Exam 21: Dynamic Programming

Find the shortest path through the following network using dynamic programming.

State variables are a function of a state variable and a decision.

Dynamic programming, when used for the shortest route problem, requires complete enumeration of paths from the beginning to ending node.

The knapsack problem is to determine how many units of each item to place in the knapsack to:

Dynamic programming must only involve a finite number of decision alternatives and a finite number of stages.

A cargo company has a set of delivery patterns for its goods from its locations at city1 to a series of cities 2,3,4,5, and 6. The delivery times between cities are given I hours below. Find the shortest route. From To City: City: 1 2 3 4 5 6 7 1 - 6 10 7 - - - 2 6 - 4 - 5 - - 3 10 4 - 4 2 4 - 4 7 - 5 - - 8 - 5 - 5 3 - - - 7 6 - - 4 8 - - 5 7 - - - - 7 5 -

Audio Disks will be opening outlets in the greater Phoenix area. The estimated sales at each store are dependent not only on the store location, but on the number of sales personnel, as presented in the table below ($000/year). Each store requires at least 2 sales people, and a pool of 9 salespeople is available. Staff Size 2 3 4 5 Store 1 60 85 90 100 Store 2 105 120 130 150 Store 3 120 145 160 175 a.What would the states be in the dynamic programming formulation? b.Draw the network that represents the dynamic programming formulation. c.Given the above network, solve the sales personnel allocation problem by finding the longest path.

The return function for a shortest route problem refers to two directional arcs between nodes.

Dynamic programming requires that its subproblems be independent of one another.

The stage transformation function