forest resources and sustainable management（下）

《forest resources and sustainable management（下）》由会员上传分享，免费在线阅读，更多相关内容在工程资料-天天文库。

1、Chapter5Forestinventoryandplanningunits.Theaimistofindareasfordifferentschedulestomaximizetheobjectivevariablewhilemeetingtheconstraints.Constantcjindicateshowmuchoneareaunit(hectare)managedaccordingtoschedulejproducestheobjectivevariable.Constantaijgivesthequantityofconstraintiproducedorconsumedbyo

2、neareaunitunderschedulej.Besidesthe"lessthanorequal"constraints,theproblemformulationmaycontain"equal"or"greaterthanorequal"constraints.TheLPmodelassumesthatthetotalsoftheobjectiveandconstrainingvariablesresultfromaddingtherespectivevariablesoftheactivitiesincludedinthesolution.Anotherassumptionisth

3、attheobjectiveandconstrainingvariablesarelinearfunctionsofthedecisionvariables.ThefollowingexamplehelpstounderstandhowtouseLPinproductionplanning.Aprivatelandownerhas20hasuitablefortreeseedlingproduction.Growingpineseedlingsandgrowingspruceseedlingsaretheonlyrelevantactivities.Productionofspruceseed

4、lingsrequires60mandaysoflaborperhectareannually,andpineproductionrequires30mandays.Thetotalnumberofmandaysavailableis900peryear.Thelandownerwantsmaximumnetincome.ThenetannualincomeisFIM20000ha-1inpineseedlingproductionandFIM30000ha-1inspruceseedlingproduction.Theactivitiesanddecisionvariablesarethea

5、reasinhectaresallocatedtotheproductionofpineseedlings(x1)andspruceseedlings(x2).Thetaskistofindtheoptimumvaluesforx1andx2.Theobjectivefunctionexpressesthedependenceofnetincomeonx1andx2bymaximizing20000x1+30000x2=z(19)Thefirstconstraintstatesthatthetotalareainseedlingproductionmustnotexceed20hectares

6、asfollows:x1+x2·20(20)Thesecondconstraintrestrictsthelaborconsumptiontoamaximumof900mandaysperyearasfollows:30x1+60x2·900(21)TheLPproblemisthentomaximize20000x1+30000x2=z(22)subjecttox1+x2·20(23)30x1+60x2·900(24)x1;x2¸0(25)Solvingthisproblemwiththesimplexmethodgivesx1=10haandx2=10ha.Thismeansusingth

7、eentireareaforseedlingproductionwithequalareasallocatedforpineandspruce.5.2.4.3GoalprogrammingTheproblemwithlinearprogrammingisthatitallowsonlyoneobjectivevariable.Theforestowneroftenhasseveralsimulta