Uwezo Equipment Ltd. assembles precision irrigation systems. The firm’s customer contracts require high service
reliability, but the company experiences fluctuating demand driven by seasonal farming patterns and project-based
procurement.
A critical component is imported, and supplier lead times are affected by shipping delays. Management is reviewing
its ordering policy in order to minimise total relevant inventory cost while maintaining the required service level.
A supplier has proposed a quantity discount, although accepting the discount would result in larger average
inventories.
Assume that:
• Annual demand is known and constant for Economic Order Quantity (EOQ) purposes.
• Lead time is constant at four weeks.
• Demand during lead time is normally distributed.
• Safety stock is held only to achieve the required cycle-service level.
Additional information:
1. Annual demand is 80,000 units.
2. Ordering cost is Sh.4,000 per order.
3. Annual holding cost is Sh.180 per unit.
4. Purchase price is Sh.2,000 per unit.
5. A supplier offers a 5% discount for orders of 6,000 units or more.
6. Weekly demand standard deviation is 150 units.
7. Lead time is 4 weeks.
8. Desired service level is 97% (Z = 1.88).
9. There are 50 working weeks per year.
Required:
(i) Compute the economic order quantity (EOQ).
(ii) Calculate the total annual relevant cost under the EOQ policy and under the discount policy based on an order
quantity of 6,000 units. In each case, include annual purchase cost, annual ordering cost and annual holding
cost. Hence, advise management on whether the quantity discount should be accepted.
(iii) Using the standard deviation of demand during lead time derived from the weekly demand variability given
above, compute the safety stock and the re-order level required to achieve the stated service level.
(iv) Explain ONE limitation of applying the EOQ and service level-based safety stock model in this context.
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