SCM Network Design Problems
Problem 1: The Rappaport Communications Company provides cellular telephone services in several midwestern states. The company is planning to expand its customer base by offering cellular service in northeastern Ohio to the cities of Cleveland, Akron, Canton, and Youngstown. The company will install the hardware necessary to service customers in each city on preexisting communications towers in each city. The X-Y coordinates of the preexisting towers are Cleveland (5, 45), Akron (12, 21), Canton (17, 5), and Youngstown (52, 21). The location of the preexisting towers are not under the control of Rappaport.
However, the company needs to construct a new communications tower somewhere between these cities to handle intercity calls. This tower will also allow cellular calls to be routed onto the satellite system for worldwide calling service. The tower that the company is planning to build can cover areas within a 40-mile radius. Thus, the tower must be located within 40 miles of the preexisting towers in each of these cities. Rappaport wants to determine the coordinates of the new communications tower that minimizes the sum of the distances between the new tower and each the four existing towers.
a) What is the coordinate of the optimal location and the distance from each of the four existing towers?
b) If the objective is to minimize the maximum distance between the new tower and any of the four existing towers, what will be the coordinate of the optimal location and the distance from each of the four existing towers?
Question 2: Astra Chemicals has 3 plants and 8 distribution centers located in different cities. The company is planning to build a cross-docking facility where the shipments from each plant will be sorted and then delivered to each distribution center. The North American Hospital Association buys supplies from 4 supplier plants and has 10 Hospitals located in different cities (A through J). The Association is planning to build a cross-docking facility where the shipments from each plant will be sorted and then delivered to each Hospital.
For each plant, the unit shipping cost in $/ton/mile to the hub (this unit cost includes handling and sorting at the hub), volume shipped in tons, and the map coordinates are shown in the following table:
| Plant | $/ton/mile | Tons | X cord | Y Cord |
| P1 | 1 | 1000 | 500 | 700 |
| P2 | 1 | 2000 | 300 | 400 |
| P3 | 1 | 2500 | 900 | 150 |
| P4 | 1 | 3000 | 600 | 700 |
For each hospital, the unit shipping cost in $/ton/mile from the hub (this unit cost includes handling and sorting at the hub), volume shipped in tons, and the map coordinates are shown in the following table:
| City | $/ton/mile | Tons | X cord | Y Cord |
| A | 1.5 | 1300 | 450 | 750 |
| B | 1.3 | 1000 | 550 | 1050 |
| C | 0.95 | 1200 | 750 | 950 |
| D | 1.1 | 800 | 850 | 350 |
| E | 0.85 | 700 | 650 | 350 |
| F | 1.25 | 400 | 780 | 980 |
| G | 0.95 | 1100 | 500 | 800 |
| H | 1.15 | 600 | 750 | 1150 |
| I | 1.02 | 500 | 450 | 300 |
| J | 1.05 | 900 | 950 | 250 |
a) Where should we build a new hub if we are building the hub at a new location and what will be total shipping cost for the whole system? (Hint: Hub serves all 14 locations)
b) If we do not want to build hub at a new location and simply expand one of existing plants or a hospital facility to serve as a hub, which location should be used and how much will the shipping cost increase compared to building a new hub as shown in part a).
Question 3: ABC has been experiencing a significant decline in sales. The company anticipates demand for the next year to be 12,000 units in the East, 8,000 units in the South, 10,000 units in the Midwest, and 15,000 units in the West. ABC currently has six manufacturing plants. The current capacities, the annual fixed costs (if kept open) and the variable costs per unit for each of the six plants are shown in the table below, along with the shipping costs to each of the four markets.
Current Plant Sites and costs:
| Plant | Shipping Costs to Different Regions ($/unit) | Annual costs and capacity of plant | |||||
| Locations | East | South | Midwest | West | VC $/unit | FC if open | Capacity |
| Newark | 2.00 | 2.20 | 2.10 | 2.90 | $50 | 1,000,000 | 20,000 |
| Raleigh | 1.90 | 1.80 | 2.20 | 2.40 | $45 | 950,000 | 10,000 |
| Milwaukee | 2.20 | 2.30 | 1.80 | 2.20 | $48 | 980,000 | 20,000 |
| Sacramento | 2.80 | 2.50 | 2.20 | 2.10 | $52.50 | 1,000,000 | 20,000 |
| Houston | 2.00 | 1.70 | 2.20 | 2.50 | $47 | 970,000 | 20,000 |
| Indiana | 2.30 | 2.10 | 2.00 | 2.60 | $49 | 975,000 | 10,000 |
a) Assuming that all plants are going to remain open, what will be the shipping schedule and the optimum costs? Please fill out the table and summary cost details below.
| Plant | Regions | Total Shipped | Excess capacity | |||
| Locations | East | South | Midwest | West | Out of plant | Of each plant |
| Newark | ||||||
| Raleigh | ||||||
| Milwaukee | ||||||
| Sacramento | ||||||
| Houston | ||||||
| Indiana | ||||||
| Shipped |
Total Annual Shipping Cost ______________ Total Annual Variable Cost: _____________
Total Annual Fixed Cost: _______________ Total Annual Cost: ______________
b) Now assume that we can close any plant and save annual fixed cost, if it makes economic sense, what will be the shipping schedule and the optimum costs? Please fill out the table and summary cost details below.
List of plants to close: ____________________________________________________
| Plant | Regions | Total Shipped | Excess capacity | |||
| Locations | East | South | Midwest | West | Out of plant | Of each plant |
| Newark | ||||||
| Raleigh | ||||||
| Milwaukee | ||||||
| Sacramento | ||||||
| Houston | ||||||
| Indiana | ||||||
| Shipped |
Total Annual Shipping Cost ______________ Total Annual Variable Cost: _____________
Total Annual Fixed Cost: _______________ Total Annual Cost: ______________
Question 4: A company has stores at 10 locations as shown below. There is no significant difference in the volume of merchandise sold by each store and the cost of delivery is proportional to the distance from the Distribution Center (DC) to the store. Each store will be assigned to be served by a single DC. The company wants to decide if it should have one or two, or three DCs. For each of three cases, You as the Supply Chain Network designer are asked to figure out:
a) which store will be assigned to which DC?
b) The total distance travelled by the trucks to make one delivery to each of the ten stores.
c) The maximum distance from any of the ten stores to the assigned DC.
| Store | X | Y |
| Panama | 1 | 14 |
| Tallahassee | 6.1 | 15 |
| Jacksonville | 13 | 15 |
| Ocala | 12 | 11 |
| Orlando | 13.5 | 9 |
| Tampa | 11 | 7.5 |
| Ft Pierce | 17 | 6 |
| Ft Myer | 12.5 | 3.5 |
| West Palm | 17.5 | 4 |
| Miami | 17 | 1 |
