224:. The setup corresponds to the process of stopping the machine, cleaning it out and loading the tank of the machine with the desired fluid. This product switching must not be done too often or the setup costs will be large, but equally too long a production run of apple juice would be undesirable because it would lead to a large inventory investment and carrying cost for unsold cases of apple juice and perhaps stock-outs in orange juice and milk. The ELSP seeks the optimal trade off between these two extremes.
2418:
1999:
2798:
47:, so that one must decide both the lot size for each product and when each lot should be produced. The method illustrated by Jack D. Rogers draws on a 1956 paper from Welch, W. Evert. The ELSP is a mathematical model of a common issue for almost any company or industry: planning what to manufacture, when to manufacture and how much to manufacture.
2413:{\displaystyle {\begin{cases}t_{p_{i}}+e\geq M_{i}\theta _{i}-M_{j}\theta _{j}>e\\t_{p_{i}}+e>M_{i}\theta _{i}-M_{j}\theta _{j}\geq t_{p_{i}}+e\\t_{p_{j}}+e\geq M_{i}\theta _{i}-M_{j}\theta _{j}>t_{p_{i}}+e\\t_{p_{i}}+t_{p_{j}}+e>M_{i}\theta _{i}-M_{j}\theta _{j}\geq t_{p_{j}}+e\end{cases}}}
2826:
Of great importance in practice is to design, plan and operate shared capacity across multiple products with changeover times and costs in an uncertain demand environment. Beyond the selection of (expected) cycle times, with some amount of slack designed in ("safety time"), one has to also consider
2478:
2843:
problem since it is not currently possible to find the optimal solution without checking nearly every possibility. What has been done follows two approaches: restricting the solution to be of a specific type (which makes it possible to find the optimal solution for the narrower problem), or
1637:
To forms pairs take the i with the i+1th, i+2th, etc. If any of these inequalities is violated, calculate +Δ and -Δ for lot size increments of 2U and in order of size of cost change make step-by-step lot size changes. Repeat this step until both inequalities are
610:
2793:{\displaystyle {\begin{cases}t_{p_{i}}+e>M_{i}\theta _{i}-M_{j}\theta _{j}>e\\t_{p_{i}}+t_{p_{j}}+e>M_{i}\theta _{i}-M_{j}\theta _{j}>t_{p_{j}}+e\\t_{p_{i}}+e=M_{i}\theta _{i}-M_{j}\theta _{j}=t_{p_{j}}+e\end{cases}}}
1749:
55:
The classic ELSP is concerned with scheduling the production of several products on a single machine in order to minimize the total costs incurred (which include setup costs and inventory holding costs).
1242:
2835:
The problem is well known in the operations research community, and a large body of academic research work has been created to improve the model and to create new variations that solve specific issues.
1311:
356:
682:
2810:, pick the next larger e in sub-step 4, if i≠1 go back to sub-step 2. If some boundary condition is satisfied go to sub-step 4. If, for any pair, no non-interfering e appears, go back to Step 5.
1633:
1565:
1149:
986:
1364:
1478:
1425:
1995:
1941:
822:
478:
110:
for the m products (for example, there might be m=3 products and customers require 7 items a day of
Product 1, 5 items a day of Product 2 and 2 items a day of Product 3). Customer
2474:
108:
281:
2974:
M A Lopez, B G Kingsman: The
Economic Lot Scheduling Problem: Theory and Practice, International Journal of Production Economics, Vol. 23, October 1991, pp. 147–164
176:
489:
203:
146:
148:. When it is desired to produce a different product, the machine is stopped and another costly setup is required to begin producing the next product. Let
2971:
S E Elmaghraby: The
Economic Lot Scheduling Problem (ELSP): Review and Extensions, Management Science, Vol. 24, No. 6, February 1978, pp. 587–598
205:
is charged based on average inventory level of each item. N is the number of runs made, U the use rate, L the lot size and T the planning period.
1645:
117:
A single machine is available which can make all the products, but not in a perfectly interchangeable way. Instead the machine needs to be
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1174:
1248:
3009:
2915:: A Computational Approach to the Economic Lot Scheduling Problem, Management Science, Vol. 4, No. 3, April 1958, pp. 264–291
2902:: A Computational Approach to the Economic Lot Scheduling Problem, Management Science, Vol. 4, No. 3, April 1958, pp. 264–291
293:
121:
to produce one product, incurring a setup cost and/or setup time, after which it will produce this product at a known rate
617:
1571:
1503:
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993:
833:
1322:
1431:
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35:
that has been studied by many researchers for more than 50 years. The term was first used in 1958 by professor
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689:
40:
363:
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2425:
62:
28:
238:
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2008:
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Tayur, S. (2000). "Improving
Operations and Quoting Accurate Lead Times in a Laminate Plant".
605:{\displaystyle {\frac {d(C_{N})}{dL}}={\frac {hT\left(P-U\right)}{2P}}-{\frac {SUT}{L^{2}}}=0}
2934:
2874:
209:
151:
32:
181:
124:
2827:
the amount of safety stock (buffer stock) that is needed to meet desired service level.
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Michael Pinedo, Planning and
Scheduling in Manufacturing and Services, Springer, 2005.
2912:
2899:
36:
3003:
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217:
114:
is met from inventory and the inventory is replenished by our production facility.
2911:
Welch, W. Evert, A Case of Simple Linear
Programming, Management Methods 1956 in
2951:
Zipkin Paul H., Foundations of
Inventory Management, Boston: McGraw Hill, 2000,
213:
178:
be the setup cost when switching from product i to product j and inventory cost
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2845:
118:
43:
model to the case where there are several products to be produced on the same
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to L in the direction which incurs the least cost increase between +Δ and -Δ
2840:
1882:). Then check if one of the following boundary conditions is satisfied:
481:
44:
1744:{\displaystyle e_{ij}=d-t_{p_{i}}\leq \theta _{i}-t_{p_{i}}-t_{p_{j}}}
111:
221:
1494:=L/P for each item and list items in order of increasing θ=L/U
1237:{\displaystyle \sum _{i=1}^{m}{\frac {U_{i}T}{P_{i}}}\leq T}
2786:
2406:
1306:{\displaystyle \sum _{i=1}^{m}{\frac {U_{i}}{P_{i}}}\leq 1}
208:
To give a very concrete example, the machine might be a
2802:
If none of the boundary conditions is satisfied then e
1151:
be the incremental cost of changing from size L to L-a
988:
be the incremental cost of changing from size L to L+a
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7.Enter items in schedule and check it's feasibility
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351:{\displaystyle {\frac {hL(P-U)}{2PU}}+{\frac {S}{L}}}
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184:
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127:
65:
16:
Problem in operations management and inventory theory
677:{\displaystyle L_{0}={\sqrt {\frac {2USP}{h(P-U)}}}}
1628:{\displaystyle \theta _{j}-t_{p_{j}}\geq t_{p_{i}}}
1560:{\displaystyle \theta _{i}-t_{p_{i}}\geq t_{p_{j}}}
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1472:
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1144:{\displaystyle -\Delta =C_{N_{L-a}}-C_{N}=UT\left}
1143:
981:{\displaystyle +\Delta =C_{N_{L+a}}-C_{N}=UT\left}
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350:
275:
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170:
140:
102:
2867:Constant fill rate for the part being produced:
2861:Infinite fill rate for the part being produced:
2844:approximate solution of the full problem using
1359:{\displaystyle \theta _{0}={\frac {L_{0}}{U}}}
1473:{\displaystyle L=U\left(\theta _{0}-1\right)}
1420:{\displaystyle L=U\left(\theta _{0}+1\right)}
8:
212:and the products could be cases of bottled
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480:the total cost for N lots. To obtain the
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1162:Total production time for an item = UT/P
2892:
1159:Total quantity of an item required = UT
1990:{\displaystyle t_{p_{i}}<t_{p_{j}}}
1936:{\displaystyle t_{p_{i}}>t_{p_{j}}}
817:{\displaystyle C_{N_{L\pm a}}=UT\left}
59:We assume a known, non-varying demand
473:{\displaystyle C_{N}=NLc_{L}=UT\left}
7:
2995:Gallego: The ELSP, Columbia U., 2004
1756:Form all possible pairs as in Step 5
2469:{\displaystyle t_{p_{i}}=t_{p_{j}}}
1497:5.For each pair of items ij check:
358:, the unit cost for a lot of size L
103:{\displaystyle d_{j},j=1,\cdots ,m}
1000:
840:
14:
1373:is not an even number, calculate:
684:as the optimum lot size. Now let:
2806:is non-interfering: if i=1 in e
276:{\displaystyle \theta =T/N=L/U}
21:economic lot scheduling problem
667:
655:
512:
499:
318:
306:
39:of Berkeley, who extended the
1:
2873:Demand is random: classical
2869:Economic production quantity
3026:
2939:10.1287/inte.30.5.1.11637
2879:Demand varies over time:
2839:The model is known as a
1369:If for a certain item, θ
2863:Economic order quantity
1759:For each pair, select θ
824:be the total cost for N
41:economic order quantity
3010:Inventory optimization
2881:Dynamic lot size model
2794:
2470:
2414:
1991:
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199:
172:
171:{\displaystyle S_{ij}}
142:
104:
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278:
200:
198:{\displaystyle h_{j}}
173:
143:
141:{\displaystyle P_{j}}
105:
29:operations management
2479:
2426:
2000:
1947:
1893:
1813:Select a value for e
1646:
1572:
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1323:
1249:
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994:
834:
690:
618:
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125:
63:
1769:Determine whether t
1167:productive capacity
2850:genetic algorithms
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27:) is a problem in
1878:; ∀k∈(1,2,...,T/θ
1839:) and calculate t
1366:as a whole number
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51:Model formulation
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2875:Newsvendor model
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828:lots of size L±a
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228:Rogers algorithm
210:bottling machine
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33:inventory theory
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2966:Further reading
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2822:Stochastic ELSP
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5:
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2989:External links
2987:
2986:
2985:
2975:
2972:
2967:
2964:
2961:
2960:
2944:
2917:
2913:Jack D. Rogers
2904:
2900:Jack D. Rogers
2891:
2890:
2888:
2885:
2884:
2883:
2877:
2871:
2865:
2857:
2854:
2832:
2831:Problem status
2829:
2823:
2820:
2816:
2815:
2814:
2813:
2812:
2811:
2807:
2803:
2800:
2787:
2782:
2779:
2772:
2768:
2763:
2759:
2754:
2750:
2744:
2740:
2736:
2731:
2727:
2721:
2717:
2713:
2710:
2707:
2700:
2696:
2691:
2687:
2686:
2683:
2680:
2673:
2669:
2664:
2660:
2655:
2651:
2645:
2641:
2637:
2632:
2628:
2622:
2618:
2614:
2611:
2608:
2601:
2597:
2592:
2588:
2581:
2577:
2572:
2568:
2567:
2564:
2561:
2556:
2552:
2546:
2542:
2538:
2533:
2529:
2523:
2519:
2515:
2512:
2509:
2502:
2498:
2493:
2489:
2488:
2486:
2461:
2457:
2452:
2448:
2441:
2437:
2432:
2420:
2407:
2402:
2399:
2392:
2388:
2383:
2379:
2374:
2370:
2364:
2360:
2356:
2351:
2347:
2341:
2337:
2333:
2330:
2327:
2320:
2316:
2311:
2307:
2300:
2296:
2291:
2287:
2286:
2283:
2280:
2273:
2269:
2264:
2260:
2255:
2251:
2245:
2241:
2237:
2232:
2228:
2222:
2218:
2214:
2211:
2208:
2201:
2197:
2192:
2188:
2187:
2184:
2181:
2174:
2170:
2165:
2161:
2156:
2152:
2146:
2142:
2138:
2133:
2129:
2123:
2119:
2115:
2112:
2109:
2102:
2098:
2093:
2089:
2088:
2085:
2082:
2077:
2073:
2067:
2063:
2059:
2054:
2050:
2044:
2040:
2036:
2033:
2030:
2023:
2019:
2014:
2010:
2009:
2007:
1982:
1978:
1973:
1969:
1962:
1958:
1953:
1928:
1924:
1919:
1915:
1908:
1904:
1899:
1884:
1883:
1879:
1875:
1874:=1,2,3,...,T/θ
1871:
1867:
1863:
1859:
1855:
1851:
1848:
1844:
1840:
1835:
1833:
1828:
1826:
1822:
1821:=0,1,2,3,...,θ
1818:
1814:
1811:
1807:
1805:
1800:
1798:
1793:
1791:
1786:
1784:
1779:
1777:
1772:
1770:
1767:
1764:
1760:
1757:
1736:
1732:
1727:
1723:
1716:
1712:
1707:
1703:
1698:
1694:
1690:
1683:
1679:
1674:
1670:
1667:
1664:
1659:
1656:
1652:
1640:
1639:
1635:
1620:
1616:
1611:
1607:
1600:
1596:
1591:
1587:
1582:
1578:
1567:
1552:
1548:
1543:
1539:
1532:
1528:
1523:
1519:
1514:
1510:
1491:
1488:
1487:
1483:
1480:
1468:
1464:
1461:
1456:
1452:
1447:
1443:
1440:
1437:
1427:
1415:
1411:
1408:
1403:
1399:
1394:
1390:
1387:
1384:
1374:
1370:
1367:
1353:
1348:
1344:
1338:
1333:
1329:
1314:
1313:
1302:
1299:
1292:
1288:
1282:
1278:
1270:
1265:
1262:
1259:
1255:
1244:
1233:
1230:
1223:
1219:
1214:
1209:
1205:
1196:
1191:
1188:
1185:
1181:
1170:
1163:
1160:
1153:
1152:
1139:
1132:
1129:
1124:
1119:
1115:
1108:
1103:
1097:
1094:
1091:
1085:
1081:
1078:
1075:
1071:
1067:
1064:
1058:
1054:
1050:
1047:
1044:
1039:
1035:
1031:
1024:
1021:
1018:
1014:
1009:
1005:
1002:
999:
989:
976:
969:
966:
961:
956:
952:
945:
940:
934:
931:
928:
922:
918:
915:
912:
908:
904:
901:
894:
890:
887:
884:
879:
875:
871:
864:
861:
858:
854:
849:
845:
842:
839:
829:
825:
812:
805:
802:
799:
795:
790:
784:
781:
778:
772:
768:
765:
762:
758:
753:
749:
746:
743:
739:
735:
728:
724:
721:
718:
711:
708:
705:
701:
696:
685:
669:
666:
663:
660:
657:
654:
649:
646:
643:
640:
633:
628:
624:
612:
601:
598:
591:
587:
582:
579:
576:
570:
564:
561:
555:
551:
548:
545:
541:
537:
534:
528:
522:
519:
514:
509:
505:
501:
498:
485:
468:
462:
459:
454:
448:
445:
442:
436:
432:
429:
426:
422:
418:
415:
408:
404:
401:
398:
393:
389:
385:
382:
379:
374:
370:
359:
345:
342:
337:
331:
328:
325:
320:
317:
314:
311:
308:
305:
302:
287:
284:
272:
268:
264:
261:
258:
254:
250:
247:
244:
229:
226:
192:
188:
165:
162:
158:
135:
131:
99:
96:
93:
90:
87:
84:
81:
78:
73:
69:
52:
49:
37:Jack D. Rogers
15:
13:
10:
9:
6:
4:
3:
2:
3022:
3011:
3008:
3007:
3005:
2996:
2993:
2992:
2988:
2984:
2983:0-387-22198-0
2980:
2976:
2973:
2970:
2969:
2965:
2958:
2957:0-256-11379-3
2954:
2948:
2945:
2940:
2936:
2932:
2928:
2921:
2918:
2914:
2908:
2905:
2901:
2896:
2893:
2886:
2882:
2878:
2876:
2872:
2870:
2866:
2864:
2860:
2859:
2855:
2853:
2851:
2847:
2842:
2837:
2830:
2828:
2821:
2819:
2801:
2780:
2777:
2770:
2766:
2761:
2757:
2752:
2748:
2742:
2738:
2734:
2729:
2725:
2719:
2715:
2711:
2708:
2705:
2698:
2694:
2689:
2681:
2678:
2671:
2667:
2662:
2658:
2653:
2649:
2643:
2639:
2635:
2630:
2626:
2620:
2616:
2612:
2609:
2606:
2599:
2595:
2590:
2586:
2579:
2575:
2570:
2562:
2559:
2554:
2550:
2544:
2540:
2536:
2531:
2527:
2521:
2517:
2513:
2510:
2507:
2500:
2496:
2491:
2484:
2459:
2455:
2450:
2446:
2439:
2435:
2430:
2421:
2400:
2397:
2390:
2386:
2381:
2377:
2372:
2368:
2362:
2358:
2354:
2349:
2345:
2339:
2335:
2331:
2328:
2325:
2318:
2314:
2309:
2305:
2298:
2294:
2289:
2281:
2278:
2271:
2267:
2262:
2258:
2253:
2249:
2243:
2239:
2235:
2230:
2226:
2220:
2216:
2212:
2209:
2206:
2199:
2195:
2190:
2182:
2179:
2172:
2168:
2163:
2159:
2154:
2150:
2144:
2140:
2136:
2131:
2127:
2121:
2117:
2113:
2110:
2107:
2100:
2096:
2091:
2083:
2080:
2075:
2071:
2065:
2061:
2057:
2052:
2048:
2042:
2038:
2034:
2031:
2028:
2021:
2017:
2012:
2005:
1980:
1976:
1971:
1967:
1960:
1956:
1951:
1926:
1922:
1917:
1913:
1906:
1902:
1897:
1888:
1887:
1886:
1885:
1849:
1812:
1768:
1758:
1755:
1754:
1753:
1752:
1751:
1734:
1730:
1725:
1721:
1714:
1710:
1705:
1701:
1696:
1692:
1688:
1681:
1677:
1672:
1668:
1665:
1662:
1657:
1654:
1650:
1636:
1618:
1614:
1609:
1605:
1598:
1594:
1589:
1585:
1580:
1576:
1568:
1550:
1546:
1541:
1537:
1530:
1526:
1521:
1517:
1512:
1508:
1500:
1499:
1498:
1495:
1481:
1466:
1462:
1459:
1454:
1450:
1445:
1441:
1438:
1435:
1428:
1413:
1409:
1406:
1401:
1397:
1392:
1388:
1385:
1382:
1375:
1368:
1351:
1346:
1342:
1336:
1331:
1327:
1319:
1318:
1317:
1300:
1297:
1290:
1286:
1280:
1276:
1268:
1263:
1260:
1257:
1253:
1245:
1231:
1228:
1221:
1217:
1212:
1207:
1203:
1194:
1189:
1186:
1183:
1179:
1171:
1169:is satisfied:
1168:
1164:
1161:
1158:
1157:
1156:
1137:
1130:
1127:
1122:
1117:
1113:
1106:
1101:
1095:
1092:
1089:
1083:
1079:
1076:
1073:
1069:
1065:
1062:
1056:
1052:
1048:
1045:
1042:
1037:
1033:
1029:
1022:
1019:
1016:
1012:
1007:
1003:
997:
990:
974:
967:
964:
959:
954:
950:
943:
938:
932:
929:
926:
920:
916:
913:
910:
906:
902:
899:
892:
888:
885:
882:
877:
873:
869:
862:
859:
856:
852:
847:
843:
837:
830:
810:
803:
800:
797:
793:
788:
782:
779:
776:
770:
766:
763:
760:
756:
751:
747:
744:
741:
737:
733:
726:
722:
719:
716:
709:
706:
703:
699:
694:
686:
664:
661:
658:
652:
647:
644:
641:
638:
631:
626:
622:
614:Which yields
613:
599:
596:
589:
585:
580:
577:
574:
568:
562:
559:
553:
549:
546:
543:
539:
535:
532:
526:
520:
517:
507:
503:
496:
486:
483:
466:
460:
457:
452:
446:
443:
440:
434:
430:
427:
424:
420:
416:
413:
406:
402:
399:
396:
391:
387:
383:
380:
377:
372:
368:
360:
343:
340:
335:
329:
326:
323:
315:
312:
309:
303:
300:
285:
270:
266:
262:
259:
256:
252:
248:
245:
242:
235:
234:
233:
227:
225:
223:
219:
215:
211:
206:
190:
186:
163:
160:
156:
133:
129:
120:
115:
113:
97:
94:
91:
88:
85:
82:
79:
76:
71:
67:
57:
50:
48:
46:
42:
38:
34:
30:
26:
22:
2947:
2930:
2926:
2920:
2907:
2895:
2838:
2834:
2825:
2817:
1866:by setting M
1641:
1496:
1489:
1482:And change L
1315:
1154:
283:= use period
231:
218:orange juice
207:
116:
58:
54:
24:
20:
18:
2933:(5): 1–15.
1850:Calculate M
1490:4.Compute t
1316:3.Compute:
1165:Check that
214:apple juice
2927:Interfaces
2887:References
2846:heuristics
1638:satisfied.
232:1.Define:
2749:θ
2735:−
2726:θ
2650:θ
2636:−
2627:θ
2551:θ
2537:−
2528:θ
2378:≥
2369:θ
2355:−
2346:θ
2250:θ
2236:−
2227:θ
2213:≥
2160:≥
2151:θ
2137:−
2128:θ
2072:θ
2058:−
2049:θ
2035:≥
1722:−
1702:−
1693:θ
1689:≤
1669:−
1606:≥
1586:−
1577:θ
1538:≥
1518:−
1509:θ
1460:−
1451:θ
1398:θ
1328:θ
1298:≤
1254:∑
1229:≤
1180:∑
1128:−
1077:−
1057:−
1030:−
1020:−
1001:Δ
998:−
939:−
914:−
870:−
841:Δ
801:±
764:−
745:±
707:±
662:−
569:−
547:−
428:−
313:−
243:θ
92:⋯
3004:Category
2856:See also
1870:=k and M
1843:+e and t
2841:NP-hard
482:optimum
45:machine
2981:
2955:
1790:< t
1776:> t
1763:< θ
119:set up
112:demand
2979:ISBN
2953:ISBN
2659:>
2613:>
2560:>
2514:>
2422:for
2332:>
2259:>
2114:>
2081:>
1968:<
1914:>
1889:for
1797:or t
222:milk
220:and
31:and
25:ELSP
19:The
2935:doi
2848:or
1943:or
1832:- t
1825:- t
1804:= t
1783:, t
1155:2.
826:L±a
3006::
2931:30
2929:.
2852:.
2808:ij
2804:ij
1858:-M
1847:+e
1845:pj
1841:pi
1819:ij
1817:(e
1815:ij
1642:6.
216:,
2941:.
2937::
2781:e
2778:+
2771:j
2767:p
2762:t
2758:=
2753:j
2743:j
2739:M
2730:i
2720:i
2716:M
2712:=
2709:e
2706:+
2699:i
2695:p
2690:t
2682:e
2679:+
2672:j
2668:p
2663:t
2654:j
2644:j
2640:M
2631:i
2621:i
2617:M
2610:e
2607:+
2600:j
2596:p
2591:t
2587:+
2580:i
2576:p
2571:t
2563:e
2555:j
2545:j
2541:M
2532:i
2522:i
2518:M
2511:e
2508:+
2501:i
2497:p
2492:t
2485:{
2460:j
2456:p
2451:t
2447:=
2440:i
2436:p
2431:t
2401:e
2398:+
2391:j
2387:p
2382:t
2373:j
2363:j
2359:M
2350:i
2340:i
2336:M
2329:e
2326:+
2319:j
2315:p
2310:t
2306:+
2299:i
2295:p
2290:t
2282:e
2279:+
2272:i
2268:p
2263:t
2254:j
2244:j
2240:M
2231:i
2221:i
2217:M
2210:e
2207:+
2200:j
2196:p
2191:t
2183:e
2180:+
2173:i
2169:p
2164:t
2155:j
2145:j
2141:M
2132:i
2122:i
2118:M
2111:e
2108:+
2101:i
2097:p
2092:t
2084:e
2076:j
2066:j
2062:M
2053:i
2043:i
2039:M
2032:e
2029:+
2022:i
2018:p
2013:t
2006:{
1981:j
1977:p
1972:t
1961:i
1957:p
1952:t
1927:j
1923:p
1918:t
1907:i
1903:p
1898:t
1880:i
1876:j
1872:j
1868:i
1864:j
1862:θ
1860:j
1856:i
1854:θ
1852:i
1836:j
1834:p
1829:i
1827:p
1823:i
1808:j
1806:p
1801:i
1799:p
1794:j
1792:p
1787:i
1785:p
1780:j
1778:p
1773:i
1771:p
1765:j
1761:i
1735:j
1731:p
1726:t
1715:i
1711:p
1706:t
1697:i
1682:i
1678:p
1673:t
1666:d
1663:=
1658:j
1655:i
1651:e
1619:i
1615:p
1610:t
1599:j
1595:p
1590:t
1581:j
1551:j
1547:p
1542:t
1531:i
1527:p
1522:t
1513:i
1492:p
1484:0
1467:)
1463:1
1455:0
1446:(
1442:U
1439:=
1436:L
1414:)
1410:1
1407:+
1402:0
1393:(
1389:U
1386:=
1383:L
1371:0
1352:U
1347:0
1343:L
1337:=
1332:0
1301:1
1291:i
1287:P
1281:i
1277:U
1269:m
1264:1
1261:=
1258:i
1232:T
1222:i
1218:P
1213:T
1208:i
1204:U
1195:m
1190:1
1187:=
1184:i
1138:]
1131:L
1123:a
1118:2
1114:L
1107:S
1102:+
1096:U
1093:P
1090:2
1084:)
1080:U
1074:P
1070:(
1066:a
1063:h
1053:[
1049:T
1046:U
1043:=
1038:N
1034:C
1023:a
1017:L
1013:N
1008:C
1004:=
975:]
968:L
965:+
960:a
955:2
951:L
944:S
933:U
930:P
927:2
921:)
917:U
911:P
907:(
903:a
900:h
893:[
889:T
886:U
883:=
878:N
874:C
863:a
860:+
857:L
853:N
848:C
844:=
838:+
811:]
804:a
798:L
794:S
789:+
783:U
780:P
777:2
771:)
767:U
761:P
757:(
752:)
748:a
742:L
738:(
734:h
727:[
723:T
720:U
717:=
710:a
704:L
700:N
695:C
668:)
665:U
659:P
656:(
653:h
648:P
645:S
642:U
639:2
632:=
627:0
623:L
600:0
597:=
590:2
586:L
581:T
578:U
575:S
563:P
560:2
554:)
550:U
544:P
540:(
536:T
533:h
527:=
521:L
518:d
513:)
508:N
504:C
500:(
497:d
484::
467:]
461:L
458:S
453:+
447:U
444:P
441:2
435:)
431:U
425:P
421:(
417:L
414:h
407:[
403:T
400:U
397:=
392:L
388:c
384:L
381:N
378:=
373:N
369:C
344:L
341:S
336:+
330:U
327:P
324:2
319:)
316:U
310:P
307:(
304:L
301:h
290:=
288:L
286:c
271:U
267:/
263:L
260:=
257:N
253:/
249:T
246:=
191:j
187:h
164:j
161:i
157:S
134:j
130:P
98:m
95:,
89:,
86:1
83:=
80:j
77:,
72:j
68:d
23:(
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