I. The Childfair Company has three plants producing child push chairs that are t
ID: 360196 • Letter: I
Question
I. The Childfair Company has three plants producing child push chairs that are to be shipped to four distribution centers. Plants 1, 2, and 3 produce 12, 17, and 11 shipments per month, respectively. Each distribution center needs to receive 10 shipments per month. The distance from each plant to the respective distributing centers is given below: Distance Distribution Center 2 1800 miles 1,300 miles 400 miles 700 miles 3600 miles 1,200 miles 800 miles 900 miles The freight cost for each shipment is S100 plus 50 cents per mile. How much should Plant 21,100 miles 1,400 miles 600 miles 1,000 miles be shipped from each plant to each of the distribution centers to minimize the total shipping (a) Construct the appropriate parameter table. (b) Formulate this problem as a transportation problem. (c) Draw the network representation of this problemExplanation / Answer
The parameter table is the cost matrix representing the cost of transportation between each plant and each distribution center. the freight cost is based on the distance @ $100 plus 50cents per mile.
Therefore, freight cost matrix is as follows:
Let Xij be the decision variables representing the number of shipments from ith plant to the jth distribution center.
Therefore Objective is to minimize the total cost of transportation Z = Sigma(i)Sigma(j) CijXij
Constraints are the supply and demand as mentioned in the question:
Sigma(j) X1j <= 12, Sigma(j) X2j <= 17, and Sigma(j) X3j <= 11 Supply constraints of plants
Sigma(i) Xij >= 10 for j = 1,2,3,4 Demand at the distribution centers
Xij >= 0 being number of shipments needs to be non-negative integers.
Formulation and solution as per excel solver is as follows:
Solution
Network has three sources and four destinations and arcs are from each source to each destination as follows:
Freight Cost Matrix Cij Center1 Center2 Center3 Center4 Plant1 500 750 300 450 Plant2 650 800 400 600 Plant3 400 700 500 550