2. (50 points) A store sells refrigerator and a check the sales database to determine the weekly refrigerator sales. Store manager realize that the demand for the product is zero or one or two refrigerator in a week. He checks last 200 weeks and assumes that demand distribution can be calculated by using following table. Weekly demand 0 12 Number of 40 100 60 weeks The store uses the following inventory policy: Store manager checks the inventory level at the end of every week. If the inventory level is less than or equal to 1, store manager orders up to 3 units. Otherwise she does not order. Refrigerators are delivered at beginning of next week. This policy is called (R, S, S). In this question R = 1 week, s = 1, and S = 3. Manager also asssumes that unsatisfied demand is lost. Hint: Define X, that shows the number of refrigerators at the end of the week n. a) (10 points) An inspector is visiting the store at the end of each week. If he finds that there are 3 product in the store back to back 4 weeks, he will give a notice to the store. What is the probability that inspector will not give a notice? b) (10 points) What is the mean soujourn time that there will be 1 product in the store? Explain the meaning of the result. 2 Page c) (5 points) If store manager observes the store for five years (260 weeks), what is the fraction of time that he will have one product in the inventory? d) (15 points) Out of 100 weeks sampled randomly from a long period, what is the expected number that would be zero products in the inventory? Which interpretations of steady-state probability did you use in answering this part ? Explain. e) (10 points) If holding cost of one product for one week is 3 KD. Calculate the average weekly holding cost for the store. 2. (50 points) A store sells refrigerator and a check the sales database to determine the weekly refrigerator sales. Store manager realize that the demand for the product is zero or one or two refrigerator in a week. He checks last 200 weeks and assumes that demand distribution can be calculated by using following table. Weekly demand 0 12 Number of 40 100 60 weeks The store uses the following inventory policy: Store manager checks the inventory level at the end of every week. If the inventory level is less than or equal to 1, store manager orders up to 3 units. Otherwise she does not order. Refrigerators are delivered at beginning of next week. This policy is called (R, S, S). In this question R = 1 week, s = 1, and S = 3. Manager also asssumes that unsatisfied demand is lost. Hint: Define X, that shows the number of refrigerators at the end of the week n. a) (10 points) An inspector is visiting the store at the end of each week. If he finds that there are 3 product in the store back to back 4 weeks, he will give a notice to the store. What is the probability that inspector will not give a notice? b) (10 points) What is the mean soujourn time that there will be 1 product in the store? Explain the meaning of the result. 2 Page c) (5 points) If store manager observes the store for five years (260 weeks), what is the fraction of time that he will have one product in the inventory? d) (15 points) Out of 100 weeks sampled randomly from a long period, what is the expected number that would be zero products in the inventory? Which interpretations of steady-state probability did you use in answering this part ? Explain. e) (10 points) If holding cost of one product for one week is 3 KD. Calculate the average weekly holding cost for the store