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Product Code:- Operation-Management-PH154


  1. Consider the network given below.  Answer the proceeding questions about this network.  The weights are given in hours:


  1. What is the shortest path from node 1 to node 11?  Support your response; report the length of this path as well as the path.
  2. Suppose the weight from node 1 to node 5 changes from 3 to 5.  The change in weight changes the shortest path from node 1 to node 11.  Verify this by reporting the new path with its total weight.  Why does the path change?  Explain.


  1. Panini-ville is expecting the opening of a Delicious Sandwich restaurant in its town in 3 weeks.  The mayor of Panini-ville wishes to avoid mass chaos in the streets.  Therefore, the mayor has decided to restrict the flow of traffic through the town.  Some streets will be blocked to one-way, while others will be open in both lanes.  Numbers are given in the chart below representing thousands of cars that can travel each road each hours:
  1. How many vehicles can travel over each road before maximum flow is obtained?  What is the maximal flow?  Assume that the flow goes from 1 to 6, where 6 is the location of the new restaurant.
  2. Suppose that you (in place of the mayor) can open another road.  This road has a flow of 4 thousand cars per hour, and cannot start or end at 6.  Assuming this ONE road, where would you place the road in order to increase overall flow the most?  Explain briefly.


  1. Transportation costs for Legos are give in the following chart (see right):
  1. How should the legos be shipped to satisfy demand and minimize cost?  Provide detailed solution with analysis.
  2. Suppose that you consider building a new source to satisfy demand.  Choose a location and assign values for shipping to the 4 destinations.  Assuming the production levels of this new facility put supply equal to demand in the table above, how should the legos be shipped to minimize costs?  Comment on the change in shipping plans from what you found previously.
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1. Shortest Path Problem a)The objective is to minimize the distance Let Xij is the amount of flow in the arc(i,j) Xij = 1 if flow is there from I to j , 0 otherwise Wij = Weight of the arc i-j Objective is Minimize Z =Wij*Xij Constraints Total Input flow = Total Output Flow =>Total Out-Total In = 0 for intermediate nodes We have to reach from node 1 to 11 For node 1 1= X12+X15+X16 For node 11

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