A company has two factories, one at Liverpool and one at Brighton.[20] In addition it has four depots with storage facilities at Newcastle, Birmingham, London and Exeter. The company sells its product to six customers C1, C2, ?, C6. Customers can be supplied either from a depot or from the factory direct (see Figure 19.1).

Figure 19.1:

Table 19.1:

	Supplier[a]
	Liverpool	Brighton	Newcastle	Birmingham	London	Exeter
Supplied to	factory	factory	depot	depot	depot	depot
Depots
Newcastle	0.5	?
Birmingham	0.5	0.3
London	1.0	0.5
Exeter	0.2	0.2
Customers
C1	1.0	2.0	?	1.0	?	?
C2	?	?	1.5	0.5	1.5	?
C3	1.5	?	0.5	0.5	2.0	0.2
C4	2.0	?	1.5	1.0	?	1.5
C5	?	?	?	0.5	0.5	0.5
C6	1.0	?	1.0	?	1.5	1.5
[a] A dash indicates the impossibility of certain suppliers for certain depots or customers.

The distribution costs (which are borne by the company) are known; they are given in Table 19.1 (in ? per ton delivered).

Certain customers have expressed preferences for being supplied from factories or depots which they are used to. The preferred suppliers are

C1	Liverpool (factory)
C2	Newcastle (depot)
C3	No preferences
C4	No preferences
C5	Birmingham (depot)
C6	Exeter or London (depots)

Each factory has a monthly capacity given below which cannot be exceeded:

Liverpool	150,000 tons
Brighton	200,000 tons

Each depot has a maximum monthly throughput given below which cannot be exceeded:

Newcastle	70,000 tons
Birmingham	50,000 tons
London	100,000 tons
Exeter	40,000 tons

Each customer has a monthly requirement given below which must be met:

C1	50,000 tons
C2	10,000 tons
C3	40,000 tons
C4	35,000 tons
C5	60,000 tons
C6	20,000 tons

The company would like to determine:

a- What distribution pattern would minimize overall cost?

b- What the effect of increasing factory and depot capacities would be on distribution costs?

c- What the effects of small changes in costs, capacities and requirements would be on the distribution pattern?

d- Would it be possible to meet all customers preferences regarding suppliers and if so what would the extra cost of doing this be?

Liverpool Brighton Factories Newcastle Birmingham London Exeter Depots C1 C2 C3 C4 C5 C6 Customers