Problem 13-28 Regional Supermarket is open 355 days per year. Daily use of cash
ID: 330225 • Letter: P
Question
Problem 13-28 Regional Supermarket is open 355 days per year. Daily use of cash register tape averages 16 rolls. Usage appears normally distributed with a standard deviation of 3 rolls per day. The cost of ordering tape is $.75, and carrying costs are 40 cents per roll a year. Lead time is 3 days. Use Tablet and Table2. a. What is the EOQ? (Round your answer to the nearest whole number.) EOQ b. What ROP will provide a lead time service level of 95 percent? (Round your answer to the nearest whole number.) ROP c. What is the expected number of units short per cycle with 95 percent? Per year? (Round your answers to 4 decimal places.) Expected number of units Per cycle Per year d. What is the annual service level? (Round your answer to 4 decimal places.) Annual service levelExplanation / Answer
A.
EOQ = (2*annual demand*ordering cost / carrying cost)^.5 =
EOQ = (2*16*355*.75/.4)^.5 = 195.95 or 196 units
B.
At 95%, value of Z = 1.64
ROP = Daily demand*lead time + Z*SD*L^.5 = 16*3 + 1.64*3*3^.5
ROP = 56.52 or 57 units
C.
L(Z) at 95% = .021 ( as per the Z chart & loss table)
Expected number of units short per cycle = .021*(3^.5 *3) = .1091
Expected number of units short per year = .1091*(355*16/195.95) = 3.1625 rolls / year
D.
Annual service level = 1 - 3.1625/(355*16)
Annual service level = 99.9443%