Module 4 Individual Problems M4_IND1. A trauma center keeps ambulances at locations throughout the east side of a city in an attempt to minimize the response time in the event of an emergency. The times in minutes, from ambulance locations to population centers are given in the table below. POPULATION CENTERS AMBULANCE LOCATIONS Site 1 Site 2 Site 3 Site 4 EAST 8 9 12 15 NORTHEAST SOUTHEAST CENTRAL 9 11 14 12 12 10 12 13 13 8 11 9 Find the optimal assignment of ambulances to population centers that will minimize the total emergency response time. a) What is the total minimum response time of all ambulances to their assigned population centers? b) To what population center is the Site 1 ambulance location assigned to? c) To what population center is the Site 2 ambulance location assigned to? d) To what population center is the Site 3 ambulance location assigned to? e) To what population center is the Site 4 ambulance location assigned to? 1 M4_IND2. A food distribution company ships fresh spinach from its four packing plants (Eaglestown, Farrier, Guyton, and Hayesville) to large East-coast cities (Atlanta, Boston, Charlestown, and Dover). The shipping costs per crate, the supply and demand are shown in the table below. MARKETS PACKING PLANTS Eaglestown Farrier Guyton Hayesville Demand ATLANTA BOSTON CHARLESTOWN DOVER SUPPLY $6.50 $6.00 $7.00 $8.00 8,000 $7.50 $6.00 $6.00 $8.50 9,000 $8.00 $4.50 $7.50 $8.50 11,000 $8.00 $7.50 $8.00 $7.50 5,000 9,000 10,000 7,000 7,000 Formulate a model that will permit the company to meet its demand ant the lowest cost. a) b) c) d) What is the total cost to meet the demands in the four markets? How much product is shipped from Hayesville to Boston? How much product is shipped from Eaglestown to Charlestown? Which of the possible paths (packing plant to market) have no product shipped along that route? 2 M4_IND3. A supply chain consists of three plants (A, B, and C), three distributors (J, K, and L), and three stores (X, Y, and Z). The relevant supply, demand, and unit shipping costs are given in the tables below. PLANT A B C SUPPLY (units) 400 600 350 STORES X Y Z DEMAND (units) 450 450 350 The unit transportation costs ($) for the shipments from the plants to the distributors and from the distributors to the stores are shown below: FROM PLANT J $8 $5 $6 A B C FROM DISTRIBUTOR TO DISTRIBUTOR K $5 $7 $8 J K L X $2 $5 $6 TO STORE Y $6 $5 $8 L $6 $4 $7 Z $8 $7 $9 Formulate this problem in Excel and solve to determine the minimum shipping costs required to meet demands. a) b) c) d) e) What is the total cost to minimize shipping costs from the plants? Which routes had zero units shipped? Which supplier did not ship out all of its supply? How many units should be shipped from C to J? How many units should be from K to Y? 3 M4_IND4. A hospital is planning an addition to existing facility and have secured funds so that they can spend up to $7 million for the improvements. The architect has been asked to consider the following design parameters: (1) there should be at least 15 intensive care units (ICU) rooms. There should be no more than 20 ICU rooms; (2) there should be at least 10 cardiac care unit (CCU) rooms. There should be no more than 20 CCU rooms; (3) there should be no more than 40 double rooms; (4) there should be at least 35 single rooms; and, (5) all patient rooms should fit into the allotted 40,000 square foot space (not including hallways). The following table summarizes the relevant room data: ROOM TYPES DOUBLE ICU SINGLE Cost per room to build and finish (in thousands of $) Minimum square feet required Profit per room per month (in thousands of $) CCU $48 $59 $95 $88 310 450 340 350 $21 $28 $48 $41 How many room of each type should the architect include in the hospital design to maximize the total profit per month? a) b) c) d) e) What is the total profit per month for the hospital design (in thousands of $)? How many Single rooms should be included? How many Double rooms should be included? How many ICU rooms should be included? How many CCU rooms should be included? 4 M4_IND5. A truck with the capacity to load 2,000 cubic feet of cargo is available to transport items selected from the following table. ITEM VALUE A B C D E F G $1,800 $1,400 $1,100 $900 $1,600 $1,100 $1,200 VOLUME (cu. ft.) 700 600 450 400 650 350 600 If selected, an item must be shipped in its entirety (i.e.no partial shipments or multiple shipments). Of items B, C, and D - at least two of these items must be selected. If item B is selected, the G cannot be selected. The shipment must include at least four of these items. Which of these items should be selected to maximize the value of the shipment? a) What is the total value for the shipment? 5