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EOQ and ROP
EOQ and ReOrder Point
This template can be used to calculate different values
for an EOQ model. It can also be used for models involving
stochastic demand patterns.
INPUT:
Annual Demand: D/year D 21900
Cost per Unit C
Inventory charge (% of unit cost) i
Holding cost: H (if not given,H = i*C) H $0.50
Ordering Cost S $10.00
Length of year: N(months,weeks,days) N 365
demand per (month,week,day) d 60
Std. Deviation/(month,week,day) σd 7
Lead TimeL L(months,weeks,days)) L 6
Lead-time Standard Deviation: σL 17.15
Service Level P 95%
Safety Stock(if given) SS 0
OUTPUT:
Optimal Order Quantity (Qopt) = 935
Annual Inventory Holding Cost = $233.75
Annual Ordering Cost = $234.22
Annual Unit Cost =
Total Cost = $467.97
Safety Factor - z: (use E(z) & table below) = 1.64
E(z) = 0.092
Cycle Time - T(in days) = 15.58
Number of Orders per year = 23
Safety Stock = 28.1201422Reorder Point, R = 388
Expected Number Out of Stock versus Standard Deviation
(Normalized to a Standard Deviation of 1)
SL z E(z)
0.0000 -4.50 4.5000
Page 1
EOQ and ROP
0.0000 -4.49 4.4900
0.0000 -4.48 4.4800
0.0000 -4.47 4.4700
0.0000 -4.46 4.4600
0.0000 -4.45 4.4500
0.0000 -4.44 4.4400
0.0000 -4.43 4.4300
0.0000 -4.42 4.4200
0.0000 -4.41 4.4100
0.0000 -4.40 4.4000
0.0000 -4.39 4.3900
0.0000 -4.38 4.3800
0.0000 -4.37 4.3700
0.0000 -4.36 4.3600
0.0000 -4.35 4.3500
0.0000 -4.34 4.3400
0.0000 -4.33 4.3300
0.0000 -4.32 4.3200
0.0000 -4.31 4.3100
0.0000 -4.30 4.3000
0.0000 -4.29 4.2900
0.0000 -4.28 4.2800
0.0000 -4.27 4.2700
0.0000 -4.26 4.2600
0.0000 -4.25 4.2500
0.0000 -4.24 4.2400
0.0000 -4.23 4.2300
0.0000 -4.22 4.2200
0.0000 -4.21 4.2100
0.0000 -4.20 4.2000
0.0000 -4.19 4.1900
0.0000 -4.18 4.1800
0.0000 -4.17 4.1700
0.0000 -4.16 4.1600
0.0000 -4.15 4.1500
0.0000 -4.14 4.1400
0.0000 -4.13 4.1300
0.0000 -4.12 4.1200
0.0000 -4.11 4.1100
0.0000 -4.10 4.1000
0.0000 -4.09 4.0900
0.0000 -4.08 4.0800
0.0000 -4.07 4.0700
0.0000 -4.06 4.0600
0.0000 -4.05 4.0500
0.0000 -4.04 4.0400
0.0000 -4.03 4.0300
0.0000 -4.02 4.0200
0.0000 -4.01 4.0100
0.0000 -4.00 4.0000
0.0000 -3.99 3.9900
0.0000 -3.98 3.9800
Page 2
EOQ and ROP
0.0000 -3.97 3.9700
0.0000 -3.96 3.9600
0.0000 -3.95 3.9500
0.0000 -3.94 3.9400
0.0000 -3.93 3.9300
0.0000 -3.92 3.9200
0.0000 -3.91 3.9100
0.0000 -3.90 3.9000
0.0001 -3.89 3.8900
0.0001 -3.88 3.8800
0.0001 -3.87 3.8700
0.0001 -3.86 3.8600
0.0001 -3.85 3.8500
0.0001 -3.84 3.8400
0.0001 -3.83 3.8300
0.0001 -3.82 3.8200
0.0001 -3.81 3.8100
0.0001 -3.80 3.8000
0.0001 -3.79 3.7900
0.0001 -3.78 3.7800
0.0001 -3.77 3.7700
0.0001 -3.76 3.7600
0.0001 -3.75 3.7500
0.0001 -3.74 3.7400
0.0001 -3.73 3.7300
0.0001 -3.72 3.7200
0.0001 -3.71 3.7100
0.0001 -3.70 3.7000
0.0001 -3.69 3.6900
0.0001 -3.68 3.6800
0.0001 -3.67 3.6700
0.0001 -3.66 3.6600
0.0001 -3.65 3.6500
0.0001 -3.64 3.6400
0.0001 -3.63 3.6300
0.0001 -3.62 3.6200
0.0002 -3.61 3.6100
0.0002 -3.60 3.6000
0.0002 -3.59 3.5900
0.0002 -3.58 3.5800
0.0002 -3.57 3.5700
0.0002 -3.56 3.5600
0.0002 -3.55 3.5500
0.0002 -3.54 3.5400
0.0002 -3.53 3.5301
0.0002 -3.52 3.5201
0.0002 -3.51 3.5101
0.0002 -3.50 3.5001
0.0002 -3.49 3.4901
0.0003 -3.48 3.4801
0.0003 -3.47 3.4701
0.0003 -3.46 3.4601
Page 3
EOQ and ROP
0.0003 -3.45 3.4501
0.0003 -3.44 3.4401
0.0003 -3.43 3.4301
0.0003 -3.42 3.4201
0.0003 -3.41 3.4101
0.0003 -3.40 3.4001
0.0003 -3.39 3.3901
0.0004 -3.38 3.3801
0.0004 -3.37 3.3701
0.0004 -3.36 3.3601
0.0004 -3.35 3.3501
0.0004 -3.34 3.3401
0.0004 -3.33 3.3301
0.0005 -3.32 3.3201
0.0005 -3.31 3.3101
0.0005 -3.30 3.3001
0.0005 -3.29 3.2901
0.0005 -3.28 3.2801
0.0005 -3.27 3.2701
0.0006 -3.26 3.2601
0.0006 -3.25 3.2502
0.0006 -3.24 3.2402
0.0006 -3.23 3.2302
0.0006 -3.22 3.2202
0.0007 -3.21 3.2102
0.0007 -3.20 3.2002
0.0007 -3.19 3.1902
0.0007 -3.18 3.1802
0.0008 -3.17 3.1702
0.0008 -3.16 3.1602
0.0008 -3.15 3.1502
0.0008 -3.14 3.1402
0.0009 -3.13 3.1302
0.0009 -3.12 3.1202
0.0009 -3.11 3.1103
0.0010 -3.10 3.1003
0.0010 -3.09 3.0903
0.0010 -3.08 3.0803
0.0011 -3.07 3.0703
0.0011 -3.06 3.0603
0.0011 -3.05 3.0503
0.0012 -3.04 3.0403
0.0012 -3.03 3.0303
0.0013 -3.02 3.0204
0.0013 -3.01 3.0104
0.0013 -3.00 3.0004
0.0014 -2.99 2.9904
0.0014 -2.98 2.9804
0.0015 -2.97 2.9704
0.0015 -2.96 2.9604
0.0016 -2.95 2.9505
0.0016 -2.94 2.9405
Page 4
EOQ and ROP
0.0017 -2.93 2.9305
0.0018 -2.92 2.9205
0.0018 -2.91 2.9105
0.0019 -2.90 2.9005
0.0019 -2.89 2.8906
0.0020 -2.88 2.8806
0.0021 -2.87 2.8706
0.0021 -2.86 2.8606
0.0022 -2.85 2.8506
0.0023 -2.84 2.8407
0.0023 -2.83 2.8307
0.0024 -2.82 2.8207
0.0025 -2.81 2.8107
0.0026 -2.80 2.8008
0.0026 -2.79 2.7908
0.0027 -2.78 2.7808
0.0028 -2.77 2.7708
0.0029 -2.76 2.7609
0.0030 -2.75 2.7509
0.0031 -2.74 2.7409
0.0032 -2.73 2.7310
0.0033 -2.72 2.7210
0.0034 -2.71 2.7110
0.0035 -2.70 2.7011
0.0036 -2.69 2.6911
0.0037 -2.68 2.6811
0.0038 -2.67 2.6712
0.0039 -2.66 2.6612
0.0040 -2.65 2.6512
0.0041 -2.64 2.6413
0.0043 -2.63 2.6313
0.0044 -2.62 2.6214
0.0045 -2.61 2.6114
0.0047 -2.60 2.6015
0.0048 -2.59 2.5915
0.0049 -2.58 2.5816
0.0051 -2.57 2.5716
0.0052 -2.56 2.5617
0.0054 -2.55 2.5517
0.0055 -2.54 2.5418
0.0057 -2.53 2.5318
0.0059 -2.52 2.5219
0.0060 -2.51 2.5119
0.0062 -2.50 2.5020
0.0064 -2.49 2.4921
0.0066 -2.48 2.4821
0.0068 -2.47 2.4722
0.0069 -2.46 2.4623
0.0071 -2.45 2.4523
0.0073 -2.44 2.4424
0.0075 -2.43 2.4325
0.0078 -2.42 2.4226
Page 5
EOQ and ROP
0.0080 -2.41 2.4126
0.0082 -2.40 2.4027
0.0084 -2.39 2.3928
0.0087 -2.38 2.3829
0.0089 -2.37 2.3730
0.0091 -2.36 2.3631
0.0094 -2.35 2.3532
0.0096 -2.34 2.3433
0.0099 -2.33 2.3334
0.0102 -2.32 2.3235
0.0104 -2.31 2.3136
0.0107 -2.30 2.3037
0.0110 -2.29 2.2938
0.0113 -2.28 2.2839
0.0116 -2.27 2.2740
0.0119 -2.26 2.2641
0.0122 -2.25 2.2542
0.0125 -2.24 2.2444
0.0129 -2.23 2.2345
0.0132 -2.22 2.2246
0.0136 -2.21 2.2147
0.0139 -2.20 2.2049
0.0143 -2.19 2.1950
0.0146 -2.18 2.1852
0.0150 -2.17 2.1753
0.0154 -2.16 2.1655
0.0158 -2.15 2.1556
0.0162 -2.14 2.1458
0.0166 -2.13 2.1360
0.0170 -2.12 2.1261
0.0174 -2.11 2.1163
0.0179 -2.10 2.1065
0.0183 -2.09 2.0966
0.0188 -2.08 2.0868
0.0192 -2.07 2.0770
0.0197 -2.06 2.0672
0.0202 -2.05 2.0574
0.0207 -2.04 2.0476
0.0212 -2.03 2.0378
0.0217 -2.02 2.0280
0.0222 -2.01 2.0183
0.0228 -2.00 2.0085
0.0233 -1.99 1.9987
0.0239 -1.98 1.9890
0.0244 -1.97 1.9792
0.0250 -1.96 1.9694
0.0256 -1.95 1.9597
0.0262 -1.94 1.9500
0.0268 -1.93 1.9402
0.0274 -1.92 1.9305
0.0281 -1.91 1.9208
0.0287 -1.90 1.9111
Page 6
EOQ and ROP
0.0294 -1.89 1.9013
0.0301 -1.88 1.8916
0.0307 -1.87 1.8819
0.0314 -1.86 1.8723
0.0322 -1.85 1.8626
0.0329 -1.84 1.8529
0.0336 -1.83 1.8432
0.0344 -1.82 1.8336
0.0351 -1.81 1.8239
0.0359 -1.80 1.8143
0.0367 -1.79 1.8046
0.0375 -1.78 1.7950
0.0384 -1.77 1.7854
0.0392 -1.76 1.7758
0.0401 -1.75 1.7662
0.0409 -1.74 1.7566
0.0418 -1.73 1.7470
0.0427 -1.72 1.7374
0.0436 -1.71 1.7278
0.0446 -1.70 1.7183
0.0455 -1.69 1.7087
0.0465 -1.68 1.6992
0.0475 -1.67 1.6897
0.0485 -1.66 1.6801
0.0495 -1.65 1.6706
0.0505 -1.64 1.6611
0.0516 -1.63 1.6516
0.0526 -1.62 1.6422
0.0537 -1.61 1.6327
0.0548 -1.60 1.6232
0.0559 -1.59 1.6138
0.0571 -1.58 1.6044
0.0582 -1.57 1.5949
0.0594 -1.56 1.5855
0.0606 -1.55 1.5761
0.0618 -1.54 1.5667
0.0630 -1.53 1.5574
0.0643 -1.52 1.5480
0.0655 -1.51 1.5386
0.0668 -1.50 1.5293
0.0681 -1.49 1.5200
0.0694 -1.48 1.5107
0.0708 -1.47 1.5014
0.0721 -1.46 1.4921
0.0735 -1.45 1.4828
0.0749 -1.44 1.4736
0.0764 -1.43 1.4643
0.0778 -1.42 1.4551
0.0793 -1.41 1.4459
0.0808 -1.40 1.4367
0.0823 -1.39 1.4275
0.0838 -1.38 1.4183
Page 7
EOQ and ROP
0.0853 -1.37 1.4092
0.0869 -1.36 1.4000
0.0885 -1.35 1.3909
0.0901 -1.34 1.3818
0.0918 -1.33 1.3727
0.0934 -1.32 1.3636
0.0951 -1.31 1.3546
0.0968 -1.30 1.3455
0.0985 -1.29 1.3365
0.1003 -1.28 1.3275
0.1020 -1.27 1.3185
0.1038 -1.26 1.3095
0.1056 -1.25 1.3006
0.1075 -1.24 1.2917
0.1093 -1.23 1.2827
0.1112 -1.22 1.2738
0.1131 -1.21 1.2650
0.1151 -1.20 1.2561
0.1170 -1.19 1.2473
0.1190 -1.18 1.2384
0.1210 -1.17 1.2296
0.1230 -1.16 1.2209
0.1251 -1.15 1.2121
0.1271 -1.14 1.2034
0.1292 -1.13 1.1946
0.1314 -1.12 1.1859
0.1335 -1.11 1.1773
0.1357 -1.10 1.1686
0.1379 -1.09 1.1600
0.1401 -1.08 1.1514
0.1423 -1.07 1.1428
0.1446 -1.06 1.1342
0.1469 -1.05 1.1257
0.1492 -1.04 1.1172
0.1515 -1.03 1.1087
0.1539 -1.02 1.1002
0.1562 -1.01 1.0917
0.1587 -1.00 1.0833
0.1611 -0.99 1.0749
0.1635 -0.98 1.0665
0.1660 -0.97 1.0582
0.1685 -0.96 1.0499
0.1711 -0.95 1.0416
0.1736 -0.94 1.0333
0.1762 -0.93 1.0250
0.1788 -0.92 1.0168
0.1814 -0.91 1.0086
0.1841 -0.90 1.0004
0.1867 -0.89 0.9923
0.1894 -0.88 0.9842
0.1922 -0.87 0.9761
0.1949 -0.86 0.9680
Page 8
EOQ and ROP
0.1977 -0.85 0.9600
0.2005 -0.84 0.9520
0.2033 -0.83 0.9440
0.2061 -0.82 0.9360
0.2090 -0.81 0.9281
0.2119 -0.80 0.9202
0.2148 -0.79 0.9123
0.2177 -0.78 0.9045
0.2206 -0.77 0.8967
0.2236 -0.76 0.8889
0.2266 -0.75 0.8812
0.2296 -0.74 0.8734
0.2327 -0.73 0.8658
0.2358 -0.72 0.8581
0.2389 -0.71 0.8505
0.2420 -0.70 0.8429
0.2451 -0.69 0.8353
0.2483 -0.68 0.8278
0.2514 -0.67 0.8203
0.2546 -0.66 0.8128
0.2578 -0.65 0.8054
0.2611 -0.64 0.7980
0.2643 -0.63 0.7906
0.2676 -0.62 0.7833
0.2709 -0.61 0.7759
0.2743 -0.60 0.7687
0.2776 -0.59 0.7614
0.2810 -0.58 0.7542
0.2843 -0.57 0.7471
0.2877 -0.56 0.7399
0.2912 -0.55 0.7328
0.2946 -0.54 0.7257
0.2981 -0.53 0.7187
0.3015 -0.52 0.7117
0.3050 -0.51 0.7047
0.3085 -0.50 0.6978
0.3121 -0.49 0.6909
0.3156 -0.48 0.6840
0.3192 -0.47 0.6772
0.3228 -0.46 0.6704
0.3264 -0.45 0.6637
0.3300 -0.44 0.6569
0.3336 -0.43 0.6503
0.3372 -0.42 0.6436
0.3409 -0.41 0.6370
0.3446 -0.40 0.6304
0.3483 -0.39 0.6239
0.3520 -0.38 0.6174
0.3557 -0.37 0.6109
0.3594 -0.36 0.6045
0.3632 -0.35 0.5981
0.3669 -0.34 0.5918
Page 9
EOQ and ROP
0.3707 -0.33 0.5855
0.3745 -0.32 0.5792
0.3783 -0.31 0.5730
0.3821 -0.30 0.5668
0.3859 -0.29 0.5606
0.3897 -0.28 0.5545
0.3936 -0.27 0.5484
0.3974 -0.26 0.5424
0.4013 -0.25 0.5363
0.4052 -0.24 0.5304
0.4090 -0.23 0.5244
0.4129 -0.22 0.5186
0.4168 -0.21 0.5127
0.4207 -0.20 0.5069
0.4247 -0.19 0.5011
0.4286 -0.18 0.4954
0.4325 -0.17 0.4897
0.4364 -0.16 0.4840
0.4404 -0.15 0.4784
0.4443 -0.14 0.4728
0.4483 -0.13 0.4673
0.4522 -0.12 0.4618
0.4562 -0.11 0.4564
0.4602 -0.10 0.4509
0.4641 -0.09 0.4456
0.4681 -0.08 0.4402
0.4721 -0.07 0.4349
0.4761 -0.06 0.4297
0.4801 -0.05 0.4244
0.4840 -0.04 0.4193
0.4880 -0.03 0.4141
0.4920 -0.02 0.4090
0.4960 -0.01 0.4040
0.5000 0.00 0.3989
0.5040 0.01 0.3940
0.5080 0.02 0.3890
0.5120 0.03 0.3841
0.5160 0.04 0.3793
0.5199 0.05 0.3744
0.5239 0.06 0.3697
0.5279 0.07 0.3649
0.5319 0.08 0.3602
0.5359 0.09 0.3556
0.5398 0.10 0.3509
0.5438 0.11 0.3464
0.5478 0.12 0.3418
0.5517 0.13 0.3373
0.5557 0.14 0.3328
0.5596 0.15 0.3284
0.5636 0.16 0.3240
0.5675 0.17 0.3197
0.5714 0.18 0.3154
Page 10
EOQ and ROP
0.5753 0.19 0.3111
0.5793 0.20 0.3069
0.5832 0.21 0.3027
0.5871 0.22 0.2986
0.5910 0.23 0.2944
0.5948 0.24 0.2904
0.5987 0.25 0.2863
0.6026 0.26 0.2824
0.6064 0.27 0.2784
0.6103 0.28 0.2745
0.6141 0.29 0.2706
0.6179 0.30 0.2668
0.6217 0.31 0.2630
0.6255 0.32 0.2592
0.6293 0.33 0.2555
0.6331 0.34 0.2518
0.6368 0.35 0.2481
0.6406 0.36 0.2445
0.6443 0.37 0.2409
0.6480 0.38 0.2374
0.6517 0.39 0.2339
0.6554 0.40 0.2304
0.6591 0.41 0.2270
0.6628 0.42 0.2236
0.6664 0.43 0.2203
0.6700 0.44 0.2169
0.6736 0.45 0.2137
0.6772 0.46 0.2104
0.6808 0.47 0.2072
0.6844 0.48 0.2040
0.6879 0.49 0.2009
0.6915 0.50 0.1978
0.6950 0.51 0.1947
0.6985 0.52 0.1917
0.7019 0.53 0.1887
0.7054 0.54 0.1857
0.7088 0.55 0.1828
0.7123 0.56 0.1799
0.7157 0.57 0.1771
0.7190 0.58 0.1742
0.7224 0.59 0.1714
0.7257 0.60 0.1687
0.7291 0.61 0.1659
0.7324 0.62 0.1633
0.7357 0.63 0.1606
0.7389 0.64 0.1580
0.7422 0.65 0.1554
0.7454 0.66 0.1528
0.7486 0.67 0.1503
0.7517 0.68 0.1478
0.7549 0.69 0.1453
0.7580 0.70 0.1429
Page 11
EOQ and ROP
0.7611 0.71 0.1405
0.7642 0.72 0.1381
0.7673 0.73 0.1358
0.7704 0.74 0.1334
0.7734 0.75 0.1312
0.7764 0.76 0.1289
0.7794 0.77 0.1267
0.7823 0.78 0.1245
0.7852 0.79 0.1223
0.7881 0.80 0.1202
0.7910 0.81 0.1181
0.7939 0.82 0.1160
0.7967 0.83 0.1140
0.7995 0.84 0.1120
0.8023 0.85 0.1100
0.8051 0.86 0.1080
0.8078 0.87 0.1061
0.8106 0.88 0.1042
0.8133 0.89 0.1023
0.8159 0.90 0.1004
0.8186 0.91 0.0986
0.8212 0.92 0.0968
0.8238 0.93 0.0950
0.8264 0.94 0.0933
0.8289 0.95 0.0916
0.8315 0.96 0.0899
0.8340 0.97 0.0882
0.8365 0.98 0.0865
0.8389 0.99 0.0849
0.8413 1.00 0.0833
0.8438 1.01 0.0817
0.8461 1.02 0.0802
0.8485 1.03 0.0787
0.8508 1.04 0.0772
0.8531 1.05 0.0757
0.8554 1.06 0.0742
0.8577 1.07 0.0728
0.8599 1.08 0.0714
0.8621 1.09 0.0700
0.8643 1.10 0.0686
0.8665 1.11 0.0673
0.8686 1.12 0.0659
0.8708 1.13 0.0646
0.8729 1.14 0.0634
0.8749 1.15 0.0621
0.8770 1.16 0.0609
0.8790 1.17 0.0596
0.8810 1.18 0.0584
0.8830 1.19 0.0573
0.8849 1.20 0.0561
0.8869 1.21 0.0550
0.8888 1.22 0.0538
Page 12
EOQ and ROP
0.8907 1.23 0.0527
0.8925 1.24 0.0517
0.8944 1.25 0.0506
0.8962 1.26 0.0495
0.8980 1.27 0.0485
0.8997 1.28 0.0475
0.9015 1.29 0.0465
0.9032 1.30 0.0455
0.9049 1.31 0.0446
0.9066 1.32 0.0436
0.9082 1.33 0.0427
0.9099 1.34 0.0418
0.9115 1.35 0.0409
0.9131 1.36 0.0400
0.9147 1.37 0.0392
0.9162 1.38 0.0383
0.9177 1.39 0.0375
0.9192 1.40 0.0367
0.9207 1.41 0.0359
0.9222 1.42 0.0351
0.9236 1.43 0.0343
0.9251 1.44 0.0336
0.9265 1.45 0.0328
0.9279 1.46 0.0321
0.9292 1.47 0.0314
0.9306 1.48 0.0307
0.9319 1.49 0.0300
0.9332 1.50 0.0293
0.9345 1.51 0.0286
0.9357 1.52 0.0280
0.9370 1.53 0.0274
0.9382 1.54 0.0267
0.9394 1.55 0.0261
0.9406 1.56 0.0255
0.9418 1.57 0.0249
0.9429 1.58 0.0244
0.9441 1.59 0.0238
0.9452 1.60 0.0232
0.9463 1.61 0.0227
0.9474 1.62 0.0222
0.9484 1.63 0.0216
0.9495 1.64 0.0211
0.9505 1.65 0.0206
0.9515 1.66 0.0201
0.9525 1.67 0.0197
0.9535 1.68 0.0192
0.9545 1.69 0.0187
0.9554 1.70 0.0183
0.9564 1.71 0.0178
0.9573 1.72 0.0174
0.9582 1.73 0.0170
0.9591 1.74 0.0166
Page 13
EOQ and ROP
0.9599 1.75 0.0162
0.9608 1.76 0.0158
0.9616 1.77 0.0154
0.9625 1.78 0.0150
0.9633 1.79 0.0146
0.9641 1.80 0.0143
0.9649 1.81 0.0139
0.9656 1.82 0.0136
0.9664 1.83 0.0132
0.9671 1.84 0.0129
0.9678 1.85 0.0126
0.9686 1.86 0.0123
0.9693 1.87 0.0119
0.9699 1.88 0.0116
0.9706 1.89 0.0113
0.9713 1.90 0.0111
0.9719 1.91 0.0108
0.9726 1.92 0.0105
0.9732 1.93 0.0102
0.9738 1.94 0.0100
0.9744 1.95 0.0097
0.9750 1.96 0.0094
0.9756 1.97 0.0092
0.9761 1.98 0.0090
0.9767 1.99 0.0087
0.9772 2.00 0.0085
0.9778 2.01 0.0083
0.9783 2.02 0.0080
0.9788 2.03 0.0078
0.9793 2.04 0.0076
0.9798 2.05 0.0074
0.9803 2.06 0.0072
0.9808 2.07 0.0070
0.9812 2.08 0.0068
0.9817 2.09 0.0066
0.9821 2.10 0.0065
0.9826 2.11 0.0063
0.9830 2.12 0.0061
0.9834 2.13 0.0060
0.9838 2.14 0.0058
0.9842 2.15 0.0056
0.9846 2.16 0.0055
0.9850 2.17 0.0053
0.9854 2.18 0.0052
0.9857 2.19 0.0050
0.9861 2.20 0.0049
0.9864 2.21 0.0047
0.9868 2.22 0.0046
0.9871 2.23 0.0045
0.9875 2.24 0.0044
0.9878 2.25 0.0042
0.9881 2.26 0.0041
Page 14
EOQ and ROP
0.9884 2.27 0.0040
0.9887 2.28 0.0039
0.9890 2.29 0.0038
0.9893 2.30 0.0037
0.9896 2.31 0.0036
0.9898 2.32 0.0035
0.9901 2.33 0.0034
0.9904 2.34 0.0033
0.9906 2.35 0.0032
0.9909 2.36 0.0031
0.9911 2.37 0.0030
0.9913 2.38 0.0029
0.9916 2.39 0.0028
0.9918 2.40 0.0027
0.9920 2.41 0.0026
0.9922 2.42 0.0026
0.9925 2.43 0.0025
0.9927 2.44 0.0024
0.9929 2.45 0.0023
0.9931 2.46 0.0023
0.9932 2.47 0.0022
0.9934 2.48 0.0021
0.9936 2.49 0.0021
0.9938 2.50 0.0020
0.9940 2.51 0.0019
0.9941 2.52 0.0019
0.9943 2.53 0.0018
0.9945 2.54 0.0018
0.9946 2.55 0.0017
0.9948 2.56 0.0017
0.9949 2.57 0.0016
0.9951 2.58 0.0016
0.9952 2.59 0.0015
0.9953 2.60 0.0015
0.9955 2.61 0.0014
0.9956 2.62 0.0014
0.9957 2.63 0.0013
0.9959 2.64 0.0013
0.9960 2.65 0.0012
0.9961 2.66 0.0012
0.9962 2.67 0.0012
0.9963 2.68 0.0011
0.9964 2.69 0.0011
0.9965 2.70 0.0011
0.9966 2.71 0.0010
0.9967 2.72 0.0010
0.9968 2.73 0.0010
0.9969 2.74 0.0009
0.9970 2.75 0.0009
0.9971 2.76 0.0009
0.9972 2.77 0.0008
0.9973 2.78 0.0008
Page 15
EOQ and ROP
0.9974 2.79 0.0008
0.9974 2.80 0.0008
0.9975 2.81 0.0007
0.9976 2.82 0.0007
0.9977 2.83 0.0007
0.9977 2.84 0.0007
0.9978 2.85 0.0006
0.9979 2.86 0.0006
0.9979 2.87 0.0006
0.9980 2.88 0.0006
0.9981 2.89 0.0006
0.9981 2.90 0.0005
0.9982 2.91 0.0005
0.9982 2.92 0.0005
0.9983 2.93 0.0005
0.9984 2.94 0.0005
0.9984 2.95 0.0005
0.9985 2.96 0.0004
0.9985 2.97 0.0004
0.9986 2.98 0.0004
0.9986 2.99 0.0004
0.9987 3.00 0.0004
0.9987 3.01 0.0004
0.9987 3.02 0.0004
0.9988 3.03 0.0003
0.9988 3.04 0.0003
0.9989 3.05 0.0003
0.9989 3.06 0.0003
0.9989 3.07 0.0003
0.9990 3.08 0.0003
0.9990 3.09 0.0003
0.9990 3.10 0.0003
0.9991 3.11 0.0003
0.9991 3.12 0.0002
0.9991 3.13 0.0002
0.9992 3.14 0.0002
0.9992 3.15 0.0002
0.9992 3.16 0.0002
0.9992 3.17 0.0002
0.9993 3.18 0.0002
0.9993 3.19 0.0002
0.9993 3.20 0.0002
0.9993 3.21 0.0002
0.9994 3.22 0.0002
0.9994 3.23 0.0002
0.9994 3.24 0.0002
0.9994 3.25 0.0002
0.9994 3.26 0.0001
0.9995 3.27 0.0001
0.9995 3.28 0.0001
0.9995 3.29 0.0001
0.9995 3.30 0.0001
Page 16
EOQ and ROP
0.9995 3.31 0.0001
0.9995 3.32 0.0001
0.9996 3.33 0.0001
0.9996 3.34 0.0001
0.9996 3.35 0.0001
0.9996 3.36 0.0001
0.9996 3.37 0.0001
0.9996 3.38 0.0001
0.9997 3.39 0.0001
0.9997 3.40 0.0001
0.9997 3.41 0.0001
0.9997 3.42 0.0001
0.9997 3.43 0.0001
0.9997 3.44 0.0001
0.9997 3.45 0.0001
0.9997 3.46 0.0001
0.9997 3.47 0.0001
0.9997 3.48 0.0001
0.9998 3.49 0.0001
0.9998 3.50 0.0001
0.9998 3.51 0.0001
0.9998 3.52 0.0001
0.9998 3.53 0.0001
0.9998 3.54 0.0000
0.9998 3.55 0.0000
0.9998 3.56 0.0000
0.9998 3.57 0.0000
0.9998 3.58 0.0000
0.9998 3.59 0.0000
0.9998 3.60 0.0000
0.9998 3.61 0.0000
0.9999 3.62 0.0000
0.9999 3.63 0.0000
0.9999 3.64 0.0000
0.9999 3.65 0.0000
0.9999 3.66 0.0000
0.9999 3.67 0.0000
0.9999 3.68 0.0000
0.9999 3.69 0.0000
0.9999 3.70 0.0000
0.9999 3.71 0.0000
0.9999 3.72 0.0000
0.9999 3.73 0.0000
0.9999 3.74 0.0000
0.9999 3.75 0.0000
0.9999 3.76 0.0000
0.9999 3.77 0.0000
0.9999 3.78 0.0000
0.9999 3.79 0.0000
0.9999 3.80 0.0000
0.9999 3.81 0.0000
0.9999 3.82 0.0000
Page 17
EOQ and ROP
0.9999 3.83 0.0000
0.9999 3.84 0.0000
0.9999 3.85 0.0000
0.9999 3.86 0.0000
0.9999 3.87 0.0000
0.9999 3.88 0.0000
0.9999 3.89 0.0000
1.0000 3.90 0.0000
1.0000 3.91 0.0000
1.0000 3.92 0.0000
1.0000 3.93 0.0000
1.0000 3.94 0.0000
1.0000 3.95 0.0000
1.0000 3.96 0.0000
1.0000 3.97 0.0000
1.0000 3.98 0.0000
1.0000 3.99 0.0000
1.0000 4.00 0.0000
1.0000 4.01 0.0000
1.0000 4.02 0.0000
1.0000 4.03 0.0000
1.0000 4.04 0.0000
1.0000 4.05 0.0000
1.0000 4.06 0.0000
1.0000 4.07 0.0000
1.0000 4.08 0.0000
1.0000 4.09 0.0000
1.0000 4.10 0.0000
1.0000 4.11 0.0000
1.0000 4.12 0.0000
1.0000 4.13 0.0000
1.0000 4.14 0.0000
1.0000 4.15 0.0000
1.0000 4.16 0.0000
1.0000 4.17 0.0000
1.0000 4.18 0.0000
1.0000 4.19 0.0000
1.0000 4.20 0.0000
1.0000 4.21 0.0000
1.0000 4.22 0.0000
1.0000 4.23 0.0000
1.0000 4.24 0.0000
1.0000 4.25 0.0000
1.0000 4.26 0.0000
1.0000 4.27 0.0000
1.0000 4.28 0.0000
1.0000 4.29 0.0000
1.0000 4.30 0.0000
1.0000 4.31 0.0000
1.0000 4.32 0.0000
1.0000 4.33 0.0000
1.0000 4.34 0.0000
Page 18
EOQ and ROP
1.0000 4.35 0.0000
1.0000 4.36 0.0000
1.0000 4.37 0.0000
1.0000 4.38 0.0000
1.0000 4.39 0.0000
1.0000 4.40 0.0000
1.0000 4.41 0.0000
1.0000 4.42 0.0000
1.0000 4.43 0.0000
1.0000 4.44 0.0000
1.0000 4.45 0.0000
1.0000 4.46 0.0000
1.0000 4.47 0.0000
1.0000 4.48 0.0000
1.0000 4.49 0.0000
1.0000 4.50 0.0000
Page 19
EOQ and ROP
Expected Number Out of Stock versus Standard Deviation
(Normalized to a Standard Deviation of 1)
Page 20
Single Period Model - Full Marginal Cost Analysis Approach
Co = 0.20$ Cost per unit of demand overestimated
Cu = 0.20$ Cost per unit of demand underestimated
Units
DemandedProbability 1800 2000 2200 2400 2600 2800 3000
1800 0.050 - 40 80 120 160 200 240
2000 0.100 40 - 40 80 120 160 200
2200 0.200 80 40 - 40 80 120 160
2400 0.300 120 80 40 - 40 80 120
2600 0.200 160 120 80 40 - 40 80
2800 0.100 200 160 120 80 40 - 40
3000 0.050 240 200 160 120 80 40 -
Total Cost 120 84 56 44 56 84 120
Number of Units Purchased
0
20
40
60
80
100
120
140
1800 2000 2200 2400 2600 2800 3000
Exp
ecte
d C
os
t ($
)
Number Purchased
- - - -
Number of Units Purchased
Fixed Quantity Model
Annual demand (D ) 1000
Ordering cost (S ) $5.00
Holding cost per unit per year (H ) $1.25
Days in operation per year = 360
Lead time (L ) 5
Cost per unit (C ) $12.50
Total Annual Holding and Ordering Cost =
Total Cost =
Q0 =
Average Inventory =
Reorder point =
Days per cycle =
Number of cycles per year =
0.0
50.0
100.0
0 20 40 60 80 100 120
Qu
an
tity
Time Horizon
X ROP
0 13.9
162.0 13.9
T CumProd Q y
63 0 0 1000
63 300.0 162.0
Time InvLevel Usage CumProd
CumInv 0.0 90.0 0
CumInv 0.0 90.0 0.0 0
UseInv 0.0 90.0 90.0 0
UseInv 32.4 0.0 0
CumInv 32.4 90.0 0
CumInv 32.4 90.0 0.0 0
UseInv 32.4 90.0 90.0 0
UseInv 64.8 0.0 0
CumInv 64.8 90.0 0.0 0
CumInv 64.8 90.0 90.0 0
UseInv 64.8 90.0 0
UseInv 97.2 0.0 0
CumInv 97.2 90.0 0.0 0
CumInv 97.2 90.0 90.0 0
UseInv 97.2 90.0 0
UseInv 129.6 0.0 0
CumInv 129.6 90.0 0.0 0
CumInv 129.6 90.0 90.0 0
UseInv 129.6 90.0 0
UseInv 162.0 0.0 0
90
45.0
13.9
32.4
11.1
111.81$
12,611.81
Total Annual Holding and Ordering Cost =
Total Cost =
Q0 =
Average Inventory =
Reorder point =
Days per cycle =
Number of cycles per year =
90.0
13.9
140 160 180
Order Received
Usage Rate
Reorder Point
13.9
13.9
13.9
13.9
13.9
13.9
13.9
13.9
13.9
13.9
13.9
13.9
13.9
13.9
13.9
13.9
13.9
13.9
13.9
13.9
Fixed Time Period Model with Safety Stock
30 T Number of days between reviews
14 L Lead time in days
10 d-bar Forecast average daily demand (d-bar)
3 s d Standard deviation of demand
98% L Service Level
150 I Current inventory level
19.900 s T+L Standard deviation of demand over the review and lead time
2.054 z z-value for the stated service level
440 Average demand over the vulnerable period
40.87 Safety stock
330 q Order Quantity
EOQ and Total Cost Graph
Annual demand (D ) 1000
Per Order cost (S ) $5.00
Holding cost per unit per year (H ) $1.25
Qopt = 90
$150.0
0
100
200
300
400
500
600
0 50 100 150 200 250 300 350 400
Co
st
($)
Order Quantity
Q
Total Holding Cost
Total Setup Cost
Total Cost
Increment Q 10
Q CumProd QBEP TC
200 0 0 90 0 150
200 150 112 90 200 150
Q THC TSC TC
0 0.0 0 0.0
10 6.3 500.0 506.3
20 12.5 250.0 262.5
30 18.8 166.7 185.4
40 25.0 125.0 150.0
50 31.3 100.0 131.3
60 37.5 83.3 120.8
70 43.8 71.4 115.2
80 50.0 62.5 112.5
90 56.3 55.6 111.8
100 62.5 50.0 112.5
110 68.8 45.5 114.2
120 75.0 41.7 116.7
130 81.3 38.5 119.7
140 87.5 35.7 123.2
150 93.8 33.3 127.1
160 100.0 31.3 131.3
170 106.3 29.4 135.7
180 112.5 27.8 140.3
190 118.8 26.3 145.1
200 125.0 25.0 150.0
210 131.3 23.8 155.1
220 137.5 22.7 160.2
230 143.8 21.7 165.5
240 150.0 20.8 170.8
250 156.3 20.0 176.3
260 162.5 19.2 181.7
270 168.8 18.5 187.3
280 175.0 17.9 192.9
290 181.3 17.2 198.5
300 187.5 16.7 204.2
310 193.8 16.1 209.9
320 200.0 15.6 215.6
330 206.3 15.2 221.4
340 212.5 14.7 227.2
350 218.8 14.3 233.0
360 225.0 13.9 238.9
370 231.3 13.5 244.8
380 237.5 13.2 250.7
390 243.8 12.8 256.6
400 250.0 12.5 262.5
410 256.3 12.2 268.4
420 262.5 11.9 274.4
430 268.8 11.6 280.4
450 500
Total Holding Cost
Total Setup Cost
Total Cost
