A new logistics analyst has approached you regarding a potential problem. Her analysis indicates the cost of a back order is $40 for our Autographed Footballs, but she is not sure what the appropriate safety stock should be. Given this back order cost, what would you suggest as the appropriate level of safety stock? Football cost Annual Demand Cost per Order Cost to hold the item per year Economic order quantity Lead Time Standard Deviation of Forecasted Demand During Lead Time $200 5000 units $250 40% 177 2 weeks 20 Kto Service Level Conversion k 0.0 0.1 0.2 0.3 0.4 0.5 0.00 0.5000 0.5398 0.5793 0.6179 0.6554 0.6915 0.01 0.5040 0.5438 0.5832 0.6217 0.6591 0.6960 0.02 0.03 0.04 0.5080 0.5120 0.5160 0.5478 0.5517 0.5557 0.58710.5910 0.5948 0.62550.6293 0.6331 0.6628 0.66640.6700 0,6985 0.7019 0.7054 0.7324 0.7357 0.7389 0.7642 0.7673 0.7704 0.05 0.5199 0.5596 0.5987 0.6368 0.6736 0.7088 0.7422 0.7734 0.06 0.5239 0.5636 0.6026 0.6406 0.6772 0.7123 0.7454 0.7764 0.07 0.5279 0.5675 0.6064 0.6443 0.6808 0.08 0.09 0.5319 0.5359 0.5714 0.5753 0.61030.6141 0.6480 0.6517 0.68440.6879 0.7157 0.7190 0.7224 0.6 0.7 0.7257 0.7580 0.7291 0.7611 0.7486 0.7794 0.7517 0.7823 0.7549 0.7852 0.8 0.9 0.7881 0.8159 0.7910 0.8186 0.7939 0.8212 0.7967 0.8238 0.7995 0.8264 0.8023 0.8289 0.8051 0.8315 0.8078 0.8340 0.8106 0.8365 0.8133 0.8389 1.0 0.8413 1.11 0.8643 0.8438 0.86660 0.8461 .8686 0.8485 0.8708 0.8508 0.8729 0.8531 0.8749 0.8554 0.8770 0.8577 0.8599 0.8790 0.8810 0.8621 0.88.30 0.8944 0.89620.8980 0.8997 0.9015 1.2 13 0.8849 0.9032 0.8869 0.9049 0.8888 | 0.8907 0.9066 0.9082 0.9115 0.9131 0.9147 0.9162 0.9177 14 0.9192 0.9207 0.9222 0.9236 0.9265 0.9278 0.9292 0.9306 0.9319 1.5 0.9332 0.9346 0.9357 0.9370 0.9394 0.9106 0.9418 0.9429 0.9441 0.8925 0.9099 0.9251 0.9382 0.9495 0.9591 0.9671 0.9738 1.6 0.9452 0.9463 0.9474 0.9484 0.9505 0.9515 0.9525 0.9535 0.9545 1.7 1.8 0.9554 0.9641 0.95640.9673 0.9649 0.9656 0.9582 0.9664 0.9699 0.9678 0.9744 0.9608 0.9616 0.9625 0.96860.9693 0.9699 0.9750 0.97560.9761 0.9633 0.9706 0.9767 1.9 0.97130.9719 0.9725 0.9732 k N[k] Conversion * 0. 0 0.1 0.2 .00 3989 -3509 -3069 .2668 2304 .01 3940 3464 3 027 2630 .02 3890 3418 2986 2592 .03 3841 -3373 2944 -2555 .04 3793 3328 2904 2518 .05 3744 3284 286 2481 .08 -3697 -3240 2824 .2445 .07 -3649 3 197 2784 2409 .08 3602 -3154 2745 .2374 .09 .3656 .3111 2706 .2339 2270 2236 2203 2169 2137 2104 2072 2009 1978 1947 1917 1887 1857 .1687 1659 06 07 1429 0.8 .1202 091004 .1633 1606 .1580 .1405 .1381 .1358 1334 .1181 .1160 1140 1120 0986009680 .09503 09328 08174 0801907866 07716 067271206595 06465 06336 .05496 .05384 .0527405165 1828 1799 1771 1742 1714 1554 .1528 .1503 .1478 1453 .1312 .1289 1 267 .1245 .1223 1100 1000 1061 1042 1023 .09156 .089860881908654 08491 0756807422 07279 0711006999 06210 .080B6 .05084 .05844 .05726 05059 04954 .0405120475004650 1.0 1.1 .08332 .06862 1.2 .05610 1.3 1.04553 04457 .04363 ,04270 04179 .04090 204002 0 3916 0.3831 03748 1.4 1.03667 1.5 .02931 03587 1.03508 .02865 .02800 .03431 .02736 203356 .02674 .03281 .02612 .03208 .02552 0 3208 .02494 .03137 0 2436 .02998 .02380 - 20 o 20 30 o 31 o 33 35 A new logistics analyst has approached you regarding a potential problem. Her analysis indicates the cost of a back order is $40 for our Autographed Footballs, but she is not sure what the appropriate safety stock should be. Given this back order cost, what would you suggest as the appropriate level of safety stock? Football cost Annual Demand Cost per Order Cost to hold the item per year Economic order quantity Lead Time Standard Deviation of Forecasted Demand During Lead Time $200 5000 units $250 40% 177 2 weeks 20 Kto Service Level Conversion k 0.0 0.1 0.2 0.3 0.4 0.5 0.00 0.5000 0.5398 0.5793 0.6179 0.6554 0.6915 0.01 0.5040 0.5438 0.5832 0.6217 0.6591 0.6960 0.02 0.03 0.04 0.5080 0.5120 0.5160 0.5478 0.5517 0.5557 0.58710.5910 0.5948 0.62550.6293 0.6331 0.6628 0.66640.6700 0,6985 0.7019 0.7054 0.7324 0.7357 0.7389 0.7642 0.7673 0.7704 0.05 0.5199 0.5596 0.5987 0.6368 0.6736 0.7088 0.7422 0.7734 0.06 0.5239 0.5636 0.6026 0.6406 0.6772 0.7123 0.7454 0.7764 0.07 0.5279 0.5675 0.6064 0.6443 0.6808 0.08 0.09 0.5319 0.5359 0.5714 0.5753 0.61030.6141 0.6480 0.6517 0.68440.6879 0.7157 0.7190 0.7224 0.6 0.7 0.7257 0.7580 0.7291 0.7611 0.7486 0.7794 0.7517 0.7823 0.7549 0.7852 0.8 0.9 0.7881 0.8159 0.7910 0.8186 0.7939 0.8212 0.7967 0.8238 0.7995 0.8264 0.8023 0.8289 0.8051 0.8315 0.8078 0.8340 0.8106 0.8365 0.8133 0.8389 1.0 0.8413 1.11 0.8643 0.8438 0.86660 0.8461 .8686 0.8485 0.8708 0.8508 0.8729 0.8531 0.8749 0.8554 0.8770 0.8577 0.8599 0.8790 0.8810 0.8621 0.88.30 0.8944 0.89620.8980 0.8997 0.9015 1.2 13 0.8849 0.9032 0.8869 0.9049 0.8888 | 0.8907 0.9066 0.9082 0.9115 0.9131 0.9147 0.9162 0.9177 14 0.9192 0.9207 0.9222 0.9236 0.9265 0.9278 0.9292 0.9306 0.9319 1.5 0.9332 0.9346 0.9357 0.9370 0.9394 0.9106 0.9418 0.9429 0.9441 0.8925 0.9099 0.9251 0.9382 0.9495 0.9591 0.9671 0.9738 1.6 0.9452 0.9463 0.9474 0.9484 0.9505 0.9515 0.9525 0.9535 0.9545 1.7 1.8 0.9554 0.9641 0.95640.9673 0.9649 0.9656 0.9582 0.9664 0.9699 0.9678 0.9744 0.9608 0.9616 0.9625 0.96860.9693 0.9699 0.9750 0.97560.9761 0.9633 0.9706 0.9767 1.9 0.97130.9719 0.9725 0.9732 k N[k] Conversion * 0. 0 0.1 0.2 .00 3989 -3509 -3069 .2668 2304 .01 3940 3464 3 027 2630 .02 3890 3418 2986 2592 .03 3841 -3373 2944 -2555 .04 3793 3328 2904 2518 .05 3744 3284 286 2481 .08 -3697 -3240 2824 .2445 .07 -3649 3 197 2784 2409 .08 3602 -3154 2745 .2374 .09 .3656 .3111 2706 .2339 2270 2236 2203 2169 2137 2104 2072 2009 1978 1947 1917 1887 1857 .1687 1659 06 07 1429 0.8 .1202 091004 .1633 1606 .1580 .1405 .1381 .1358 1334 .1181 .1160 1140 1120 0986009680 .09503 09328 08174 0801907866 07716 067271206595 06465 06336 .05496 .05384 .0527405165 1828 1799 1771 1742 1714 1554 .1528 .1503 .1478 1453 .1312 .1289 1 267 .1245 .1223 1100 1000 1061 1042 1023 .09156 .089860881908654 08491 0756807422 07279 0711006999 06210 .080B6 .05084 .05844 .05726 05059 04954 .0405120475004650 1.0 1.1 .08332 .06862 1.2 .05610 1.3 1.04553 04457 .04363 ,04270 04179 .04090 204002 0 3916 0.3831 03748 1.4 1.03667 1.5 .02931 03587 1.03508 .02865 .02800 .03431 .02736 203356 .02674 .03281 .02612 .03208 .02552 0 3208 .02494 .03137 0 2436 .02998 .02380 - 20 o 20 30 o 31 o 33 35