Maximum Utility System or Saturation System

This system is basically used to decide the priority among various proposed highway alignment, It depends upon length of road, population, production etc. 

The factors which are taken for obtaining the utility per unit length of road are:

1. Population served by the road network 
2. Productivity served by the network

• Agricultural products
• Industrial products

Steps to find maximum utility per unit length :

1. Population Unit : 

Since the area under consideration consists of number of towns and villages with different different population range this all are grouped into some convenient population ranges and some reasonable utility units are assigned to each group of population. 

2. Productivity Unit :

The total industrial products and agricultural products served by each road system are to be worked out, The productivity served may be assigned appropriate values of utility unites per unit weight.

3. Utility or Best Road Length : 

The total utility of proposed alignment is found out by adding both Population Units and Productivity Units. Then the total utility units are divided by the total road length of each system to obtain the utility rate per unit length.

Rules to Decide the Utility Values :

1. Provide a utility value of 0.5 to lowest population range group and increase the utility value in multiple of two as the population range group increases i.e. 0.5, 1, 2, 4, 8, 16, 32,..................etc.

2. Provide the utility value of 1 to production but if Agricultural and Industrial Productions are compared then assign utility value of 1 to agricultural production and 10 to industrial production.

Lets solve the problem,

Priorities the following road proposal based on the utility value, 

Proposed Road	Length (km)	Number of villages with Population ranges				Industrial Product
		1001-2000	2001-5000	5001-10000	> 10000
A	250	150	169	78	1	210
B	300	301	142	64	3	240
C	350	289	99	49	1	320
D	400	421	131	51	4	340

Solution:

step 1: Assign the utility value: 

Proposed Road	Length (km)	Number of villages with Population ranges				Industrial Product
		1001-2000	2001-5000	5001-10000	> 10000
A	250	150	169	78	1	210
B	300	301	142	64	3	240
C	350	289	99	49	1	320
D	400	421	131	51	4	340
Utility Value		0.5	1.0	2.0	4.0	1

Step 2: Calculate the utility of each proposed road,

For A, 

              = [(0.5x150)+(1.0x169)+(2.0x78)+(4.0x1)+(1x210)] / 250

    For A = 2.456

    For B = 2.241

    For C = 1.901

    For D = 1.998

So we have to give high priority to road having high utility value,

A>B>D>C