each player
Understanding what is meant by a stable solution (saddle point)
Reducing a pay-off matrix using dominance arguments
Determining the optimal mixed strategy for a game with no stable solution
Determining the optimal mixed strategy for the player with two choices in a 2 x 3 or 3x2 game
Determining the optimal mixed strategy for the player with three choices in a 2 x 3 or 3x2 game
Converting 2 x 3, 3 x 2 and 3 x 3 games into linear programming problems
Network flows
Knowing some of the terminology used in analysing flows through networks
Understanding what is meant by a cut
Finding an initial flow through a capacitated directed network
Using the labelling procedure to find flow-augmenting routes to increase the flow through the network
Confirming that a flow is maximal using the maximum flow-minimum cut theorem
Adapting the algorithm to deal with networks with multiple sources and/or sinks
Dynamic programming
Understanding the terminology and principles of dynamic programming, including Bellman's principle of optimality
Using dynamic programming to solve maximum and minimum problems, presented in network form
Using dynamic programming to solve minimax and maximin problems, presented in network form
Using dynamic programming to solve maximum, minimum, minimax or maximin problems, presented in table form
Revision using past papers
Mock examination