Appendix: Standard Normal Loss Function Table Appendix: Standard Normal Distribution Table ( Z table) Appendix: Standard Normal Loss Function Table (continued) Standard Normal Loss Function Table, L(z) (Concluded) \begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|} \hlinez & 0.00 & 0.01 & 0.02 & 0.03 & 0.04 & 0.05 & 0.06 & 0.07 & 0.08 & 0.09 \\ \hline 0.0 & 0.3989 & 0.3940 & 0.3890 & 0.3841 & 0.3793 & 0.3744 & 0.3697 & 0.3649 & 0.3602 & 0.3556 \\ \hline 0.1 & 0.3509 & 0.3464 & 0.3418 & 0.3373 & 0.3328 & 0.3284 & 0.3240 & 0.3197 & 0.3154 & 0.3111 \\ \hline 0.2 & 0.3069 & 0.3027 & 0.2986 & 0.2944 & 0.2904 & 0.2863 & 0.2824 & 0.2784 & 0.2745 & 0.2706 \\ \hline 0.3 & 0.2668 & 0.2630 & 0.2592 & 0.2555 & 0.2518 & 0.2481 & 0.2445 & 0.2409 & 0.2374 & 0.2339 \\ \hline 0.4 & 0.2304 & 0.2270 & 0.2236 & 0.2203 & 0.2169 & 0.2137 & 0.2104 & 0.2072 & 0.2040 & 0.2009 \\ \hline 0.5 & 0.1978 & 0.1947 & 0.1917 & 0.1887 & 0.1857 & 0.1828 & 0.1799 & 0.1771 & 0.1742 & 0.1714 \\ \hline 0.6 & 0.1687 & 0.1659 & 0.1633 & 0.1606 & 0.1580 & 0.1554 & 0.1528 & 0.1503 & 0.1478 & 0.1453 \\ \hline 0.7 & 0.1429 & 0.1405 & 0.1381 & 0.1358 & 0.1334 & 0.1312 & 0.1289 & 0.1267 & 0.1245 & 0.1223 \\ \hline 0.8 & 0.1202 & 0.1181 & 0.1160 & 0.1140 & 0.1120 & 0.1100 & 0.1080 & 0.1061 & 0.1042 & 0.1023 \\ \hline 0.9 & 0.1004 & 0.0986 & 0.0968 & 0.0950 & 0.0933 & 0.0916 & 0.0899 & 0.0882 & 0.0865 & 0.0849 \\ \hline 1.0 & 0.0833 & 0.0817 & 0.0802 & 0.0787 & 0.0772 & 0.0757 & 0.0742 & 0.0728 & 0.0714 & 0.0700 \\ \hline 1.1 & 0.0686 & 0.0673 & 0.0659 & 0.0646 & 0.0634 & 0.0621 & 0.0609 & 0.0596 & 0.0584 & 0.0573 \\ \hline 1.2 & 0.0561 & 0.0550 & 0.0538 & 0.0527 & 0.0517 & 0.0506 & 0.0495 & 0.0485 & 0.0475 & 0.0465 \\ \hline 1.3 & 0.0455 & 0.0446 & 0.0436 & 0.0427 & 0.0418 & 0.0409 & 0.0400 & 0.0392 & 0.0383 & 0.0375 \\ \hline 1.4 & 0.0367 & 0.0359 & 0.0351 & 0.0343 & 0.0336 & 0.0328 & 0.0321 & 0.0314 & 0.0307 & 0.0300 \\ \hline 1.5 & 0.0293 & 0.0286 & 0.0280 & 0.0274 & 0.0267 & 0.0261 & 0.0255 & 0.0249 & 0.0244 & 0.0238 \\ \hline 1.6 & 0.0232 & 0.0227 & 0.0222 & 0.0216 & 0.0211 & 0.0206 & 0.0201 & 0.0197 & 0.0192 & 0.0187 \\ \hline 1.7 & 0.0183 & 0.0178 & 0.0174 & 0.0170 & 0.0166 & 0.0162 & 0.0158 & 0.0154 & 0.0150 & 0.0146 \\ \hline 1.8 & 0.0143 & 0.0139 & 0.0136 & 0.0132 & 0.0129 & 0.0126 & 0.0123 & 0.0119 & 0.0116 & 0.0113 \\ \hline 1.9 & 0.0111 & 0.0108 & 0.0105 & 0.0102 & 0.0100 & 0.0097 & 0.0094 & 0.0092 & 0.0090 & 0.0087 \\ \hline 2.0 & 0.0085 & 0.0083 & 0.0080 & 0.0078 & 0.0076 & 0.0074 & 0.0072 & 0.0070 & 0.0068 & 0.0066 \\ \hline 2.1 & 0.0065 & 0.0063 & 0.0061 & 0.0060 & 0.0058 & 0.0056 & 0.0055 & 0.0053 & 0.0052 & 0.0050 \\ \hline 2.2 & 0.0049 & 0.0047 & 0.0046 & 0.0045 & 0.0044 & 0.0042 & 0.0041 & 0.0040 & 0.0039 & 0.0038 \\ \hline 2.3 & 0.0037 & 0.0036 & 0.0035 & 0.0034 & 0.0033 & 0.0032 & 0.0031 & 0.0030 & 0.0029 & 0.0028 \\ \hline 2.4 & 0.0027 & 0.0026 & 0.0026 & 0.0025 & 0.0024 & 0.0023 & 0.0023 & 0.0022 & 0.0021 & 0.0021 \\ \hline 2.5 & 0.0020 & 0.0019 & 0.0019 & 0.0018 & 0.0018 & 0.0017 & 0.0017 & 0.0016 & 0.0016 & 0.0015 \\ \hline 2.6 & 0.0015 & 0.0014 & 0.0014 & 0.0013 & 0.0013 & 0.0012 & 0.0012 & 0.0012 & 0.0011 & 0.0011 \\ \hline 2.7 & 0.0011 & 0.0010 & 0.0010 & 0.0010 & 0.0009 & 0.0009 & 0.0009 & 0.0008 & 0.0008 & 0.0008 \\ \hline 2.8 & 0.0008 & 0.0007 & 0.0007 & 0.0007 & 0.0007 & 0.0006 & 0.0006 & 0.0006 & 0.0006 & 0.0006 \\ \hline 2.9 & 0.0005 & 0.0005 & 0.0005 & 0.0005 & 0.0005 & 0.0005 & 0.0004 & 0.0004 & 0.0004 & 0.0004 \\ \hline 3.0 & 0.0004 & 0.0004 & 0.0004 & 0.0003 & 0.0003 & 0.0003 & 0.0003 & 0.0003 & 0.0003 & 0.0003 \\ \hline 3.1 & 0.0003 & 0.0003 & 0.0002 & 0.0002 & 0.0002 & 0.0002 & 0.0002 & 0.0002 & 0.0002 & 0.0002 \\ \hline 3.2 & 0.0002 & 0.0002 & 0.0002 & 0.0002 & 0.0002 & 0.0002 & 0.0001 & 0.0001 & 0.0001 & 0.0001 \\ \hline 3.3 & 0.0001 & 0.0001 & 0.0001 & 0.0001 & 0.0001 & 0.0001 & 0.0001 & 0.0001 & 0.0001 & 0.0001 \\ \hline 3.4 & 0.0001 & 0.0001 & 0.0001 & 0.0001 & 0.0001 & 0.0001 & 0.0001 & 0.0001 & 0.0001 & 0.0001 \\ \hline 3.5 & 0.0001 & 0.0001 & 0.0001 & 0.0001 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 \\ \hline 3.6 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 \\ \hline 3.7 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 \\ \hline 3.8 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 \\ \hline 3.9 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 \\ \hline 4.0 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 \\ \hline \end{tabular} You are the store manager at a large furniture store. One of your products is a study desk. Weekly demand for the desk is normally distributed with mean 40 and standard deviation 20, and demands across different periods are independent from each other. The lead time from the assembly plant to your store is two weeks. Suppose you use the order-up-to model to manage inventory, and inventory is reviewed every week. (A) Suppose your order-up-to level is S=220. You are about to place an order and note that your current on-hand inventory level is 100 and you have 85 desks still in transit (i.e., in pipeline). How many desks will you order? (B) What is the optimal order-up-to level (rounded to the nearest integer) if you want to target a 98% cycle service level? (C) Now suppose you decide to adopt a continuous review policy to manage inventory, and the reorder point (ROP) is set to be 80 . The demand and lead time information remain unchanged. What is the average number of lost sales in a replenishment cycle