Question

A manufacturing firm has four plants and wants to find the most efficient means of meeting the requirements of its four customers. The relevant information for the plants and customers, along with shipping costs in dollars per unit, are shown in the table below:

	Customer (requirement)
Factory (capacity)	Customer 1 (125)			Customer 2 (150)			Customer 3 (175)			Customer 4 (75)
A (100)	$	15		$	10		$	20		$	17
B (75)	$	20		$	12		$	19		$	20
C (100)	$	22		$	20		$	25		$	14
D (250)	$	21		$	15		$	28		$	12

How many arcs will the network have?

		7
		3
		4
		12
		16

Answer 1

• Total demand = Total capacity = 525

We will use lowest unit cost method to assign Factory to satisfy customer demand.

• Lowest unit cost of transport is 10.
  • Arc 1 - 100 units from Factory A will go to Customer 2. Pending demand at customer 2 = 50, pending capacity at A = 0
• Next Lowest Unit cost of transport is $12
  • Arc 2 - 75 units from Factory D will go to Customer 4. Pending demand at customer 4 = 0. Pending capacity at Factory D = 175.
  • Arc 3 - 50 units from Factory B will go to Customer 2. Pending demand at customer 2 = 0. Pending capacity at Factory B = 25
• Now there are pending demands at Customer 1 and Customer 3. Lowest cost among pending options = $19 and next option is $21
  • Arc 4 - 50 units from Factory B will go to Customer 3. Pending demand at customer 3 = 150. Pending capacity at Factory B = 0
  • Arc 5 - 125 units from Factory D will go to Customer 1. Pending demand at customer 1 = 0. Pending capacity at Factory D = 50.
  • Arc 6 & 7 Now Balance from Factory C (100) and Factory D (50) will go to Customer 3 to satisfy the demand.

Total arcs = 7