Problem 3. (Chapter 9: Inventory Policy Decisions) Suppose that an auto part in a manufacturer's inventory has the following characteristics: Forecast of demand = 900 cases per week Forecast error, std. dev. =125 cases per week Lead time 4 weeks Carrying cost =30 % per year Purchase price, delivered $60 per case Replenishment order cost =$40 per order Stockout cost =$10 per case Probability of being in stock during the lead time =85% a. The manufacturer uses ROP method to control the inventory of this item. The manufacturer operates 52 weeks a year. What is the economic order quantity? b. What is the reorder point? What's the expected number of units out of stock annually? d. What is the annual service level? What's the total annual cost including annual fixed ordering cost, inventory holding cost, and stockout cost? f. If the lead time is normally distributed with a standard deviation of 0.5 weeks, what's the ROP? c. e. Lead Time Service Level Lead Time Service Level Lead Time Service Level Lead Time Service Level E[2) 2 El 2 E12) 2 ELZ 0082 0091 7881 .7995 8106 8212 .8315 8413 8508 8599 8686 8770 -2.40 -2.36 -232 -228 -2.24 - 2.20 -2.16 - 2.12 -2.08 - 204 -2.00 -1.96 -1.92 - 188 -1.84 -1.80 -1.76 -1.72 -1.68 - 164 -1.60 -1.56 -1.52 -1.48 -1.44 -1.40 -1.36 - 1.32 - 1.28 0102 .0113 0125 0139 .0154 0170 .0188 0207 .0228 0250 .0274 0301 .0329 ,0359 .0392 .0427 .0465 0505 0548 0594 0643 ,0694 .0749 0808 .0869 0934 1003 1075 .1151 .1230 .1314 1401 1492 1587 .1685 .1788 .1894 -2005 2.403 2.363 2.323 2.284 2.244 2.205 2.165 2.126 2.087 2.048 2.008 1.969 1.930 1.892 1.853 1.814 1.776 1.737 1.699 1.661 1.623 1.586 1.548 1.511 1.474 1.437 1.400 1.364 1.328 1.292 1.256 1.221 1.186 1.151 1.117 1,083 1.049 1.017 0.984 0.952 - 80 -.76 -72 -68 -64 -.60 -.56 --52 -.48 -44 40 -36 -32 -28 -24 - 20 - 16 -12 -.08 -04 .00 04 .08 12 16 20 24 28 32 36 40 .44 .48 .52 .56 .60 64 .68 72 .76 2119 2236 2358 .2483 2611 2743 2877 3015 3156 3300 3446 3594 3745 3897 4052 4207 4364 4522 4681 4840 5000 5160 -5319 5478 5636 .5793 5948 920 1889 858 828 .798 .769 -740 .712 684 .657 630 597 .576 555 530 507 484 462 440 .419 399 379 360 342 324 307 290 275 256 237 230 .217 204 .192 .180 169 158 148 138 129 0.80 0.84 0.88 0.92 0.96 1.00 1.04 1.08 1.12 1.16 1.20 1.24 1.28 1.32 1.36 1.40 1.44 1.48 1.52 1.56 1.60 1.64 1.68 1.72 1.76 1.80 1.84 1.88 1.92 1.96 2.00 2.04 2.08 2.12 2.16 .8849 8925 8997 9066 9131 9192 9251 9306 9357 9406 9452 9495 120 .112 104 097 089 .083 077 071 066 ,061 .056 052 048 044 040 037 ,034 ,031 028 026 023 021 240 2.44 2.48 2.52 2.56 2.60 2.64 2.68 2.72 2.76 2.80 2.84 2.88 2.92 2.96 300 3.04 3.08 3.12 3.16 3.20 3.24 3.28 3.32 3.36 3.40 9918 9927 9934 9941 9948 9953 9959 9963 9967 9971 .9974 9977 9980 9982 9985 9987 9988 9990 9991 9992 9993 9994 9995 9995 9996 .9997 0030 0020 0020 0020 0020 .0010 .0010 0010 0010 0010 0008 .0007 0006 .0005 0004 .0004 0003 0003 0002 .0002 0002 0001 .0001 0001 0001 0001 9535 .019 .6103 9573 .9608 9641 9671 .9699 9726 9750 9772 9793 .9812 9830 9846 - 1.24 .6255 6406 .6554 .6700 6844 .6985 .7123 7257 7389 .7517 7642 .7764 - 1.20 - 1.16 - 1.12 -1.08 -104 - 1.00 -96 - 92 -88 - 84 017 016 014 013 012 2010 .009 .008 008 ,007 006 005 005 004 ,004 .003 .003 2.20 9861 2.24 2.28 232 2.36 .9875 9887 9898 .9909