**ENGM 535**

*Optimization Techniques*

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Mail S. Kellogg

*Linear Programming*

Given a word problem, be able to develop an appropriate linear programming that when solved would yield an optimal solution.

Given a two variable problem with 2-4 constraints be able to find an optimal solution graphically.

Given a graphical model, be able to label the feasible region and corner point soluitions both feasible and infeasible.

Given a simple linear programming model, be able to use the simplex tableau to find the optimal solution.

Given a simple linear programming model, be able to write the dual formulation to the primal.

Given a simplex tableau be able to identify both the primal solution and the dual solution at any iteration.

Given a final simplex tableau, be able to determine the new value of the objecttive function for a given unit change in a constraint. .

Given an optimal simplex tableau, be able to use the S matrix to find a range on one or more constraints before the optimal basis will change.

Given an optimal simplex tableau, be able to determine a range on an objective function coefficient before the optimal basis will change. .

Given a word problem, be able to develop an appropriate transportation model that when solved would yield an optimal solution.

Given a transportation tableau with costs, be able to use the Northwest Corner rule or Vogels approximation method to find an initial feasible solution. .

Given a transportation tableau with intermediate solution, be able to use the transportation algorithm to find a better solution.

Given a transporation tablau with intermediiate solution, be able to determine if the solution is optimal.

Assignment Problems

Given a word problem, be able to develop an appropriate asssignment model that when solved would yield an optimal solution.

Given an assignment tableau with costs, be able to use the Hungarian method to find an optimal solution

Given a network be able to find the minimal spanning tree for the network.

Given a network with origin and termination nodes, be able to find the shortest path from origin to termination.

Given a network with origin and termination nodes and flow capactiy for each arc, be able to determine the maximal flow from origin to termination.

Given a set of activities with precedence relationships, be able to draw a logic diagram for the critical path method. .

Given a logic network, be able to find the critical path for the network. .

For each activity on a CPM network, be able to determine the total slack and free slack for each activity.

Given a set of normal times and crash times with associated costs, be able to crash project time by k days.

Given a criticzal path with optimistic, most likely, and worst case times, be able to determine the likelihood a project will be completed in T days.

*Dynamic Programming *

Given a simple deterministic, discrete problem, be able to develop a dynamic programming model and determine an optimal solution.

Given a set of optimal tables and a given state, be able to determine an optimal solution from that state forward.

Given a simple probabilistic, discrete problem, be able to perform one to two iterations using backward recursion.

Given a simple deterministic, continuous problem, be able to perform one iteration using backward recursion.