实例15_经济定货量模型EOQ1.xls

EOQ 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 123456789 10 11 12 13 14 15 16 17 18 19 20 21 22 23 123456123456789 10 11123456 YEAR 24 25 26 27 28 29 30 789 10 11 12 13 AnnualdemandD8000 Ordering cost per orderk30Ordering Cost Holding Cost per unit per yearh3 81200 Quantity orderedQ2001002400 1501600 Ordering cost12002001200 Holding cost380250960 Total cost1580300800 350686 400600 450533 500480 550436 600400 E Ec co on no om mi ic c O Or rd de er r Q Qu ua an nt ti it ty y 6 60 0 0 0 5 50 0 0 0 4 4 0 0 0 0 3 30 0 0 0 2 20 0 0 0 1 10 0 0 0 0 0 5 50 00 0 1 10 00 00 0 1 15 50 00 0 2 20 00 00 0 2 25 50 00 0 Q Qu ua an nt ti it ty y o or rd de er re ed d O Or rd de er ri in ng g C Co os st t H Ho ol ld di in ng g C Co os st t T To ot ta al l C Co os st t Holding Cost Total Cost 3801580 1902590EOQY 28518853550 38015803552500 4751435 5701370 6651351 7601360 8551388 9501430 10451481 11401540 EOQOrdering cost 1200 AnnualdemandD8000 1002400 00 Ordering cost per orderk301501600 00 Holding Cost per unit per year h3 82001200 00 250960 00 Order quantity200200300800 00 Ordering cost1200350685 71 Holding Cost380400600 00 Total cost1580450533 33 500480 00 Economic order quantity EOQ 355 41550436 36 Ordering cost EOQ 675 28600400 00 Holding Cost EOQ 675 28 Total cost EOQ 1350 56 固定数量订货下的总成本 C kD Q hQ 2 最优数量Q dC dQ kD Q2 h 2 0 Q0 Sqrt 2kD h 订货成本 存储成本时总成本最小 kD Q0 hQ0 2 Sqrt khD 2 Cmin Sqrt 2khD 最优订货周期 T0 Sqrt 2k hD 通货膨胀时的EOQ 特点 存货具有随通货膨胀升值的特点 这部 分的升值可以部分 甚至全部 抵消存货的 存储成本 尽管存货的存储成本可能也在不 断地上涨 设 P为存货购买的单价 i代表存货价格上涨 率 r代表单位存储成本上涨率 b代表批量订 货成本的上涨率 固定数量订货下的总成本 C k 1 b D Q h 1 r Pi Q 2 最优数量Q dC dQ k 1 b D Q2 h 1 r Pi 2 0 Q0 Sqrt 2k 1 b D h 1 r Pi The Bauinol Tobin Model 诺贝尔经济学奖 每次实际货币需求 M P Sqrt 2bQ i 实际货币余额 其中 P 价格 b 交易成本 Q 总货币数量 i 利率 Holding CostTotal cost 38015801580 05000 06000 07000 08000 09000 0 190 002590 00100 01690 01990 02290 02590 02890 0 285 001885 00150 01285 01485 01685 01885 02085 0 380 001580 00200 01130 01280 01430 01580 01730 0 475 001435 00250 01075 01195 01315 01435 01555 0 570 001370 00300 01070 01170 01270 01370 01470 0 665 001350 71350 01093 61179 31265 01350 71436 4 760 001360 00400 01135 01210 01285 01360 01435 0 855 001388 33450 01188 31255 01321 71388 31455 0 950 001430 00500 01250 01310 01370 01430 01490 0 1045 001481 36550 01317 71372 31426 81481 41535 9 1140 001540 00600 01390 01440 01490 01540 01590 0 355 4105000 06000 07000 08000 09000 0 355 412500355 41 280 9757 307 7935332 455 355 4093 376 9685 1350 56 1067 708 1169 615 1263 329 1350 5551432 48 2000 200380355 410 2001200355 411350 56 2001580355 412500 2002500 3 38 80 0 1 12 20 00 0 1 15 58 80 0 E EO OQ Q 6 60 00 05 50 00 04 40 00 03 30 00 02 20 00 01 10 00 0 0 0 0 00 0 5 50 00 0 0 00 0 1 10 00 00 0 0 00 0 1 15 50 00 0 0 00 0 2 20 00 00 0 0 00 0 2 25 50 00 0 0 00 0 O Or rd de er ri in ng g c co os st tH Ho ol ld di in ng g C Co os st tT To ot ta al l c co os st tE EO OQ QO Or rd de er r q qu ua an nt ti it ty y 1350 56 600 0500 0400 0300 0200 0100 0 500 0 900 0 1300 0 1700 0 2100 0 2500 0 The Bauinol Tobin Model 诺贝尔经济学奖 每次实际货币需求 M P Sqrt 2bQ i 实际货币余额 其中 P 价格 b 交易成本 Q 总货币数量 i 利率 3 38 80 0 1 12 20 00 0 1 15 58 80 0 E EO OQ Q 6 60 00 05 50 00 04 40 00 03 30 00 02 20 00 01 10 00 0 0 0 0 00 0 5 50 00 0 0 00 0 1 10 00 00 0 0 00 0 1 15 50 00 0 0 00 0 2 20 00 00 0 0 00 0 2 25 50 00 0 0 00 0 O Or rd de er ri in ng g c co os st tH Ho ol ld di in ng g C Co os st tT To ot ta al l c co os st tE EO OQ QO Or rd de er r q qu ua an nt ti it ty y 10000 01580 3190 0100 02590 0 2285 0150 01885 0 1880 0200 01580 0 1675 0250 01435 0 1570 0300 01370 0 1522 1350 01350 7 1510 0400 01360 0 1521 7450 01388 3 1550 0500 01430 0 1590 5550 01481 4 1640 0600 01540 0 10000 080001000 397 359780001500 1509 967 0 00355 41 8000 00355 8000 001350 56 10000 001351 10000 09000 08000 07000 06000 0 250 300 350 400 450 500 1000 1100 1200 1300 1400 1500 3 38 80 0 1 12 20 00 0 1 15 58 80 0 E EO OQ Q 6 60 00 05 50 00 04 40 00 03 30 00 02 20 00 01 10 00 0 0 0 0 00 0 5 50 00 0 0 00 0 1 10 00 00 0 0 00 0 1 15 50 00 0 0 00 0 2 20 00 00 0 0 00 0 2 25 50 00 0 0 00 0 O Or rd de er ri in ng g c co os st tH Ho ol ld di in ng g C Co os st tT To ot ta al l c co os st tE EO OQ QO Or rd de er r q qu ua an nt ti it ty y 1350 56 600 0500 0400 0300 0200 0100 0 500 0 900 0 1300 0 1700 0 2100 0 2500 0 3 38 80 0 1 12 20 00 0 1 15 58 80 0 E EO OQ Q 6 60 00 05 50 00 04 40 00 03 30 00 02 20 00 01 10 00 0 0 0 0 00 0 5 50 00 0 0 00 0 1 10 00 00 0 0 00 0 1 15 50 00 0 0 00 0 2 20 00 00 0 0 00 0 2 25 50 00 0 0 00 0 O Or rd de er ri in ng g c co os st tH Ho ol ld di in ng g C Co os st tT To ot ta al l c co os st tE EO OQ QO Or rd de er r q qu ua an nt ti it ty y 10000 09000 08000 07000 06000 0 250 300 350 400 450 500 1000 1100 1200 1300 1400 1500 AnnualdemandD8000 Ordering cost per orderk30 Holding Cost per unit per year h3 8 Quantity orderedQ200 Initial inventoryI50 Daily demand22 Daily unit holding cost0 01 Ordering cost1200 00 Holding cost378 31 Total cost1578 31Daily Day demand 122 222 322 422 522 622 722 822 922 1022 1122 1222 1322 1422 1522 1622 1722 1822 1922 2022 2122 2222 2322 2422 2522 2622 2722 2822 2922 3022 3122 3222 3322 3422 3522 3622 3722 3822 3922 4022 4122 4222 4322 4422 4522 4622 4722 4822 4922 5022 5122 5222 5322 5422 5522 5622 5722 5822 5922 6022 6122 6222 6322 6422 6522 6622 6722 6822 6922 7022 7122 7222 7322 7422 7522 7622 7722 7822 7922 8022 8122 8222 8322 8422 8522 8622 8722 8822 8922 9022 9122 9222 9322 9422 9522 9622 9722 9822 9922 10022 10122 10222 10322 10422 10522 10622 10722 10822 10922 11022 11122 11222 11322 11422 11522 11622 11722 11822 11922 12022 12122 12222 12322 12422 12522 12622 12722 12822 12922 13022 13122 13222 13322 13422 13522 13622 13722 13822 13922 14022 14122 14222 14322 14422 14522 14622 14722 14822 14922 15022 15122 15222 15322 15422 15522 15622 15722 15822 15922 16022 16122 16222 16322 16422 16522 16622 16722 16822 16922 17022 17122 17222 17322 17422 17522 17622 17722 17822 17922 18022 18122 18222 18322 18422 18522 18622 18722 18822 18922 19022 19122 19222 19322 19422 19522 19622 19722 19822 19922 20022 20122 20222 20322 20422 20522 20622 20722 20822 20922 21022 21122 21222 21322 21422 21522 21622 21722 21822 21922 22022 22122 22222 22322 22422 22522 22622 22722 22822 22922 23022 23122 23222 23322 23422 23522 23622 23722 23822 23922 24022 24122 24222 24322 24422 24522 24622 24722 24822 24922 25022 25122 25222 25322 25422 25522 25622 25722 25822 25922 26022 26122 26222 26322 26422 26522 26622 26722 26822 26922 27022 27122 27222 27322 27422 27522 27622 27722 27822 27922 28022 28122 28222 28322 28422 28522 28622 28722 28822 28922 29022 29122 29222 29322 29422 29522 29622 29722 29822 29922 30022 30122 30222 30322 30422 30522 30622 30722 30822 30922 31022 31122 31222 31322 31422 31522 31622 31722 31822 31922 32022 32122 32222 32322 32422 32522 32622 32722 32822 32922 33022 33122 33222 33322 33422 33522 33622 33722 33822 33922 34022 34122 34222 34322 34422 34522 34622 34722 34822 34922 35022 35122 35222 35322 35422 35522 35622 35722 35822 35922 36022 Order times40Ordering Total costs1200 00 378 31 1578 31cost Inventory Inventory Order OrderHolding TotalDay1200 00 morning evening signal costcostcost501002370 1501590 5028000 300 3002001200 2861300 0630 060250960 6184001 941 940300810 184162001 711 710350690 162140001 481 480400600 140118001 251 250450540 11896001 011 010500480 9674000 780 780550450 7452000 550 550600420 5230000 320 320 3081300 0830 080 8186001 961 960 186164001 731 730 164142001 501 500 142120001 271 270 12098001 031 030 9876000 800 800 7654000 570 570 5432000 340 340 32101300 1130 110 10188001 981 980 188166001 751 750 166144001 521 520 144122001 291 290 122100001 061 060 10078000 820 820 7856000 590 590 5634000 360 360 34121300 1330 130 12190002 012 010 190168001 771 770 168146001 541 540 146124001 311 310 124102001 081 080 10280000 840 840 8058000 610 610 5836000 380 380 36141300 1530 150 14192002 032 030 192170001 791 790 170148001 561 560 148126001 331 330 126104001 101 100 10482000 870 870 8260000 630 630 6038000 400 400 38161300 1730 170 16194002 052 050 194172001 821 820 172150001 581 58150 150128001 351 350 128106001 121 120 10684000 890 890 8462000 650 650 6240000 420 420 40181300 1930 190 18196002 072 070 196174001 841 840 174152001 601 600 152130001 371 370 130108001 141 140 10886000 910 910 8664000 680 680 6442000 440 440 42201300 2130 210 20198002 092 090 198176001 861 860 176154001 631 630 154132001 391 390 132110001 161 160 11088000 930 930 8866000 700 700 6644000 460 460 4422000 230 230 2201300 0030 000 0178001 881 880 178156001 651 650 156134001 411 410 134112001 181 180 11290000 950 950 9068000 720 720 6846000 490 490 4624000 250 250 2421300 0230 020 2180001 901 900 180158001 671 670 158136001 441 440 136114001 201 200 11492000 970 970 9270000 740 740 7048000 510 510 4826000 270 270 2641300 0430 040 4182001 921 920 182160001 691 690 160138001 461 460 138116001 221 220 11694000 990 990 9472000 760 760 7250000 530 530 5028000 300 300 2861300 0630 060 6184001 941 940 184162001 711 710 162140001 481 480 140118001 251 250 11896001 011 010 9674000 780 780 7452000 550 550 5230000 320 320 3081300 0830 080 8186001 961 960 186164001 731 730 164142001 501 500 142120001 271 270 12098001 031 030 9876000 800 800 7654000 570 570 5432000 340 340 32101300 1130 110 10188001 981 980 188166001 751 750 166144001 521 520 144122001 291 290 122100001 061 060 10078000 820 820 7856000 590 590 5634000 360 360 34121300 1330 130 12190002 012 010 190168001 771 770 168146001 541 540 146124001 311 310 124102001 081 080 10280000 840 840 8058000 610 610 5836000 380 380 36141300 1530 150 14192002 032 030 192170001 791 790 170148001 561 560 148126001 331 330 126104001 101 100 10482000 870 870 8260000 630 630 6038000 400 400 38161300 1730 170 16194002 052 050 194172001 821 820 172150001 581 580 150128001 351 350 128106001 121 120 10684000 890 890 8462000 650 650 6240000 420 420 40181300 1930 190 18196002 072 070 196174001 841 840 174152001 601 600 152130001 371 370 130108001 141 140 10886000 910 910 8664000 680 680 6442000 440 440 42201300 2130 210 20198002 092 090 198176001 861 860 176154001 631 630 154132001 391 390 132110001 161 160 11088000 930 930 8866000 700 700 6644000 460 460 4422000 230 230 2201300 0030 000 0178001 881 880 178156001 651 650 156134001 411 410 134112001 181 180 11290000 950 950 9068000 720 720 6846000 490 490 4624000 250 250 2421300 0230 020 2180001 901 900 180158001 671 670 158136001 441 440 136114001 201 200 11492000 970 970 9270000 740 740 7048000 510 510 4826000 270 270 2641300 0430 040 4182001 921 920 182160001 691 690 160138001 461 460 138116001 221 220 11694000 990 990 9472000 760 760 7250000 530 530 5028000 300 300 2861300 0630 060 6184001 941 940 184162001 711 710 162140001 481 480 140118001 251 250 11896001 011 010 9674000 780 780 7452000 550 550 5230000 320 320 3081300 0830 080 8186001 961 960 186164001 731 730 164142001 501 500 142120001 271 270 12098001 031 030 9876000 800 800 7654000 570 570 5432000 340 340 32101300 1130 110 10188001 981 980 188166001 751 750 166144001 521 520 144122001 291 290 122100001 061 060 10078000 820 820 7856000 590 590 5634000 360 360 34121300 1330 130 12190002 012 010 190168001 771 770 168146001 541 540 146124001 311 310 124102001 081 080 10280000 840 840 8058000 610 610 5836000 380 380 36141300 1530 150 14192002 032 030 192170001 791 790 170148001 561 560 148126001 331 330 126104001 101 100 10482000 870 870 8260000 630 630 6038000 400 400 38161300 1730 170 16194002 052 050 194172001 821 820 172150001 581 580 150128001 351 350 128106001 121 120 10684000 890 890 8462000 650 650 6240000 420 420 40181300 1930 190 18196002 072 070 196174001 841 840 174152001 601 600 152130001 371 370 130108001 141 140 10886000 910 910 8664000 680 680 6442000 440 440 42201300 2130 210 20198002 092 090 198176001 861 860 176154001 631 630 154132001 391 390 132110001 161 160 11088000 930 930 8866000 700 700 6644000 460 460 4422000 230 230 2201300 0030 000 0178001 881 880 178156001 651 650 156134001 411 410 134112001 181 180 11290000 950 950 9068000 720 720 6846000 490 490 4624000 250 250 2421300 0230 020 2180001 901 900 180158001 671 670 158136001 441 440 136114001 201 200 11492000 970 970 9270000 740 740 7048000 510 510 4826000 270 270 2641300 0430 040 4182001 921 920 182160001 691 690 160138001 461 460 138116001 221 220 11694000 990 990 9472000 760 760 7250000 530 530 5028000 300 300 2861300 0630 060 6184001 941 940 184162001 711 710 162140001 481 480 140118001 251 250 11896001 011 010 9674000 780 780 7452000 550 550 5230000 320 320 3081300 0830 080 8186001 961 960 186164001 731 730 164142001 501 500 142120001 271 270 12098001 031 030 9876000 800 800 7654000 570 570 5432000 340 340 32101300 1130 110 10188001 981 980 188166001 751 750 166144001 521 520 144122001 291 290 122100001 061 060 10078000 820 820 7856000 590 590 5634000 360 360 34121300 1330 130 12190002 012 010 190168001 771 770 168146001 541 540 146124001 311 310 124102001 081 080 10280000 840 840 8058000 610 610 5836000 380 380 36141300 1530 150 14192002 032 030 192170001 791 790 170148001 561 560 148126001 331 330 126104001 101 100 10482000 870 870 8260000 630 630 6038000 400 400 38161300 1730 170 16194002 052 050 194172001 821 820 172150001 581 580 150128001 351 350 128106001 121 120 10684000 890 890 8462000 650 650 6240000 420 420 40181300 1930 190 18196002 072 070 196174001 841 840 174152001 601 600 152130001 371 370 HoldingTotal costcost 378 311578 31 1862556 2811871 3781578 4721432 5691379 6651355 7601360 8561396 9491429 10361486 11431563 I In nv ve en nt to or ry y v va ar ri ia at ti io on n o ov ve er r 1 10 00 0 d da ay ys s f fo or r r re eg gu ul la ar r d de em ma an nd d 1 15 59 91 13 31 17 72 21 1 2 25 52 29 93 33 33 37 74 41 1 4 45 54 49 95 53 35 57 76 61 1 6 65 56 69 97 73 37 77 78 81 1 8 85 58 89 99 93 39 97 7 0 50 100 150 200 250 I In nv ve en nt to or ry y v va ar ri ia at ti io on n o ov ve er r 1 10 00 0 d da ay ys s f fo or r r re eg gu ul la ar r d de em ma an nd d 1 15 59 91 13 31 17 72 21 1 2 25 52 29 93 33 33 37 74 41 1 4 45 54 49 95 53 35 57 76 61 1 6 65 56 69 97 73 37 77 78 81 1 8 85 58 89 99 93 39 97 7 0 50 100 150 200 250 AnnualdemandD8000Daily demand min Ordering cost per orderk30Daily demand max Holding Cost per unit per year h3 8 Quantity orderedQ200Random demand Initial inventoryI50 Daily demand22Safe inventory Daily unit holding cost0 011Delay day Ordering cost1230 Holding cost382 Total cost1612 Order times41 Out Of Stock9 Ordering cost average1199 Holding cost average378 2 07 Total cost average1577 Order times average40 I In nv ve en nt to or ry y v va ar ri ia at ti io on n o ov ve er r 1 10 00 0 d da ay ys s f fo or r r ra an nd do om m d de em ma an nd d 1 16 61 11 11 16 62 21 12 26 63 31 13 36 64 41 14 46 65 51 15 56 66 61 16 66 67 71 17 76 68 81 18 86 69 91 19 96 6 0 50 100 150 200 250 0 44 10 22 4 DailyInventory Inventory Order OrderHolding TotalOut Of Stock Day demand morning evening signal costcostcostsignal 1105040000 420 420 2354051300 0530 050 0 003225183001 931 930 413183170001 791 790 54170166001 751 750 65166161001 701 700 736161125001 321 320 83712588000 930 930 9358853000 560 560 1025351000 540 540 11215130000 320 320 1223028000 300 300 131728111300 1230 120 143211179001 891 890 1517179162001 711 710 162162160001 691 690 1711160149001 571 570 1818149131001 381 380 194413187000 920 920 20118776000 800 800 21157661000 640 640 22186143000 450 450 232943141300 1530 150 241314201002 122 120 2510201191002 022 020 2625191166001 751 750 2742166124001 311 310 283912485000 900 900 29188567000 710 710 I In nv ve en nt to or ry y v va ar ri ia at ti io on n o ov ve er r 1 10 00 0 d da ay ys s f fo or r r ra an nd do om m d de em ma an nd d 1 16 61 11 11 16 62 21 12 26 63 31 13 36 64 41 14 46 65 51 15 56 66 61 16 66 67 71 17 76 68 81 18 86 69 91 19 96 6 0 50 100 150 200 250 30136754000 570 570 314254121300 1330 130 323612176001 861 860 3314176162001 711 710 3420162142001 501 500 354314299001 051 050 36419958000 610 610 3705858000 610 610 38265832000 340 340 39273251300 0530 050 4075198002 092 090 4137198161001 701 700 4237161124001 311 310 432812496001 011 010 44449652000 550 550 45145238000 400 400 4603838000 400 400 47293891300 1030 100 4809209002 212 210 4923209186001 961 960 5041186145001 531 530 5119145126001 331 330 5224126102001 081 080 533010272000 760 760 54207252000 550 550 553552171300 1830 180 561617201002 122 120 5719201182001 921 920 5826182156001 651 650 5928156128001 351 350 606128122001 291 290 613812284000 890 890 6288476000 800 800 6307676000 800 800 64227654000 570 570 65165438000 400 400 66143824000 250 250 674124 171300 0030 001 681 17182001 921 920 6917182165001 741 740 7037165128001 351 350 7119128109001 151 150 723610973000 770 770 73137360000 630 630 74186042000 440 440 75174225000 260 260 76182571300 0730 070 77107197002 082 080 7831197166001 751 750 794166162001 711 710 802162160001 691 690 8124160136001 441 440 823136133001 401 400 8327133106001 121 120 843410672000 760 760 85237249000 520 520 863949101300 1130 110 872710183001 931 930 888183175001 851 850 893175172001 821 820 908172164001 731 730 9139164125001 321 320 924112584000 890 890 93298455000 580 580 94155540000 420 420 95154025000 260 260 9602525000 260 260 971325121300 1330 130 982312189002 002 000 9911189178001 881 880 10020178158001 671 670 10123158135001 431 430 1024313592000 970 970 103109282000 870 870 104148268000 720 720 105256843000 450 450 106364371300 0730 070 107217186001 961 960 10811186175001 851 850 1094175171001 811 810 11031171140001 481 480 1116140134001 411 410 11222134112001 181 180 1132211290000 950 950 114259065000 690 690 115436522000 230 230 1163022 81300 0030 001 1171 8191002 022 020 11814191177001 871 870 11934177143001 511 510 12029143114001 201 200 1213911475000 790 790 122157560000 630 630 12366054000 570 570 1243954151300 1630 160 1251915196002 072 070 12613196183001 931 930 12736183147001 551 550 12816147131001 381 380 12912131119001 261 260 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