Please show calculations and explanations. Do not provide handwritten answers. You may refer to the formulas below. Thanks!

ROL

Safety Stock

Asia Furnishing is a retailer of modular toilet products. Currently, the lead time for one of the products, the toilet door, is relatively high, at 5 weeks. The average demand for toilet doors is 200 per week. The standard deviation of demand during the lead time is 85 doors. The store plans to provide a service level of 99 per cent. (a) The store is looking for another supplier who can supply the doors in one week at the same price. Analyse how much safety stock can be reduced by moving to the new supplier without reducing the 99 per cent cycle-service level. (15 marks) (b) The store hired a new manager who insists on using a probability distribution for the lead time of supply, instead of a fixed lead time. Based on the historical data from the present supplier, she estimated that the standard deviation of lead time is 1 week. How will the amount of safety stock change after including this information? What should be the reorder level for the store? (10 marks) It is evident that if we want to have a higher service level, we need to hold more safety stock. Higher service levels will increase the responsiveness of the company and enhance customer satisfaction, but this comes with increased inventory level and cost. As a result, service level is related to customer satisfaction as well as the profit objectives of the organisation. To provide higher service level to its customers, an organisation should keep additional stock in the form of safety stock, to satisfy the demand variations during the lead time. This can be done by raising the ROL by safety stock on top of mean 3.2 shows graphically how ROL changes when safety stock is added. The ROL for variable demand or supply, Reorder level (R)= mean LTD+ safety stock Figure 3.2 ROL and Safety Stock discuss how service level is used to compute safety stocks and reorder levels for various types of uncertainties. The amount of safety stock depends on the service level the organisation would like to provide. Higher service level would require more safety stock. If LTD is normally distributed, the service level indicates how many standard deviations of LTD need to be kept as a safety stock. If the variability is more, standard deviation of LTD ( LTD ) will be higher. In Figure 3.3, the shaded area indicates the service level provided to the customers and Z is the number of standard deviations from the mean. e.g., 97.7% service level corresponds to Z value of 2 . The Z value for different probabilities (service levels) can be found in a Normal Table. rigure 3.3 bervice level in Normally distributed demand If Z is the number of standard deviations from the mean that corresponds to the specified service level, the amount of safety stock required is given as Safetystock=ZLTD For example, a 95\% service level has a probability of 0.05 (= 10.95) that LTD is higher than safety stock. From the normal tables, a probability of 0.05 corresponds to Z=1.65 and the safety stock becomes Safety stock =SS=1.65LTD