a) Explain any three uses of an inventory (3mks)
b) Describe the three main costs considered in inventory management (3mks)
c) Why would we adopt simulation in place of other known mathematical techniques (3mks)
d) The table below shows the demand for a particular brand of razor in a shop for each of the last nine months
Month 1 2 3 4 5 6 7 8 9
Demand 10 12 13 17 15 19 20 21 20
i. Calculate a three month moving average for months three to nine. What would be forecast for the demand in the month tenth
ii. Apply exponential smoothing with a smoothing constant of 0.3 to derive a forecast for the demand in month ten.
iii. Which of the two forecasts for the month ten do you prefer and why? (9mks)
e) Consider a situation where the mean arrival rate is one customer every 4 minutes and the mean service time is two and a half minutes. Calculate;
i. The average number of customers in the system
ii. Average queue length
iii. Average a customer spends in the system
iv. Average time a customer waits before being served (6mks)
f) The wizard computer company purchases 5000 hard drives per year for use in its computers. Each order costs $70. The inventory holding cost is 25% of the unit price. the supplier has provided the following price list.
Order quantity Price per unit
1-499 $50
500-649 $45
650 and above $42.50
Assuming instantaneous delivery find
i. Optimal order delivery
ii. Optimal total annual cost (5mks)
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