Question

BADM 3963 Transportation & Assignment models homework Write the formulations for #1, 2, 3 in a Word document NOTE: for decision variables, you may type them as X11, X12, X13 etc without subscripting format. Solve the transportation problems #4, 5 on the tables in the same Word document- show work on the table as well as reporting the solution and cost. Submit Word file in BB Assignment Due 4/25, 9pm 1. Consider a small company with three sources of supply: Toronto, Montreal, and Halifax. These may either be manufacturing facilities or warehouses for a foreign firm doing business in Canada. The capacities of each of these locations are 500, 400 and 300 units respectively. These locations need to supply markets in four other cities: London, Ottawa, Kingston and Quebec City. The requirements of each of these locations are respectively: 450, 350, 250 and 150 units. The major costs are from the transportation of the units. The following costs per unit have been estimated for each of the routes. To London Otawa Kingston Quebee City From Toronto $6 98 Montreal 12 17 6 Halitax I 13 14 13 10 Write the formulation for this problem as a transportation problem 2. ABC Inc has factories at A, B, and C which supply warehouses at D, E, F and G. The monthly capacities of each factory and requirements of each warehouse in units per month are: Factory Capacity Warehouse Demand A 160 D 80 90 110 160 140 190 The shipping costs per unit along each route are: ToDEF G From A 4450 40 45 В 4052 5050 С 50404043 Write the formulation for this problem as a transportation problem 3. Consider a small machine shop where each worker can operate all the machines but operates some of the machines better than others. On any given day there are a number of jobs which have to be completed. For this situation, the problem facing management, is how to obtain the fastest turnaround time for all iobs The time it takes to perform an average job for each of these workers is as follows Drilling Grinding Lathework Joe 5 Jack 9 John 15 10 13 11 Write the appropriate formulation for this as an assignment problem to determine which worker should be assigned to which machine to minimize total time for the iobs 4. Company X produces widgets at three plants and ships them to four customers. The table below indicates the cost per unit for shipping from each plant to each customer, as well as the supply at each plant and each customer's demand Using the Northwest Corner method, find a feasible solution for the problem. o Show the assigned amounts in the table Customer ACustomer B Customer CCustmer D Supply Plant $4 Plant 2 S12 Plant 3 ss Demand 80 S7 100 S3 S8 S8 200 S10 S16 150 120 160 a. Write out the NW corner solution b. Calculate the total cost of the NW corner solution 5. Company X produces widgets at three plants and ships them to four customers. The table below indicates the cost per unit for shipping from each plant to each customer, as well as the supply at each plant and each customer's demand. Using the Minimum cost method, find a feasible solution for the problem. Show the assigned amounts in thetable Customer A Customer BCustomer CCustomer DSupply S7 S8 S16 Plan S4 Plant 2S12 Plant 3S8 Demand 80 S7 S3 S10 S1 100 S8 200 150 S5 90 120 160 c. Write out the Minimum cost solution d. Calculate the total cost of Minimum cost solution

Answer 1

1)

	London	Ottawa	Kinngston	Quebecc	Capacities
Toronto	6	9	8	13	500
Montreal	12	17	6	7	400
halifax	1	14	13	10	300
Requirements	450	350	250	150

The objective here is to minimize the transportation cost Z.

Let X be the number of units.

i = 1 toronto, 2 montreal, 3 halifax

j= 1 london, 2 ottawa, 3 kingston ,4 quebecc

1 1 represent units transferred from toronto to london

1 2 represents units from toronto to ottawa

1 3 represent units from toronto to kingston likewise 1 4 represent units from toronto to quebecc

formulations:

Minimize Z = 6X₁₁ + 9X₁₂ + 8X₁₃+13X₁₄+12X₂₁+17X₂₂+6X₂₃+7X₂₄+1X₃₁+14X₃₂+13X₃₃+10X₃₄

Subject to constraints:

X11+X12+X13+X14 =500

X21+X22+X23+X24=400

X31+X32+X33+X34=300

X11+X21+X31 =450

X12+X22+X32=350

X13+X23+X33=250

X14+X24+X34=150

X11$\geq$0

X12$\geq$0

X13$\geq$0

X14$\geq$0

X21$\geq$0

X22$\geq$0

X23$\geq$0

X24$\geq$0

X31$\geq$0

X32$\geq$0

X33$\geq$0

X34$\geq$0