I. The Childfair Company has three plants producing child push chairs that are to be shipped to fourdistribution 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 tothe respective distributing centers is given to the right:DistanceDistribution Center12418001300400700231100140060010006001200800900The freight cost for each shipment is $100 plus 50 cents per mile.How much should be shipped from each plant to each of the distribution centers to minimize the totalshipping cost?(a) Formulate this problem as a transportation problem by constructing the appropriate parametertable.(b) Draw the network representation of this problem.(c) Obtain an optimal solution.

Transportation Problem: Given details: Distribution Center Plant 1 2 3 4 Capacity 1…

Answered: I. The Childfair Company has three…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter5: Network Models

Section5.4: Other Logistics Models

Problem 24P

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A company has n factories. Factory i is located at point(xi, yi), in the x–y plane. The company wants to locate awarehouse at a point (x, y) that minimizes ini1(distance from factory i to warehouse)2Where should the warehouse be located?
Draw the network for this transportation problem. (Let xij represent the flow from node i to node j.) Min 2x13 + 4x14 + 6x15 + 8x23 + 11x24 + 9x25 s.t. x13 + x14 + x15 ≤ 500 x23 + x24 + x25 ≤ 400 x13 + x23 = 300 x14 + x24 = 300 x15 + x25 = 300 xij ≥ 0
Design a spreadsheet to compute the total rectilinear distance from a set of up to10 existing locations to any other location. Assume that existing locations areplaced in Columns A and B and the new location in cells D1 and E1. Initializecolumn A with the value of cell D1 and column B with the value of cell E1, so thatthe total distance will be computed correctly when there are fewer than10 locations.a. Suppose that existing facilities are located at (0, 0), (5, 15), (110, 120), (35, 25),(80, 10), (75, 20), (8, 38), (50, 65), (22, 95), and (44, 70), and the new facility is tobe located at (50, 50). Determine the total rectilinear distance of the new facilityto the existing facilities.b. Suppose the new facility in part (a) can be located only at x =0, 5, 10, . . . , 100and y = 0, 10, 20, . . . , 100. By systematically varying the x and y coordinates,find the optimal location of the new facility
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