A company begins a review of ordering policies for its continuous review system by checking the current policies for a sample of SKUs. Following are the characteristics of one item:
follows≻Demand
(D) =
80 units/week (Assume
50 weeks per year)
follows≻Ordering
and setup cost (S) =90/order
follows≻Holding
cost (H) =18/unit/year
follows≻Lead
time (L) =
22
week(s)
follows≻Standard
deviation of weekly demand =
2020
units
follows≻Cycle-service
level =
9292
percent
follows≻EOQ
=
200200
units
Using the above information, develop the best policies for a periodic review system. Refer to the standard normal table
LOADING...
for z-values.
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.
Z |
0.00 |
0.01 |
0.02 |
0.03 |
0.04 |
0.05 |
0.06 |
0.07 |
0.08 |
0.09 |
0.0 |
0.5000 |
0.5040 |
0.5080 |
0.5120 |
0.5160 |
0.5199 |
0.5239 |
0.5279 |
0.5319 |
0.5359 |
0.1 |
0.5398 |
0.5438 |
0.5478 |
0.5517 |
0.5557 |
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 |
0.6628 |
0.6664 |
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 |
0.7258 |
0.7291 |
0.7324 |
0.7357 |
0.7389 |
0.7422 |
0.7454 |
0.7486 |
0.7518 |
0.7549 |
0.7 |
0.7580 |
0.7612 |
0.7642 |
0.7673 |
0.7704 |
0.7734 |
0.7764 |
0.7794 |
0.7823 |
0.7852 |
0.8 |
0.7881 |
0.7910 |
0.7939 |
0.7967 |
0.7996 |
0.8023 |
0.8051 |
0.8079 |
0.8106 |
0.8133 |
0.9 |
0.8159 |
0.8186 |
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 |
0.9821 |
0.9826 |
0.9830 |
0.9834 |
0.9838 |
0.9842 |
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 |
0.9922 |
0.9925 |
0.9927 |
0.9929 |
0.9931 |
0.9932 |
0.9934 |
0.9936 |
2.5 |
0.9938 |
0.9940 |
0.9941 |
0.9943 |
0.9945 |
0.9946 |
0.9948 |
0.9949 |
0.9951 |
0.9952 |
2.6 |
0.9953 |
0.9955 |
0.9956 |
0.9957 |
0.9959 |
0.9960 |
0.9961 |
0.9962 |
0.9963 |
0.9964 |
2.7 |
0.9965 |
0.9966 |
0.9967 |
0.9968 |
0.9969 |
0.9970 |
0.9971 |
0.9972 |
0.9973 |
0.9974 |
2.8 |
0.9974 |
0.9975 |
0.9976 |
0.9977 |
0.9977 |
0.9978 |
0.9979 |
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 |
0.9987 |
0.9987 |
0.9987 |
0.9988 |
0.9988 |
0.9989 |
0.9989 |
0.9989 |
0.9990 |
0.9990 |
3.1 |
0.9990 |
0.9991 |
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 |
0.9994 |
0.9994 |
0.9994 |
0.9995 |
0.9995 |
0.9995 |
3.3 |
0.9995 |
0.9995 |
0.9995 |
0.9995 |
0.9996 |
0.9996 |
0.9996 |
0.9996 |
0.9996 |
0.9997 |
a. What value of P gives the same approximate number of orders per year as the EOQ?
nothing
weeks. (Enter your response rounded to the nearest whole number.)
b. To provide a 92 percent cycle-service level, the average safety stock is
nothing
units. (Enter your response rounded to the nearest whole number.)
To provide a
92 percent cycle-service level, the target inventory level is
nothing
units. (Enter your response rounded to the nearest whole number.)
EOQ = 200 units
Number of orders per year = annual demand / EOQ = 80x50/200 =20
Time between the orderes = No. of weeks / No of orders = 50/20 =2.5
which is equivalent to P.
Safety stock = z x sigma ( P+L)1/2
= 1.41 x 20 ( 2.5+2)1/2 = 59.82 = 60 units
Order up to level or target inventory level = (P+L) x weekly demand + Safety stock
= 4.5 x80+60 = 420
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