Sam\'s Cat Hotel operates 52 weeks per year, 7 days per week, and uses a continu

Question

Sam's Cat Hotel operates 52 weeks per year, 7 days per week, and uses a continuous review inventory system. It purchases kitty litter for $10.75 per bag. The following information is available about these bags. Refer to the standard normal table LOADING... for z-values.

Demand = 95 bags/week follows

Order cost = $55/order follows

Annual holding cost = 28 percent of cost

Desired cycle-service level = 99 percent

Lead time = 4 week(s) (28 working days)

Standard deviation of weekly demand = 13 bags

Current on-hand inventory is 325 bags, with no open orders or backorders.

a. What is the EOQ? Sam's optimal order quantity is nothing bags. (Enter your response rounded to the nearest whole number.)

Sam's optimal order quantity is _____bags. (Enter your response rounded to the nearest whole number.)

What would be the average time between orders (in weeks)? The average time between orders is _____weeks. (Enter your response rounded to one decimal place.)

The table below shows the total area under the normal curve for a point that is Z standard deviations to the right of the mean 0.02 0.03 0.04 0.05 0.06 0.07 0.080.09 0.0 0.50000.5040 0.5080 0.5120 0.5160 0.5199 0.5239 0.5279 0.5319 0.5359 0.1 0.5398 0.5438 0.5478 0.55170.5557 0.5596 | 0.5636 0.5675 0.5714 0.5754 0.2 0.5793 0.5832 0.5871 0.5910 0.5948 0.5987 0.6026 0.6064 0.6103 0.6141 0.3 0.6179 0.6217 0.6255 0.6293 0.6331 0.6368 0.6406 0.6443 0.6480 0.6517 0.4 0.6554 0.6591 0.66280.6664 0.6700 0.6736 0.6772 0.6808 0.6844 0.6879 0.5 0.6915 0.6950 0.6985 0.7019 0.7054 0.7088 0.7123 0.7157 0.7190 0.7224 0.6 0.72580.7291 0.7324 0.7357 0.7389 0.7422 0.7454 0.7486 0.7518 0.7549 0.7 0.75800.7612 0.7642 0.7673 0.7704 0.7734 0.7764 0.7794 0.7823 0.7852 0.8 0.78810.7910 0.7939 0.7967 0.7996 0.8023 0.8051 0.8079 0.8106 0.8133 0.9 0.81590.8186 0.8212 0.8238 0.8264 0.8289 0.8315 0.8340 0.8365 0.8389 1.0 0.8413 0.8438 0.8461 0.8485 0.8508 0.8531 0.8554 0.8577 0.8599 0.8621 1.1 0.8643 0.8665 0.8686 0.8708 0.8729 0.8749 0.8770 0.8790 0.8810 0.8830 1.2 0.8849 0.8869 0.8888 0.8907 0.8925 0.8944 0.8962 0.8980 0.8997 0.9015 1.3 0.9032 0.9049 0.9066 0.9082 0.9099 0.9115 0.9131 0.9147 0.9162 0.9177 1.4 0.9192 0.9207 0.9222 0.9236 0.9251 0.9265 0.9279 0.9292 0.9306 0.9319 1.5 0.9332 0.9345 0.9357 0.9370 0.9382 0.9394 0.9406 0.9418 0.9430 0.9441 1.6 0.9452 0.9463 0.9474 0.9485 0.9495 0.9505 0.9515 0.9525 0.9535 0.9545 1.7 0.9554 0.9564 0.9573 0.9582 0.9591 0.9599 0.9608 0.9616 0.9625 0.9633 1.8 0.9641 0.9649 0.9656 0.9664 0.9671 0.9678 0.9686 0.9693 0.9700 0.9706 1.9 0.9713 0.9719 0.9726 0.9732 0.9738 0.9744 0.9750 0.9756 0.9762 0.9767 2.0 0.9773 0.9778 0.9783 0.9788 0.9793 0.9798 0.9803 0.9808 0.9812 0.9817 2.1 0.98210.9826 0.9830 0.9834 0.98380.9842 0.9846 0.9850 0.9854 0.9857 2.2 0.9861 0.9865 0.9868 0.9871 0.9875 0.9878 0.9881 0.9884 0.9887 0.9890 2.3 0.9893 0.9896 0.9898 0.9901 0.9904 0.9906 0.9909 0.9911 0.9913 0.9916 2.4 0.9918 0.9920 0.99220.9925 0.9927 0.9929 0.9931 0.9932 0.9934 0.9936 2.5 0.99380.9940 0.9941 0.9943 0.9945 0.9946 0.9948 0.9949 0.9951 0.9952 2.6 0.99530.9955 0.9956 0.9957 0.9959 0.9960 0.9961 0.9962 0.9963 0.9964 2.7 0.99650.9966 0.9967 0.9968 0.9969 0.9970 0.9971 0.9972 0.9973 0.9974 2.8 0.99740.9975 0.9976 0.9977 0.9977 0.99780.9979 0.9980 0.9980 0.9981 2.9 0.9981 0.9982 0.9983 0.9983 0.9984 0.9984 0.9985 0.9985 0.9986 0.9986 3.0 0.99870.9987 0.9987 0.9988 0.9988 0.9989 0.9989 0.9989 0.9990 0.9990 3.1 0.99900.9991 0.9991 0.9991 0.9992 0.9992 0.9992 0.9992 0.9993 0.9993 3.2 0.9993 0.9993 0.9994 0.9994 0.99940.9994 0.9994 0.9995 0.9995 0.9995 3.3 0.99950.9995 0.9995 0.9995 0.9996 0.9996 0.9996 0.9996 0.9996 0.9997

Explanation / Answer

EOQ = (2DS/H)1/2

D= Requirement per week * number of weeks = 95 * 52 = 4940 bags per year

S= $ 55 / order

H = 28% of 10.75 = 3.01

EOQ = 424.89 or 425 bags

Reorder point, R = demand during protection interval + safety stock

Demand during protection interval = dL = 95* 4 = 380 bags

Safety stock = zl

When the desired cycle-service level is 99%, z = 2.33

l = d * Lead time ^1/2 = 13 * 2 = 26 bags

Safety Stock for service level 99% = 2.33 * 26 = 61 bags

Reorder point, R = 360 + 61 = 421 bags

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