Question 2 (20 marks) Speedy Sports Ltd (Speedy) sells one style of sports shoe. These shoes are purchased from several manufacturers in mainland China. Speedy has a warehouse in Shenzhen where the manufacturers deliver the finished products to Speedy. The annual demand for shoes by Speedys customers is approximately 228,000 pairs. The ordering cost is $100 per order. The annual carrying cost of one pair of shoes is $3.8. Speedy estimates the average weekly demand to be 4,750 pairs. However, demand each week may vary with the following probability distribution: Total demand for one week 4,250 pairs 4,500 pairs 4,750 pairs 5,000 pairs 5,250 pairs Probability (sums to 1.00 0.05 0.15 0.55 0.20 0.05

Speedy adopts an EOQ model to determine the number of shoes to order from these manufacturers. According to the supply agreements with its manufacturers, if Speedy encounters a situation of urgent demand from customers but the company is out of stock, Speedy can rush the shoes from manufacturers at an additional cost of $3.00 per pair.

Required: a What is the optimal number of pairs of shoe per order according to the EOQ model? (3 marks) b Assume each month consists of approximately four weeks. The agreed purchase-order lead time is one week. At what point should Speedy reorder shoes? (3 marks) c How much safety stock should Speedy hold? How will this affect the reorder point and reorder quantity? (11 marks) d Speedy is considering implementing a JIT system and believes that JIT has advantages over the EOQ model. Do you agree and why? (3 marks)