Sam\'s Cat Hotel in Kirkland operates 50 weeks per year, 5 days per week. It pur

Question

Sam's Cat Hotel in Kirkland operates 50 weeks per year, 5 days per week. It purchases kitty litter for $7.50 per bag. The following information is available about these bags: Demand = 65 bags/week Order cost = $50/order Annual holding cost = 30 percent of cost Desired cycle-service level = 92 percent Lead time = 2 week(s) (10 working days) Standard deviation of weekly demand = 8 bags Current on-hand inventory is 200 bags, with no open orders or back orders. Suppose that Sam's Cat Hotel uses a P system. The average daily demand, d, is 13 bags (65/5), and the standard deviation of daily demand, Standard Deviation of Weekly Demand/Squareroot Days per Week, is 3.578 bags. Refer to the standard normal table for z-values. a. What P (in working days) and T should be used to approximate the cost trade-off's of the EOQ? The time between orders, P, should be days. (Enter your response rounded to the nearest whole number.) The target inventory, T, should be bags. (Enter your response rounded to the nearest whole number.) b. How mu Ch more safety stock is needed than with a Q system? bags. (Enter your response rounded to the nearest whole number.) c. It is time for the periodic review. How mu Ch kitty litter should be ordered? bags. (Enter your response as an integer.)

Explanation / Answer

P = 15.84 days

T = 351.82

Order Quantity = 151.82

Daily Demand µD = 13 Standard Deviation of Daily Demand D = 3.578 Working Days per year Y = 250 Annual Demand D = Y*µD 3250 Lead Time (Days) L = 10 Service level SL = 92.00% Z-value corresponding to Service Level Z = 1.41 Safety stock ss = Z(L*D2 + µD*L2 ) 15.90 Cost of Item C = $7.50 Annual Holding Cost Rate HR = 30% Annual Holding Cost per Unit H = C*HR $2.25 Ordering Cost per Order O = $50.00 Lot Size / Optimal Order Qty Q* = (2*D*O/H) 380.06 Cycle Stock cs = Q*/2 190 Average Inventory I = cs + ss 206 Inventory turnover ITO = D/I 15.78 Review Period P = Y/ITO 15.84 Target Inventory Level T = µD*(L+P) + ss 351.82 On-Hand Inventory OH = 200.00 Order Quantity Q = µD*(L+P) + ss - OH 151.82

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