1752:
1408:
In order to find the optimal order quantity under different quantity discount schemes, one should use algorithms; these algorithms are developed under the assumption that the EOQ policy is still optimal with quantity discounts. Perera et al. (2017) establish this optimality and fully characterize the
81:
for a product is constant over a period of time (such as a year) and each new order is delivered in full when inventory reaches zero. There is a fixed cost for each order placed, regardless of the quantity of items ordered; an order is assumed to contain only one type of inventory item. There is also
3419:
Another important extension of the EOQ model is to consider items with imperfect quality. Salameh and Jaber (2000) were the first to study the imperfect items in an EOQ model very thoroughly. They consider an inventory problem in which the demand is deterministic and there is a fraction of imperfect
3432:
model (EPQ), have been criticised for "their restrictive set of assumptions. Guga and Musa make use of the model for an
Albanian business case study and conclude that the model is "perfect theoretically, but not very suitable from the practical perspective of this firm". However, James Cargal notes
1417:
In presence of a strategic customer, who responds optimally to discount schedules, the design of an optimal quantity discount scheme by the supplier is complex and has to be done carefully. This is particularly so when the demand at the customer is itself uncertain. An interesting effect called the
92:
The required parameters to the solution are the total demand for the year, the purchase cost for each item, the fixed cost to place the order for a single item and the storage cost for each item per year. Note that the number of times an order is placed will also affect the total cost, though this
2429:
978:
709:
2298:
1582:
1551:
2055:
2585:
86:, sometimes expressed as a percentage of the purchase cost of the item. Although the EOQ formulation is straightforward, factors such as transportation rates and quantity discounts factor into its real-world application.
1379:
1287:
1195:
2304:
1403:
All units discount: an order of 1–1000 units costs $ 50 each; an order of 1001–5000 units costs $ 45 each; an order of more than 5000 units costs $ 40 each. So when 1500 units are ordered, the total cost is $
3073:
2724:
430:
3983:
Tsan-Ming Choi (Ed.) Handbook of EOQ Inventory
Problems: Stochastic and Deterministic Models and Applications, Springer's International Series in Operations Research and Management Science, 2014.
356:
1396:
An important extension to the EOQ model is to accommodate quantity discounts. There are two main types of quantity discounts: (1) all-units and (2) incremental. Here is a numerical example:
887:
546:
3275:
3349:
1400:
Incremental unit discount: Units 1–100 cost $ 30 each; Units 101–199 cost $ 28 each; Units 200 and up cost $ 26 each. So when 150 units are ordered, the total cost is $ 30*100 + $ 28*50.
1106:
823:
3382:
1017:
891:
487:
2760:
1426:
Several extensions can be made to the EOQ model, including backordering costs and multiple items. In the case backorders are permitted, the inventory carrying costs per cycle are:
560:
2094:
1903:
2853:
2818:
2623:
759:
2082:
1850:
1804:
2672:
1747:{\displaystyle \pi s+{\hat {\pi }}\int \limits _{0}^{T_{2}}\lambda tdt=\pi s+{\frac {1}{2}}{\hat {\pi }}\lambda T_{2}^{2}=\pi s+{\frac {{\hat {\pi }}s^{2}}{2\lambda }},}
2649:
1574:
2792:
1432:
1911:
192:
2651:
is optimal. In the first case the optimal lot is given by the classic EOQ formula, in the second case an order is never placed and minimum yearly cost is given by
1775:
3445:
and specialist software allows for more versatility in the use of the formula and adoption of "assumptions which are more realistic" than in the original model.
1199:
If we check the total cost for any order quantity other than 400(=EOQ), we will see that the cost is higher. For instance, supposing 500 units per order, then
262:
236:
214:
163:
141:
119:
2444:
3953:
Perera, Sandun; Janakiraman, Ganesh; Niu, Shun-Chen (2018). "Optimality of (s, S) Inventory
Policies under Renewal Demand and General Cost Structures".
3408:(2013) has introduced the multi-criteria EOQ models where the criteria could be minimizing the total cost, Order quantity (inventory), and Shortages.
89:
The EOQ indicates the optimal number of units to order to minimize the total cost associated with the purchase, delivery, and storage of the product.
1297:
4031:
290:
Ordering cost: This is the cost of placing orders: each order has a fixed cost K, and we need to order D/Q times per year. This is K × D/Q
1205:
1113:
3731:
2424:{\displaystyle {\frac {\partial {\mathcal {K}}}{\partial s}}=-{\frac {IC}{Q}}(Q-s)+{\frac {1}{Q}}\pi \lambda +{\frac {1}{Q}}{\hat {\pi }}s=0}
1418:"reverse bullwhip" takes place where an increase in consumer demand uncertainty actually reduces order quantity uncertainty at the supplier.
3932:
Perera, Sandun; Janakiraman, Ganesh; Niu, Shun-Chen (2017). "Optimality of (s,S) policies in EOQ models with general cost structures".
3611:
Perera, Sandun; Janakiraman, Ganesh; Niu, Shun-Chen (2017). "Optimality of (s,S) policies in EOQ models with general cost structures".
3549:
Perera, Sandun; Janakiraman, Ganesh; Niu, Shun-Chen (2017). "Optimality of (s,S) policies in EOQ models with general cost structures".
2861:
2677:
264:= annual holding cost per unit, also known as carrying cost or storage cost (capital cost, warehouse space, refrigeration, insurance,
3510:
58:
4052:
3479:
372:
300:
3464:
3429:
3388:
287:
Purchase cost: This is the variable cost of goods: purchase unit price × annual demand quantity. This is P × D
3402:
function, where a person's holdings of money balances can be seen in a way parallel to a firm's holdings of inventory.
293:
Holding cost: the average quantity in stock (between fully replenished and empty) is Q/2, so this cost is h × Q/2
3677:
Caplin, Andrew; Leahy, John (2010). "Economic Theory and the World of
Practice: A Celebration of the (s, S) Model".
852:
501:
3895:
Plossel, George. Orlicky's
Material Requirement's Planning. Second Edition. McGraw Hill. 1984. (first edition 1975)
54:
3996:
3079:
3287:
1024:
3774:
Salameh, M.K.; Jaber, M.Y. (March 2000). "Economic production quantity model for items with imperfect quality".
973:{\displaystyle ={\sqrt {\frac {2\cdot 10000\cdot 40}{4+50\cdot 2\%}}}={\sqrt {\frac {2\cdot 10000\cdot 40}{5}}}}
764:
3808:
Tao, Z., A. L. Guiffrida, and M. D. Troutt, "A green cost based economic production/order quantity model", in
3354:
986:
704:{\displaystyle T={\frac {DK}{Q}}+{\frac {hQ}{2}}+PD={\frac {h}{2Q}}(Q-{\sqrt {2DK/h}})^{2}+{\sqrt {2hDK}}+PD,}
2293:{\displaystyle {\frac {\partial {\mathcal {K}}}{\partial Q}}=-{\frac {1}{Q^{2}}}\left+{\frac {IC}{Q}}(Q-s)=0}
441:
3420:
items in the lot and are screened by the buyer and sold by them at the end of the circle at discount price.
3650:
Goyal, S.K. (1987). "A simple heuristic method for determining economic order interval for linear demand".
2729:
1905:. The average annual variable cost is the sum of order costs, holding inventory costs and backorder costs:
3686:
3474:
1855:
2823:
3747:
Trippi, Robert R.; Lewin, Donald E. (1974). "A Present Value
Formulation of the Classical Eoq Problem".
3576:
Altintas, Nihat; Erhun, Feryal; Tayur, Sridhar (2008). "Quantity
Discounts Under Demand Uncertainty".
2797:
2593:
366:
of the total cost with respect to Q (assume all other variables are constant) and set it equal to 0:
3691:
2063:
717:
3997:"Optimization of fuel injection in GDI engine using economic order quantity and Lambert W function"
2085:
1809:
1780:
50:
2654:
3920:
3704:
3593:
3391:
model (which determines the optimal production quantity) can be determined in a similar fashion.
2435:
1546:{\displaystyle IC\int \limits _{0}^{T_{1}}(Q-s-\lambda t)\,dt={\frac {IC}{2\lambda }}(Q-s)^{2},}
2628:
2050:{\displaystyle {\mathcal {K}}={\frac {\lambda }{Q}}A+{\frac {1}{2Q}}IC(Q-s)^{2}+{\frac {1}{Q}}}
1383:
This illustrates that the economic order quantity is always in the best interests of the firm.
4020:
3791:
3727:
3637:
3506:
3434:
3433:
that the formula was developed when business calculations were undertaken "by hand", or using
1559:
242:
per unit, typically cost of ordering and shipping and handling. This is not the cost of goods)
2764:
4008:
3984:
3970:
3962:
3941:
3912:
3783:
3756:
3696:
3659:
3620:
3585:
3558:
3469:
3405:
265:
3822:
170:
69:
applied it extensively, and he and K. Andler are given credit for their in-depth analysis.
4037:
1760:
4012:
3839:
3411:
A version taking the time-value of money into account was developed by Trippi and Lewin.
3810:
Proceedings of the 1st Annual Kent State
International Symposium on Green Supply Chains
3760:
247:
221:
199:
148:
126:
104:
62:
3787:
4046:
3924:
3879:
Camp, W. E. "Determining the production order quantity", Management
Engineering, 1922
3663:
3454:
277:
The single-item EOQ formula finds the minimum point of the following cost function:
3459:
3399:
3395:
2580:{\displaystyle s^{2}+2\pi {\hat {\pi }}\lambda s+(\pi \lambda )^{2}-2\lambda AIC=0}
83:
46:
3387:
Additionally, the economic order interval can be determined from the EOQ and the
3442:
3945:
3916:
3624:
3562:
3988:
3438:
363:
3795:
280:
Total Cost = purchase cost or production cost + ordering cost + holding cost
3900:
3500:
3281:
17:
3589:
1556:
where s is the number of backorders when order quantity Q is delivered and
1374:{\displaystyle =50\cdot 10000+40\cdot (10000/300)+5\cdot (300/2)=502083.33}
3975:
268:(price x interest), etc. usually not related to the unit production cost)
3700:
3708:
3597:
1282:{\displaystyle =50\cdot 10000+40\cdot (10000/500)+5\cdot (500/2)=502050}
1190:{\displaystyle =50\cdot 10000+40\cdot (10000/400)+5\cdot (400/2)=502000}
3966:
1409:(s,S) optimality within the EOQ setting under general cost structures.
362:
To determine the minimum point of the total cost curve, calculate the
4019:
Renewal Demand and (s, S) Optimality by Perera, Janakiraman, and Niu
3539:
Zipkin, Paul H, Foundations of
Inventory Management, McGraw Hill 2000
78:
2434:
Substituting the second equation into the first gives the following
3068:{\displaystyle s^{*}=^{-1}\left(-\pi \lambda +\left^{1/2}\right)}
3883:
Wilson, R. H. (1934). "A Scientific Routine for Stock Control".
2719:{\displaystyle \pi >{\sqrt {\frac {2AIC}{\lambda }}}=\delta }
3640:, G. Hadley, Analysis of Inventory Systems, Prentice Hall 1963
3829:, Vol. III, Issue 12, December 2015, accessed 9 February 2024
3827:
International Journal of Economics, Commerce & Management
2316:
2106:
2069:
1917:
554:
The optimal value Q* may also be found by recognizing that
3867:
Harris, Ford W. (1913). "How many parts to make at once".
3724:
Operations and Production Systems with Multiple Objectives
551:
Q* is independent of P; it is a function of only K, D, h.
1291:
Similarly, if we choose 300 for the order quantity, then
1576:
is the rate of demand. The backorder cost per cycle is:
82:
a cost for each unit held in storage, commonly known as
425:{\displaystyle {0}=-{\frac {DK}{Q^{2}}}+{\frac {h}{2}}}
720:
3357:
3290:
3082:
2864:
2826:
2800:
2767:
2732:
2680:
2657:
2631:
2596:
2447:
2307:
2097:
2066:
1914:
1858:
1812:
1783:
1763:
1585:
1562:
1435:
1300:
1208:
1116:
1027:
989:
894:
855:
767:
714:
where the non-negative quadratic term disappears for
563:
504:
444:
435:
Solving for Q gives Q* (the optimal order quantity):
375:
303:
250:
224:
202:
173:
151:
129:
107:
3505:, Englewood Cliffs, NJ: Prentice-Hall, p. 135,
351:{\displaystyle T=PD+K{\frac {D}{Q}}+h{\frac {Q}{2}}}
93:
number can be determined from the other parameters.
3863:(Factory Management Series), Chicago: Shaw (1915)
3376:
3343:
3269:
3067:
2847:
2812:
2786:
2754:
2718:
2666:
2643:
2617:
2579:
2423:
2292:
2076:
2049:
1897:
1844:
1798:
1769:
1746:
1568:
1545:
1373:
1281:
1189:
1100:
1011:
972:
881:
817:
753:
703:
540:
481:
424:
350:
256:
230:
208:
186:
157:
135:
113:
3901:"Ford Whitman Harris's economical lot size model"
2855:solving the preceding quadratic equation yields:
2820:then there shouldn't be any inventory system. If
273:Total cost function and derivation of EOQ formula
45:, is the order quantity that minimizes the total
882:{\displaystyle {\sqrt {\frac {2D\cdot K}{h}}}}
541:{\displaystyle Q^{*}={\sqrt {\frac {2DK}{h}}}}
3934:International Journal of Production Economics
3905:International Journal of Production Economics
3776:International Journal of Production Economics
3613:International Journal of Production Economics
3551:International Journal of Production Economics
1413:Design of optimal quantity discount schedules
833:Annual requirement quantity (D) = 10000 units
8:
3270:{\displaystyle Q^{*}=\left^{1/2}\left^{1/2}}
3398:model, has also been used to determine the
3344:{\displaystyle r_{h}^{*}=\mu -mQ^{*}-s^{*}}
1101:{\displaystyle =P\cdot D+K(D/EOQ)+h(EOQ/2)}
143:= purchase unit price, unit production cost
3652:Engineering Costs and Production Economics
818:{\displaystyle T_{min}={\sqrt {2hDK}}+PD.}
3995:Ventura, Robert; Samuel, Stephen (2016).
3974:
3690:
3364:
3356:
3335:
3322:
3300:
3295:
3289:
3257:
3253:
3222:
3221:
3204:
3188:
3162:
3146:
3142:
3126:
3105:
3104:
3101:
3087:
3081:
3050:
3046:
3035:
3010:
3000:
2980:
2970:
2906:
2882:
2881:
2869:
2863:
2828:
2827:
2825:
2799:
2772:
2766:
2746:
2731:
2687:
2679:
2656:
2630:
2598:
2597:
2595:
2547:
2514:
2513:
2498:
2474:
2473:
2464:
2453:
2452:
2446:
2401:
2400:
2390:
2371:
2338:
2315:
2314:
2308:
2306:
2254:
2240:
2225:
2224:
2214:
2193:
2161:
2150:
2137:
2128:
2105:
2104:
2098:
2096:
2068:
2067:
2065:
2038:
2023:
2022:
2012:
1987:
1978:
1941:
1925:
1916:
1915:
1913:
1887:
1863:
1857:
1836:
1817:
1811:
1785:
1784:
1782:
1762:
1724:
1709:
1708:
1705:
1687:
1682:
1664:
1663:
1653:
1621:
1616:
1611:
1596:
1595:
1584:
1561:
1534:
1498:
1488:
1456:
1451:
1446:
1434:
1354:
1328:
1299:
1262:
1236:
1207:
1170:
1144:
1115:
1087:
1052:
1026:
993:
988:
983:Number of orders per year (based on EOQ)
944:
898:
893:
856:
854:
787:
772:
766:
738:
727:
719:
673:
664:
650:
639:
615:
588:
570:
562:
518:
509:
503:
461:
449:
443:
412:
401:
387:
376:
374:
338:
322:
302:
249:
223:
201:
178:
172:
150:
128:
106:
3377:{\displaystyle m\leq {\frac {\tau }{T}}}
1012:{\displaystyle ={\frac {10000}{400}}=25}
3491:
482:{\displaystyle Q^{*2}={\frac {2DK}{h}}}
3823:Inventory Management through EOQ Model
2755:{\displaystyle \pi \lambda >K_{w}}
1422:Backordering costs and multiple items
7:
4013:10.1016/j.applthermaleng.2016.02.024
3955:Production and Operations Management
3679:The Journal of Economic Perspectives
3502:Production and Operations Management
1898:{\displaystyle T_{1}=(Q-s)/\lambda }
238:= fixed cost per order, setup cost (
57:. It is one of the oldest classical
3869:Factory, the Magazine of Management
3812:, Canton, Ohio, US, 29–30 July 2010
3351:; with m being the largest integer
2848:{\displaystyle {\hat {\pi }}\neq 0}
61:models. The model was developed by
3761:10.1111/j.1540-5915.1974.tb00592.x
3527:Production and operations analysis
3428:The EOQ model and its sister, the
2638:
2323:
2311:
2113:
2101:
934:
25:
4038:Vol. III, Issue 12, December 2015
842:Yearly carrying cost per unit = 4
3821:Guga, E. and Musa, O. (2015) in
761:which provides the cost minimum
3529:. McGraw Hill Higher Education.
3480:Economic lot scheduling problem
2813:{\displaystyle \pi <\delta }
2618:{\displaystyle {\hat {\pi }}=0}
1852:, T being the cycle length and
754:{\textstyle Q={\sqrt {2DK/h}},}
3242:
3227:
3218:
3201:
3191:
3131:
3110:
3032:
3022:
3015:
2985:
2956:
2938:
2903:
2887:
2878:
2833:
2603:
2544:
2534:
2519:
2491:
2479:
2458:
2448:
2406:
2365:
2353:
2281:
2269:
2230:
2190:
2177:
2077:{\displaystyle {\mathcal {K}}}
2044:
2028:
1997:
1975:
1962:
1884:
1872:
1790:
1714:
1669:
1601:
1531:
1518:
1485:
1464:
1362:
1348:
1336:
1322:
1270:
1256:
1244:
1230:
1178:
1164:
1152:
1138:
1095:
1075:
1066:
1046:
661:
630:
1:
3788:10.1016/s0925-5273(99)00044-4
1845:{\displaystyle T_{2}=T-T_{1}}
1799:{\displaystyle {\hat {\pi }}}
121:= total annual inventory cost
3899:Erlenkotter, Donald (2014).
3664:10.1016/0167-188X(87)90025-5
3499:Hax, AC; Candea, D. (1984),
3465:Economic production quantity
3430:economic production quantity
3394:A version of the model, the
3389:economic production quantity
3384:and μ the lead time demand.
2667:{\displaystyle \pi \lambda }
65:in 1913, but the consultant
4001:Applied Thermal Engineering
1387:Extensions of the EOQ model
39:financial purchase quantity
27:Production scheduling model
4069:
3946:10.1016/j.ijpe.2016.09.017
3917:10.1016/j.ijpe.2013.12.008
3846:, accessed 9 February 2024
3625:10.1016/j.ijpe.2016.09.017
3563:10.1016/j.ijpe.2016.09.017
849:Economic order quantity =
3989:10.1007/978-1-4614-7639-9
3726:. John Wiley & Sons.
2644:{\displaystyle s=\infty }
3525:Nahmias, Steven (2005).
3284:, the reorder point is:
1569:{\displaystyle \lambda }
216:= annual demand quantity
194:= optimal order quantity
43:economic buying quantity
3885:Harvard Business Review
2787:{\displaystyle s^{*}=0}
836:Cost per order (K) = 40
496:Economic Order Quantity
31:Economic order quantity
4053:Inventory optimization
3838:Cargal, J. M. (2003),
3590:10.1287/mnsc.1070.0829
3475:Dynamic lot size model
3378:
3345:
3271:
3069:
2849:
2814:
2788:
2756:
2720:
2668:
2645:
2619:
2581:
2425:
2294:
2078:
2051:
1899:
1846:
1800:
1771:
1748:
1628:
1570:
1547:
1463:
1375:
1283:
1191:
1102:
1013:
974:
883:
819:
755:
705:
542:
483:
426:
352:
258:
232:
210:
188:
159:
137:
115:
77:EOQ applies only when
3722:Malakooti, B (2013).
3379:
3346:
3272:
3070:
2850:
2815:
2789:
2757:
2721:
2669:
2646:
2620:
2582:
2426:
2295:
2079:
2052:
1900:
1847:
1806:are backorder costs,
1801:
1772:
1749:
1607:
1571:
1548:
1442:
1376:
1284:
1192:
1103:
1014:
975:
884:
839:Cost per unit (P)= 50
820:
756:
706:
543:
484:
427:
353:
259:
233:
211:
189:
187:{\displaystyle Q^{*}}
160:
138:
116:
59:production scheduling
3701:10.1257/jep.24.1.183
3355:
3288:
3080:
2862:
2824:
2798:
2765:
2730:
2678:
2655:
2629:
2594:
2445:
2305:
2095:
2064:
1912:
1856:
1810:
1781:
1770:{\displaystyle \pi }
1761:
1583:
1560:
1433:
1298:
1206:
1114:
1025:
987:
892:
853:
845:Market interest = 2%
765:
718:
561:
502:
442:
373:
301:
248:
222:
200:
171:
149:
127:
105:
55:inventory management
3305:
2086:partial derivatives
1692:
3967:10.1111/poms.12795
3578:Management Science
3435:logarithmic tables
3374:
3341:
3291:
3267:
3065:
2845:
2810:
2784:
2752:
2716:
2664:
2641:
2615:
2577:
2436:quadratic equation
2421:
2290:
2074:
2047:
1895:
1842:
1796:
1767:
1744:
1678:
1566:
1543:
1392:Quantity discounts
1371:
1279:
1187:
1098:
1009:
970:
879:
815:
751:
701:
538:
479:
422:
348:
254:
228:
206:
184:
155:
133:
111:
3749:Decision Sciences
3733:978-1-118-58537-5
3415:Imperfect quality
3372:
3246:
3230:
3183:
3136:
3134:
3113:
3020:
3018:
2990:
2988:
2890:
2836:
2708:
2707:
2606:
2522:
2482:
2461:
2409:
2398:
2379:
2351:
2330:
2267:
2233:
2222:
2169:
2143:
2120:
2031:
2020:
1995:
1954:
1933:
1793:
1739:
1717:
1672:
1661:
1604:
1516:
1001:
968:
967:
939:
938:
877:
876:
801:
746:
687:
658:
628:
601:
583:
536:
535:
477:
420:
407:
346:
330:
257:{\displaystyle h}
231:{\displaystyle K}
209:{\displaystyle D}
158:{\displaystyle Q}
136:{\displaystyle P}
114:{\displaystyle T}
37:), also known as
16:(Redirected from
4060:
4016:
3980:
3978:
3949:
3928:
3892:
3876:
3859:Harris, Ford W.
3847:
3836:
3830:
3819:
3813:
3806:
3800:
3799:
3771:
3765:
3764:
3744:
3738:
3737:
3719:
3713:
3712:
3694:
3674:
3668:
3667:
3647:
3641:
3635:
3629:
3628:
3608:
3602:
3601:
3573:
3567:
3566:
3546:
3540:
3537:
3531:
3530:
3522:
3516:
3515:
3496:
3470:Newsvendor model
3383:
3381:
3380:
3375:
3373:
3365:
3350:
3348:
3347:
3342:
3340:
3339:
3327:
3326:
3304:
3299:
3276:
3274:
3273:
3268:
3266:
3265:
3261:
3252:
3248:
3247:
3245:
3232:
3231:
3223:
3210:
3209:
3208:
3189:
3184:
3182:
3174:
3163:
3155:
3154:
3150:
3141:
3137:
3135:
3127:
3125:
3115:
3114:
3106:
3102:
3092:
3091:
3074:
3072:
3071:
3066:
3064:
3060:
3059:
3058:
3054:
3045:
3041:
3040:
3039:
3021:
3019:
3011:
3009:
3001:
2996:
2992:
2991:
2989:
2981:
2979:
2971:
2914:
2913:
2892:
2891:
2883:
2874:
2873:
2854:
2852:
2851:
2846:
2838:
2837:
2829:
2819:
2817:
2816:
2811:
2793:
2791:
2790:
2785:
2777:
2776:
2761:
2759:
2758:
2753:
2751:
2750:
2725:
2723:
2722:
2717:
2709:
2703:
2689:
2688:
2673:
2671:
2670:
2665:
2650:
2648:
2647:
2642:
2624:
2622:
2621:
2616:
2608:
2607:
2599:
2586:
2584:
2583:
2578:
2552:
2551:
2524:
2523:
2515:
2503:
2502:
2484:
2483:
2475:
2469:
2468:
2463:
2462:
2454:
2430:
2428:
2427:
2422:
2411:
2410:
2402:
2399:
2391:
2380:
2372:
2352:
2347:
2339:
2331:
2329:
2321:
2320:
2319:
2309:
2299:
2297:
2296:
2291:
2268:
2263:
2255:
2250:
2246:
2245:
2244:
2235:
2234:
2226:
2223:
2215:
2198:
2197:
2170:
2162:
2154:
2144:
2142:
2141:
2129:
2121:
2119:
2111:
2110:
2109:
2099:
2083:
2081:
2080:
2075:
2073:
2072:
2056:
2054:
2053:
2048:
2043:
2042:
2033:
2032:
2024:
2021:
2013:
1996:
1988:
1983:
1982:
1955:
1953:
1942:
1934:
1926:
1921:
1920:
1904:
1902:
1901:
1896:
1891:
1868:
1867:
1851:
1849:
1848:
1843:
1841:
1840:
1822:
1821:
1805:
1803:
1802:
1797:
1795:
1794:
1786:
1776:
1774:
1773:
1768:
1753:
1751:
1750:
1745:
1740:
1738:
1730:
1729:
1728:
1719:
1718:
1710:
1706:
1691:
1686:
1674:
1673:
1665:
1662:
1654:
1627:
1626:
1625:
1615:
1606:
1605:
1597:
1575:
1573:
1572:
1567:
1552:
1550:
1549:
1544:
1539:
1538:
1517:
1515:
1507:
1499:
1462:
1461:
1460:
1450:
1380:
1378:
1377:
1372:
1358:
1332:
1288:
1286:
1285:
1280:
1266:
1240:
1196:
1194:
1193:
1188:
1174:
1148:
1107:
1105:
1104:
1099:
1091:
1056:
1018:
1016:
1015:
1010:
1002:
994:
979:
977:
976:
971:
969:
963:
946:
945:
940:
937:
917:
900:
899:
888:
886:
885:
880:
878:
872:
858:
857:
824:
822:
821:
816:
802:
788:
783:
782:
760:
758:
757:
752:
747:
742:
728:
710:
708:
707:
702:
688:
674:
669:
668:
659:
654:
640:
629:
627:
616:
602:
597:
589:
584:
579:
571:
547:
545:
544:
539:
537:
531:
520:
519:
514:
513:
488:
486:
485:
480:
478:
473:
462:
457:
456:
431:
429:
428:
423:
421:
413:
408:
406:
405:
396:
388:
380:
357:
355:
354:
349:
347:
339:
331:
323:
266:opportunity cost
263:
261:
260:
255:
237:
235:
234:
229:
215:
213:
212:
207:
193:
191:
190:
185:
183:
182:
165:= order quantity
164:
162:
161:
156:
142:
140:
139:
134:
120:
118:
117:
112:
21:
4068:
4067:
4063:
4062:
4061:
4059:
4058:
4057:
4043:
4042:
4028:
3994:
3952:
3931:
3898:
3882:
3875:: 135–136, 152.
3866:
3861:Operations Cost
3856:
3854:Further reading
3851:
3850:
3844:Troy University
3840:The EOQ Formula
3837:
3833:
3820:
3816:
3807:
3803:
3773:
3772:
3768:
3746:
3745:
3741:
3734:
3721:
3720:
3716:
3692:10.1.1.730.8784
3676:
3675:
3671:
3649:
3648:
3644:
3636:
3632:
3610:
3609:
3605:
3575:
3574:
3570:
3548:
3547:
3543:
3538:
3534:
3524:
3523:
3519:
3513:
3498:
3497:
3493:
3488:
3451:
3426:
3417:
3353:
3352:
3331:
3318:
3286:
3285:
3211:
3200:
3190:
3175:
3164:
3161:
3157:
3156:
3103:
3097:
3096:
3083:
3078:
3077:
3031:
3002:
2972:
2963:
2959:
2937:
2933:
2932:
2919:
2915:
2902:
2865:
2860:
2859:
2822:
2821:
2796:
2795:
2794:is optimal, if
2768:
2763:
2762:
2742:
2728:
2727:
2690:
2676:
2675:
2653:
2652:
2627:
2626:
2592:
2591:
2543:
2494:
2451:
2443:
2442:
2340:
2322:
2310:
2303:
2302:
2256:
2236:
2189:
2149:
2145:
2133:
2112:
2100:
2093:
2092:
2088:equal to zero:
2062:
2061:
2034:
1974:
1946:
1910:
1909:
1859:
1854:
1853:
1832:
1813:
1808:
1807:
1779:
1778:
1759:
1758:
1731:
1720:
1707:
1617:
1581:
1580:
1558:
1557:
1530:
1508:
1500:
1452:
1431:
1430:
1424:
1415:
1394:
1389:
1296:
1295:
1204:
1203:
1112:
1111:
1023:
1022:
985:
984:
947:
918:
901:
890:
889:
859:
851:
850:
830:
768:
763:
762:
716:
715:
660:
620:
590:
572:
559:
558:
549:
521:
505:
500:
499:
463:
445:
440:
439:
397:
389:
371:
370:
299:
298:
275:
246:
245:
220:
219:
198:
197:
174:
169:
168:
147:
146:
125:
124:
103:
102:
99:
75:
28:
23:
22:
15:
12:
11:
5:
4066:
4064:
4056:
4055:
4045:
4044:
4041:
4040:
4036:Piasecki, D.,
4034:
4027:
4026:External links
4024:
4023:
4022:
4017:
3992:
3981:
3976:2027.42/142450
3961:(2): 368–383.
3950:
3929:
3896:
3893:
3880:
3877:
3864:
3855:
3852:
3849:
3848:
3831:
3814:
3801:
3782:(1–3): 59–64.
3766:
3739:
3732:
3714:
3685:(1): 183–201.
3669:
3642:
3630:
3603:
3568:
3541:
3532:
3517:
3511:
3490:
3489:
3487:
3484:
3483:
3482:
3477:
3472:
3467:
3462:
3457:
3450:
3447:
3425:
3422:
3416:
3413:
3371:
3368:
3363:
3360:
3338:
3334:
3330:
3325:
3321:
3317:
3314:
3311:
3308:
3303:
3298:
3294:
3278:
3277:
3264:
3260:
3256:
3251:
3244:
3241:
3238:
3235:
3229:
3226:
3220:
3217:
3214:
3207:
3203:
3199:
3196:
3193:
3187:
3181:
3178:
3173:
3170:
3167:
3160:
3153:
3149:
3145:
3140:
3133:
3130:
3124:
3121:
3118:
3112:
3109:
3100:
3095:
3090:
3086:
3075:
3063:
3057:
3053:
3049:
3044:
3038:
3034:
3030:
3027:
3024:
3017:
3014:
3008:
3005:
2999:
2995:
2987:
2984:
2978:
2975:
2969:
2966:
2962:
2958:
2955:
2952:
2949:
2946:
2943:
2940:
2936:
2931:
2928:
2925:
2922:
2918:
2912:
2909:
2905:
2901:
2898:
2895:
2889:
2886:
2880:
2877:
2872:
2868:
2844:
2841:
2835:
2832:
2809:
2806:
2803:
2783:
2780:
2775:
2771:
2749:
2745:
2741:
2738:
2735:
2715:
2712:
2706:
2702:
2699:
2696:
2693:
2686:
2683:
2663:
2660:
2640:
2637:
2634:
2625:either s=0 or
2614:
2611:
2605:
2602:
2588:
2587:
2576:
2573:
2570:
2567:
2564:
2561:
2558:
2555:
2550:
2546:
2542:
2539:
2536:
2533:
2530:
2527:
2521:
2518:
2512:
2509:
2506:
2501:
2497:
2493:
2490:
2487:
2481:
2478:
2472:
2467:
2460:
2457:
2450:
2432:
2431:
2420:
2417:
2414:
2408:
2405:
2397:
2394:
2389:
2386:
2383:
2378:
2375:
2370:
2367:
2364:
2361:
2358:
2355:
2350:
2346:
2343:
2337:
2334:
2328:
2325:
2318:
2313:
2300:
2289:
2286:
2283:
2280:
2277:
2274:
2271:
2266:
2262:
2259:
2253:
2249:
2243:
2239:
2232:
2229:
2221:
2218:
2213:
2210:
2207:
2204:
2201:
2196:
2192:
2188:
2185:
2182:
2179:
2176:
2173:
2168:
2165:
2160:
2157:
2153:
2148:
2140:
2136:
2132:
2127:
2124:
2118:
2115:
2108:
2103:
2071:
2058:
2057:
2046:
2041:
2037:
2030:
2027:
2019:
2016:
2011:
2008:
2005:
2002:
1999:
1994:
1991:
1986:
1981:
1977:
1973:
1970:
1967:
1964:
1961:
1958:
1952:
1949:
1945:
1940:
1937:
1932:
1929:
1924:
1919:
1894:
1890:
1886:
1883:
1880:
1877:
1874:
1871:
1866:
1862:
1839:
1835:
1831:
1828:
1825:
1820:
1816:
1792:
1789:
1766:
1755:
1754:
1743:
1737:
1734:
1727:
1723:
1716:
1713:
1704:
1701:
1698:
1695:
1690:
1685:
1681:
1677:
1671:
1668:
1660:
1657:
1652:
1649:
1646:
1643:
1640:
1637:
1634:
1631:
1624:
1620:
1614:
1610:
1603:
1600:
1594:
1591:
1588:
1565:
1554:
1553:
1542:
1537:
1533:
1529:
1526:
1523:
1520:
1514:
1511:
1506:
1503:
1497:
1494:
1491:
1487:
1484:
1481:
1478:
1475:
1472:
1469:
1466:
1459:
1455:
1449:
1445:
1441:
1438:
1423:
1420:
1414:
1411:
1406:
1405:
1401:
1393:
1390:
1388:
1385:
1370:
1367:
1364:
1361:
1357:
1353:
1350:
1347:
1344:
1341:
1338:
1335:
1331:
1327:
1324:
1321:
1318:
1315:
1312:
1309:
1306:
1303:
1278:
1275:
1272:
1269:
1265:
1261:
1258:
1255:
1252:
1249:
1246:
1243:
1239:
1235:
1232:
1229:
1226:
1223:
1220:
1217:
1214:
1211:
1186:
1183:
1180:
1177:
1173:
1169:
1166:
1163:
1160:
1157:
1154:
1151:
1147:
1143:
1140:
1137:
1134:
1131:
1128:
1125:
1122:
1119:
1097:
1094:
1090:
1086:
1083:
1080:
1077:
1074:
1071:
1068:
1065:
1062:
1059:
1055:
1051:
1048:
1045:
1042:
1039:
1036:
1033:
1030:
1008:
1005:
1000:
997:
992:
966:
962:
959:
956:
953:
950:
943:
936:
933:
930:
927:
924:
921:
916:
913:
910:
907:
904:
897:
875:
871:
868:
865:
862:
847:
846:
843:
840:
837:
834:
829:
826:
814:
811:
808:
805:
800:
797:
794:
791:
786:
781:
778:
775:
771:
750:
745:
741:
737:
734:
731:
726:
723:
712:
711:
700:
697:
694:
691:
686:
683:
680:
677:
672:
667:
663:
657:
653:
649:
646:
643:
638:
635:
632:
626:
623:
619:
614:
611:
608:
605:
600:
596:
593:
587:
582:
578:
575:
569:
566:
534:
530:
527:
524:
517:
512:
508:
494:
490:
489:
476:
472:
469:
466:
460:
455:
452:
448:
433:
432:
419:
416:
411:
404:
400:
395:
392:
386:
383:
379:
360:
359:
345:
342:
337:
334:
329:
326:
321:
318:
315:
312:
309:
306:
295:
294:
291:
288:
274:
271:
270:
269:
253:
243:
227:
217:
205:
195:
181:
177:
166:
154:
144:
132:
122:
110:
98:
95:
74:
71:
63:Ford W. Harris
51:ordering costs
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
4065:
4054:
4051:
4050:
4048:
4039:
4035:
4033:
4032:The EOQ Model
4030:
4029:
4025:
4021:
4018:
4014:
4010:
4006:
4002:
3998:
3993:
3990:
3986:
3982:
3977:
3972:
3968:
3964:
3960:
3956:
3951:
3947:
3943:
3939:
3935:
3930:
3926:
3922:
3918:
3914:
3910:
3906:
3902:
3897:
3894:
3890:
3886:
3881:
3878:
3874:
3870:
3865:
3862:
3858:
3857:
3853:
3845:
3841:
3835:
3832:
3828:
3824:
3818:
3815:
3811:
3805:
3802:
3797:
3793:
3789:
3785:
3781:
3777:
3770:
3767:
3762:
3758:
3754:
3750:
3743:
3740:
3735:
3729:
3725:
3718:
3715:
3710:
3706:
3702:
3698:
3693:
3688:
3684:
3680:
3673:
3670:
3665:
3661:
3657:
3653:
3646:
3643:
3639:
3634:
3631:
3626:
3622:
3618:
3614:
3607:
3604:
3599:
3595:
3591:
3587:
3584:(4): 777–92.
3583:
3579:
3572:
3569:
3564:
3560:
3556:
3552:
3545:
3542:
3536:
3533:
3528:
3521:
3518:
3514:
3512:9780137248803
3508:
3504:
3503:
3495:
3492:
3485:
3481:
3478:
3476:
3473:
3471:
3468:
3466:
3463:
3461:
3458:
3456:
3455:Reorder point
3453:
3452:
3448:
3446:
3444:
3440:
3436:
3431:
3423:
3421:
3414:
3412:
3409:
3407:
3403:
3401:
3397:
3392:
3390:
3385:
3369:
3366:
3361:
3358:
3336:
3332:
3328:
3323:
3319:
3315:
3312:
3309:
3306:
3301:
3296:
3292:
3283:
3280:If there are
3262:
3258:
3254:
3249:
3239:
3236:
3233:
3224:
3215:
3212:
3205:
3197:
3194:
3185:
3179:
3176:
3171:
3168:
3165:
3158:
3151:
3147:
3143:
3138:
3128:
3122:
3119:
3116:
3107:
3098:
3093:
3088:
3084:
3076:
3061:
3055:
3051:
3047:
3042:
3036:
3028:
3025:
3012:
3006:
3003:
2997:
2993:
2982:
2976:
2973:
2967:
2964:
2960:
2953:
2950:
2947:
2944:
2941:
2934:
2929:
2926:
2923:
2920:
2916:
2910:
2907:
2899:
2896:
2893:
2884:
2875:
2870:
2866:
2858:
2857:
2856:
2842:
2839:
2830:
2807:
2804:
2801:
2781:
2778:
2773:
2769:
2747:
2743:
2739:
2736:
2733:
2713:
2710:
2704:
2700:
2697:
2694:
2691:
2684:
2681:
2661:
2658:
2635:
2632:
2612:
2609:
2600:
2574:
2571:
2568:
2565:
2562:
2559:
2556:
2553:
2548:
2540:
2537:
2531:
2528:
2525:
2516:
2510:
2507:
2504:
2499:
2495:
2488:
2485:
2476:
2470:
2465:
2455:
2441:
2440:
2439:
2437:
2418:
2415:
2412:
2403:
2395:
2392:
2387:
2384:
2381:
2376:
2373:
2368:
2362:
2359:
2356:
2348:
2344:
2341:
2335:
2332:
2326:
2301:
2287:
2284:
2278:
2275:
2272:
2264:
2260:
2257:
2251:
2247:
2241:
2237:
2227:
2219:
2216:
2211:
2208:
2205:
2202:
2199:
2194:
2186:
2183:
2180:
2174:
2171:
2166:
2163:
2158:
2155:
2151:
2146:
2138:
2134:
2130:
2125:
2122:
2116:
2091:
2090:
2089:
2087:
2039:
2035:
2025:
2017:
2014:
2009:
2006:
2003:
2000:
1992:
1989:
1984:
1979:
1971:
1968:
1965:
1959:
1956:
1950:
1947:
1943:
1938:
1935:
1930:
1927:
1922:
1908:
1907:
1906:
1892:
1888:
1881:
1878:
1875:
1869:
1864:
1860:
1837:
1833:
1829:
1826:
1823:
1818:
1814:
1787:
1764:
1741:
1735:
1732:
1725:
1721:
1711:
1702:
1699:
1696:
1693:
1688:
1683:
1679:
1675:
1666:
1658:
1655:
1650:
1647:
1644:
1641:
1638:
1635:
1632:
1629:
1622:
1618:
1612:
1608:
1598:
1592:
1589:
1586:
1579:
1578:
1577:
1563:
1540:
1535:
1527:
1524:
1521:
1512:
1509:
1504:
1501:
1495:
1492:
1489:
1482:
1479:
1476:
1473:
1470:
1467:
1457:
1453:
1447:
1443:
1439:
1436:
1429:
1428:
1427:
1421:
1419:
1412:
1410:
1402:
1399:
1398:
1397:
1391:
1386:
1384:
1381:
1368:
1365:
1359:
1355:
1351:
1345:
1342:
1339:
1333:
1329:
1325:
1319:
1316:
1313:
1310:
1307:
1304:
1301:
1292:
1289:
1276:
1273:
1267:
1263:
1259:
1253:
1250:
1247:
1241:
1237:
1233:
1227:
1224:
1221:
1218:
1215:
1212:
1209:
1200:
1197:
1184:
1181:
1175:
1171:
1167:
1161:
1158:
1155:
1149:
1145:
1141:
1135:
1132:
1129:
1126:
1123:
1120:
1117:
1108:
1092:
1088:
1084:
1081:
1078:
1072:
1069:
1063:
1060:
1057:
1053:
1049:
1043:
1040:
1037:
1034:
1031:
1028:
1019:
1006:
1003:
998:
995:
990:
981:
964:
960:
957:
954:
951:
948:
941:
931:
928:
925:
922:
919:
914:
911:
908:
905:
902:
895:
873:
869:
866:
863:
860:
844:
841:
838:
835:
832:
831:
827:
825:
812:
809:
806:
803:
798:
795:
792:
789:
784:
779:
776:
773:
769:
748:
743:
739:
735:
732:
729:
724:
721:
698:
695:
692:
689:
684:
681:
678:
675:
670:
665:
655:
651:
647:
644:
641:
636:
633:
624:
621:
617:
612:
609:
606:
603:
598:
594:
591:
585:
580:
576:
573:
567:
564:
557:
556:
555:
552:
548:
532:
528:
525:
522:
515:
510:
506:
497:
493:
474:
470:
467:
464:
458:
453:
450:
446:
438:
437:
436:
417:
414:
409:
402:
398:
393:
390:
384:
381:
377:
369:
368:
367:
365:
343:
340:
335:
332:
327:
324:
319:
316:
313:
310:
307:
304:
297:
296:
292:
289:
286:
285:
284:
281:
278:
272:
267:
251:
244:
241:
225:
218:
203:
196:
179:
175:
167:
152:
145:
130:
123:
108:
101:
100:
96:
94:
90:
87:
85:
80:
72:
70:
68:
64:
60:
56:
52:
48:
47:holding costs
44:
40:
36:
32:
19:
4004:
4000:
3958:
3954:
3937:
3933:
3908:
3904:
3888:
3884:
3872:
3868:
3860:
3843:
3834:
3826:
3817:
3809:
3804:
3779:
3775:
3769:
3755:(1): 30–35.
3752:
3748:
3742:
3723:
3717:
3682:
3678:
3672:
3655:
3651:
3645:
3633:
3616:
3612:
3606:
3581:
3577:
3571:
3554:
3550:
3544:
3535:
3526:
3520:
3501:
3494:
3460:Safety stock
3443:spreadsheets
3427:
3418:
3410:
3404:
3400:money demand
3396:Baumol-Tobin
3393:
3386:
3279:
2589:
2433:
2060:To minimize
2059:
1756:
1555:
1425:
1416:
1407:
1395:
1382:
1293:
1290:
1201:
1198:
1109:
1020:
982:
980:= 400 units
848:
713:
553:
550:
498:
495:
491:
434:
361:
282:
279:
276:
239:
91:
88:
84:holding cost
76:
67:R. H. Wilson
66:
42:
38:
34:
30:
29:
18:EOQ equation
3940:: 216–228.
3619:: 216–228.
3557:: 216–228.
2084:impose the
1294:Total cost
1202:Total cost
1110:Total cost
1021:Total cost
492:Therefore:
4007:: 112–20.
3486:References
3439:slide rule
3424:Criticisms
3282:backorders
364:derivative
3925:153794306
3911:: 12–15.
3891:: 116–28.
3796:0925-5273
3687:CiteSeerX
3658:: 53–57.
3638:T. Whitin
3441:. Use of
3406:Malakooti
3367:τ
3362:≤
3337:∗
3329:−
3324:∗
3313:−
3310:μ
3302:∗
3228:^
3225:π
3198:λ
3195:π
3186:−
3169:λ
3132:^
3129:π
3111:^
3108:π
3089:∗
3029:λ
3026:π
3016:^
3013:π
2998:−
2986:^
2983:π
2945:λ
2927:λ
2924:π
2921:−
2908:−
2888:^
2885:π
2871:∗
2840:≠
2834:^
2831:π
2808:δ
2802:π
2774:∗
2737:λ
2734:π
2714:δ
2705:λ
2682:π
2662:λ
2659:π
2639:∞
2604:^
2601:π
2560:λ
2554:−
2541:λ
2538:π
2526:λ
2520:^
2517:π
2511:π
2480:^
2477:π
2459:^
2456:π
2407:^
2404:π
2385:λ
2382:π
2360:−
2336:−
2324:∂
2312:∂
2276:−
2231:^
2228:π
2206:λ
2203:π
2184:−
2152:λ
2126:−
2114:∂
2102:∂
2029:^
2026:π
2004:λ
2001:π
1969:−
1928:λ
1893:λ
1879:−
1830:−
1791:^
1788:π
1765:π
1736:λ
1715:^
1712:π
1697:π
1676:λ
1670:^
1667:π
1645:π
1630:λ
1609:∫
1602:^
1599:π
1587:π
1564:λ
1525:−
1513:λ
1480:λ
1477:−
1471:−
1444:∫
1369:502083.33
1346:⋅
1320:⋅
1308:⋅
1254:⋅
1228:⋅
1216:⋅
1162:⋅
1136:⋅
1124:⋅
1035:⋅
958:⋅
952:⋅
935:%
929:⋅
912:⋅
906:⋅
867:⋅
637:−
511:∗
451:∗
385:−
180:∗
97:Variables
4047:Category
3709:25703488
3598:20122426
3449:See also
1404:45*1500.
73:Overview
828:Example
283:Where:
3923:
3794:
3730:
3707:
3689:
3596:
3509:
1757:where
1277:502050
1185:502000
79:demand
3921:S2CID
3705:JSTOR
3594:JSTOR
3437:or a
2674:. If
1326:10000
1311:10000
1234:10000
1219:10000
1142:10000
1127:10000
996:10000
955:10000
909:10000
3792:ISSN
3728:ISBN
3507:ISBN
2805:<
2740:>
2685:>
1777:and
49:and
4009:doi
4005:101
3985:doi
3971:hdl
3963:doi
3942:doi
3938:187
3913:doi
3909:155
3784:doi
3757:doi
3697:doi
3660:doi
3621:doi
3617:187
3586:doi
3559:doi
3555:187
2726:or
2590:If
1352:300
1334:300
1260:500
1242:500
1168:400
1150:400
999:400
240:not
53:in
41:or
35:EOQ
4049::
4003:.
3999:.
3969:.
3959:27
3957:.
3936:.
3919:.
3907:.
3903:.
3889:13
3887:.
3873:10
3871:.
3842:,
3825:,
3790:.
3780:64
3778:.
3751:.
3703:.
3695:.
3683:24
3681:.
3656:11
3654:.
3615:.
3592:.
3582:54
3580:.
3553:.
2438::
1317:40
1305:50
1225:40
1213:50
1133:40
1121:50
1007:25
961:40
926:50
915:40
4015:.
4011::
3991:.
3987::
3979:.
3973::
3965::
3948:.
3944::
3927:.
3915::
3798:.
3786::
3763:.
3759::
3753:5
3736:.
3711:.
3699::
3666:.
3662::
3627:.
3623::
3600:.
3588::
3565:.
3561::
3370:T
3359:m
3333:s
3320:Q
3316:m
3307:=
3297:h
3293:r
3263:2
3259:/
3255:1
3250:]
3243:)
3240:C
3237:I
3234:+
3219:(
3216:C
3213:I
3206:2
3202:)
3192:(
3180:C
3177:I
3172:A
3166:2
3159:[
3152:2
3148:/
3144:1
3139:]
3123:C
3120:I
3117:+
3099:[
3094:=
3085:Q
3062:)
3056:2
3052:/
3048:1
3043:]
3037:2
3033:)
3023:(
3007:C
3004:I
2994:)
2977:C
2974:I
2968:+
2965:1
2961:(
2957:)
2954:C
2951:I
2948:A
2942:2
2939:(
2935:[
2930:+
2917:(
2911:1
2904:]
2900:C
2897:I
2894:+
2879:[
2876:=
2867:s
2843:0
2782:0
2779:=
2770:s
2748:w
2744:K
2711:=
2701:C
2698:I
2695:A
2692:2
2636:=
2633:s
2613:0
2610:=
2575:0
2572:=
2569:C
2566:I
2563:A
2557:2
2549:2
2545:)
2535:(
2532:+
2529:s
2508:2
2505:+
2500:2
2496:s
2492:]
2489:C
2486:I
2471:+
2466:2
2449:[
2419:0
2416:=
2413:s
2396:Q
2393:1
2388:+
2377:Q
2374:1
2369:+
2366:)
2363:s
2357:Q
2354:(
2349:Q
2345:C
2342:I
2333:=
2327:s
2317:K
2288:0
2285:=
2282:)
2279:s
2273:Q
2270:(
2265:Q
2261:C
2258:I
2252:+
2248:]
2242:2
2238:s
2220:2
2217:1
2212:+
2209:s
2200:+
2195:2
2191:)
2187:s
2181:Q
2178:(
2175:C
2172:I
2167:2
2164:1
2159:+
2156:A
2147:[
2139:2
2135:Q
2131:1
2123:=
2117:Q
2107:K
2070:K
2045:]
2040:2
2036:s
2018:2
2015:1
2010:+
2007:s
1998:[
1993:Q
1990:1
1985:+
1980:2
1976:)
1972:s
1966:Q
1963:(
1960:C
1957:I
1951:Q
1948:2
1944:1
1939:+
1936:A
1931:Q
1923:=
1918:K
1889:/
1885:)
1882:s
1876:Q
1873:(
1870:=
1865:1
1861:T
1838:1
1834:T
1827:T
1824:=
1819:2
1815:T
1742:,
1733:2
1726:2
1722:s
1703:+
1700:s
1694:=
1689:2
1684:2
1680:T
1659:2
1656:1
1651:+
1648:s
1642:=
1639:t
1636:d
1633:t
1623:2
1619:T
1613:0
1593:+
1590:s
1541:,
1536:2
1532:)
1528:s
1522:Q
1519:(
1510:2
1505:C
1502:I
1496:=
1493:t
1490:d
1486:)
1483:t
1474:s
1468:Q
1465:(
1458:1
1454:T
1448:0
1440:C
1437:I
1366:=
1363:)
1360:2
1356:/
1349:(
1343:5
1340:+
1337:)
1330:/
1323:(
1314:+
1302:=
1274:=
1271:)
1268:2
1264:/
1257:(
1251:5
1248:+
1245:)
1238:/
1231:(
1222:+
1210:=
1182:=
1179:)
1176:2
1172:/
1165:(
1159:5
1156:+
1153:)
1146:/
1139:(
1130:+
1118:=
1096:)
1093:2
1089:/
1085:Q
1082:O
1079:E
1076:(
1073:h
1070:+
1067:)
1064:Q
1061:O
1058:E
1054:/
1050:D
1047:(
1044:K
1041:+
1038:D
1032:P
1029:=
1004:=
991:=
965:5
949:2
942:=
932:2
923:+
920:4
903:2
896:=
874:h
870:K
864:D
861:2
813:.
810:D
807:P
804:+
799:K
796:D
793:h
790:2
785:=
780:n
777:i
774:m
770:T
749:,
744:h
740:/
736:K
733:D
730:2
725:=
722:Q
699:,
696:D
693:P
690:+
685:K
682:D
679:h
676:2
671:+
666:2
662:)
656:h
652:/
648:K
645:D
642:2
634:Q
631:(
625:Q
622:2
618:h
613:=
610:D
607:P
604:+
599:2
595:Q
592:h
586:+
581:Q
577:K
574:D
568:=
565:T
533:h
529:K
526:D
523:2
516:=
507:Q
475:h
471:K
468:D
465:2
459:=
454:2
447:Q
418:2
415:h
410:+
403:2
399:Q
394:K
391:D
382:=
378:0
358:.
344:2
341:Q
336:h
333:+
328:Q
325:D
320:K
317:+
314:D
311:P
308:=
305:T
252:h
226:K
204:D
176:Q
153:Q
131:P
109:T
33:(
20:)
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