Answer to Question #155098 in Operations Research for Wachira Ann Wangari

Question

A team of 15 men is employed to unload lorries at a terminal. The team works a -6 hour day during which 36 lorries arrive (i.e 6 per hour)and it takes 7.5 minutes to attend one lorry with the team acting as a single unit. Lorries are served on a FIFO basis. It has been estimated that the cost of keeping lorries waiting is $6per hour. Members of the teams are each paid $2.50 per hour. It had been estimated that if the size of the team is increased to 20 men, the average service time would fall to 5 minutes.

Reguired

Calculate the cost of the present system and the cost of the proposed system, and determine whether an increase in the size of the team would be justified on grounds of cost.

Answer 1

For 15-men team.

1st lorry will wait for 0 min ($\frac{0}{60}\cdot 6=0$ $).

2nd lorry will wait for 7.5 min ($\frac{7.5}{60}\cdot 6=0.75$ $).

3rd lorry will wait for 15 min ($\frac{15}{60}\cdot 6=1.5$ $).

4th lorry will wait for 22.5 min ($\frac{22.5}{60}\cdot 6=2.25$ $).

5th lorry will wait for 30 min ($\frac{30}{60}\cdot 6=3$ $).

6th lorry will wait for 37.5 min ($\frac{37.5}{60}\cdot 6=3.75$ $).

In total their waiting cost is 11.25 $ in one hour (and 67.5 $ in six hours).

A team will have 2.5•15•6=225 $.

And total cost is 292.5 $.

For 20-men team.

1st lorry will wait for 0 min ($\frac{0}{60}\cdot 6=0$ $).

2nd lorry will wait for 5 min ($\frac{5}{60}\cdot 6=0.5$ $).

3rd lorry will wait for 10 min ($\frac{10}{60}\cdot 6=1$ $).

4th lorry will wait for 15 min ($\frac{15}{60}\cdot 6=1.5$ $).

5th lorry will wait for 20 min ($\frac{20}{60}\cdot 6=2$ $).

6th lorry will wait for 25 min ($\frac{25}{60}\cdot 6=2.5$ $).

In total their waiting cost is 7.5 $ in one hour (and 45 $ in six hours).

A team will have 2.5•20•6=300 $.

And total cost is 345 $.

 The size of the team would not be justified on grounds of cost.