Question

The Ace Manufacturing Company has orders for three similar products.

Product	Orders (units)
AA	2,200
BB	700
CC	1,400

Three machines are available for the manufacturing operations. All three machines can produce all the products at the same production rate. However, due to varying defect percentages of each product on each machine, the unit costs of the products vary depending on the machine used. Machine capacities for the next week and the unit costs are shown below.

Machine	Capacity (units)
11	1,800
22	1,800
33	1,100

	Machine
Product	1	2	3
A	$1.00	$1.30	$1.10
B	$1.20	$1.40	$1.00
C	$0.90	$1.20	$1.20

Use the transportation model to develop the minimum cost production schedule for the products and machines.

1. Show the production schedule.

(x_A1, x_A2, x_A3, x_B1, x_B2, x_B3, x_C1, x_C2, x_C3) = ??????

  
2. Determine the cost (in dollars) of the production schedule.

Total = $ ????

Answer 1

This is a demand supply transportation problem. Let us represent the problem tabularly:

	Machine
Product	1	2	3	Orders
A	1	1.3	1.1	2200
B	1.2	1.4	1	700
C	0.9	1.2	1.2	1400
Capacity	1800	1800	1100		4700
				4300	Total

Here we can clearly see that there is mismatch between supply and demand, this is unbalanced

	Machine
Product	1	2	3	Orders
A	1	1.3	1.1	2200
B	1.2	1.4	1	700
C	0.9	1.2	1.2	1400
Dummy	0	0	0	400
Capacity	1800	1800	1100		4700
				4700	Total

We have tried to balance it by adding a row.

Now lets solve this with Northwest corner method:

	Machine
Product	1	2	3	Orders
A	1800	400	0	2200
B	0	700	0	700
C	0	700	700	1400
Dummy	0	0	400	400
Capacity	1800	1800	1100

Now lets multiply the value and cost table to get the final answer

1800*1 + 400*1.3 + 700*1.4 + 700*1.2 + 700*1.2 + 400*0

= 4980

Hence part a) production schedule is shown

& part b) the final cost is found = $4980