A company has two grades of inspectors grade one and grade two. These inspectors

Question

A company has two grades of inspectors grade one and grade two. These inspectors are to be assigned for quality control inspection it is required that at least 1800 pieces be inspected per 8 hour day. Grade one inspectors can check pieces at the rate of 25 pieces per hour with an accuracy of 98% Grade two can check pieces at the rate of 15peces per hour with an accuracy of 95%. The wage rate of grade one inspector is Shs. 320 per hour while that of grade two inspectors is Shs. 240 per hour. Each time an error is made by an inspector the cost to the company is Shs. 160. The company has 8 grade one inspectors and 10 grade two inspectors available for the inspection job. Formulate this as a linear program mathematical model.

Explanation / Answer

Given :

Working hours in a day = 8hrs

Cost to company for

Decision Variables :

Considering the objective as minimizing the inspection cost.

Let the number of Grade I inspector = G1

and the number of Grade II inspector = G2

For Grade I inspector :-

Total pieces inspected= 25 pieces/hr X 8 hrs = 200 pieces

Considering 98% accuracy, pieces wrongly inspected = 2% of pieces inspected= 0.02 X 200= 4

Cost to company for error= 4 X 160= Shs. 640

Wages = Shs.320/ hr X 8hr= Shs. 2560

Daily cost of inspection = Shs 2560 + Shs. 640 = Shs. 3200

For Grade II inspector :-

Total pieces inspected= 15 pieces/hr X 8 hrs = 120 pieces

Considering 95% accuracy, pieces wrongly inspected = 5% of pieces inspected= 0.05 X 120= 6

Cost to company for error= 6 X 160= Shs. 960

Wages = Shs.240/ hr X 8hr= Shs. 1920

Daily cost of inspection = Shs 1920 + Shs. 960 = Shs. 2880

Objective Function : Minimize cost of inspection Z= 3200 G1 +2880 G2

Constraints:

Number of inspections: 25G1 + 15 G2 >= 1800

No. of Grade I Inspectors G1<=8

No. of Grade II Inspectors G2<=10

G1, G2 >= 0

Grade I Inspector Grade II Inspector No of pieces inspected per hour 25 15 Accuracy of inspection 98% 95% Wage Rate per hour 320 240

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