Exam 17: Dynamic Programming

Linear programming is typically applied to problems wherein one must make a decision at a specified point (or points)in time.Dynamic programming is typically applied to problems wherein one must make a sequence of decisions.

The following information is to be used for the questions below: There are seven cities (City 1-City 7)served by Acme Trucking.Route availability is limited.The distances,in hundreds of miles,are given in the table below for each route. -What is the minimum distance a load being moved from City 1 to City 7 must travel?

In dynamic programming,the decision rules defining an optimal policy give optimal decisions for any entering condition at any stage.

Table M2-3 -For the shortest route problem described in Table M2-3,which arcs comprise the shortest route?

For the questions which follow,there are six cities (City 1-City 6)serviced by a particular airline.Limited routes are available,and the distances for each of these routes are presented in the table below. -What is the minimum distance that must be traveled to get from City 1 to City 6?

In a shortest-route problem,the limit on the number of allowable decision variables from one node to another is the number of possible nodes to which one might yet travel.

Your local paper carrier could make use of the shortest-route technique.

Develop the shortest-route network for the problem below,and determine the minimum distance from node 1 to node 7.

The data below details the distances that a delivery service must travel.Use dynamic programming to solve for the shortest route from City 1 to City 8.

The following information is to be used for the questions below: GATRA,the Greater Attleboro-Taunton Regional Transit Authority serves six cities (City 1-City 6).While there are many restrictions (primarily roads on which they may not travel),they do have some choice of routes.The distances between cities,along permitted routes,are presented below. -What is the shortest route?

Table M2-3 -The above information describes a shortest-route problem with the distance in miles.How many stages will this dynamic programming problem have?

There are six cities (City 1-City 6)serviced by a particular bus line.Limited routes are available,and the distance for each of these routes is presented in the table below. -If dynamic programming were used to solve for the minimum distance from City 1 to City 6 above,how many stages would there be?

If the truck were required to take the route from City 4 to City 5,what would be the shortest distance from City 1 to City 7?

The following information describes a shortest-route problem with the distance in miles.How many stages will this dynamic problem have?

The second step in solving a dynamic programming problem is to solve the last stage of the problem for all conditions or states.

In a shortest-route problem,the nodes represent the destinations.

What are the four elements defining each stage in a dynamic programming problem?

Table M2-2 -According to Table M2-2,which gives a solution to a shortest route problem solved with dynamic programming,the total distance from City 1 to City 7 is 14.What is the shortest distance from City 3 to City 7?

Table M2-1 The data below is a dynamic programming solution for a shortest route problem. -Using the data in Table M2-1,determine the distance of stage 1 for the optimal route.

Table M2-5 The data below is a dynamic programming solution for a shortest route problem. -Using the data in Table M2-5,determine the optimal distance of stage 2.