Lecture 10 and 11
Lecture 10 and 11 CEE 270
Popular in System Analysis and Economic Civil Engineering
Popular in Civil and Environmental Engineering
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This 7 page Class Notes was uploaded by Nathaniel Bautz on Friday February 27, 2015. The Class Notes belongs to CEE 270 at University of Massachusetts taught by Bernd Schliemann in Spring2015. Since its upload, it has received 46 views. For similar materials see System Analysis and Economic Civil Engineering in Civil and Environmental Engineering at University of Massachusetts.
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Date Created: 02/27/15
LECTURE 10 COST ANALYSES 393 The LP Formulation Max 140x1160x2 ST 2x1 4x2 5x1 5x2 X1 5 2 clay i HYIT vat 5 FILIT 5 x25 393 Sensitivity Concepts gt Optimal solutions to LP problems have been examined under deterministic assumptions gt Conditions in most real world situations are dynamic and changing gt After an optimal solution to problem is found input data values are varied to assess optimal solution sensitivity gt This process is also referred to as sensitivity analysis or postoptimality analysis Managerial Questions gt Should the company increase the volume of red clay at a cost of 8m3 gt How about having workers to work overtime to increase the available hours at a cost of 30hour gt How about increasing the capacity of either vat at a cost of 5ton Other Optimization Topics gt Nonlinear programming gt Integer vs continuous decision variable gt Solutions I Unique optimal I Multiple optimal I No feasible I Unbounded feasible regions no optimal solution gt Duality no optimal solution gt Knapsack Problem Other Optimization Techniques gt Enumeration gt Exterior point techniques gt Interior point techniques gt Branchandbound search gt Tabu gt Simulation gt Heuristic 393 Important Cost Concepts gt Cost classifications gt Supply vs demand gt Community Costs I Air pollution I Climate Change I Noise I Social I Negative Community Costs gt System costs owner user community gt Factors affecting project costs 393 Economic Analysis Useful at Each Phase E e Phage Needs neareasrnent Deciding the pati rnat senedute iir eanaeity quot enpane nna 3yei em i Manning Euailuatinn at Alternat39sre entalitiinn er Recyclingfreuse Strategies baaia nit I39ITIIEIWE t W nets and rrrnnetary hene tV System Freeeree i39ien Eealluatnn nt lternatitre u A 139 Henabilitin and Maintennee E39trtaizegiee er Trtrneniiza an basin at rnrnnetary mats and l Evaluatinn at Alternative Planet W Lnti nne an l Pnieijes an herein at rnenetary eats an WEHEtEW benefits rnanetaryr benefite Eye ten inanetien nenitering Evaliuatien nrf Alternative lnepeetin Falieiea and Methnde 11 an b35115 mt m t w WEE and f E ealnatinn at Alternative Ei gne nel rnnnetaryr bene ia Hateriials an basis at rnenetary meta I and nnnnetar39jr benefits Eyei ern Elnerreiiena Er m N a Cenai ruetien Evaluatinn t Alternative petinnal F liEiE E f E t m Evaluatien ef Attematitre Enntrting Iiiltppnreelteei an Basis Elf m netanr mm and manemm innatruicti nnj Techniquea en ans nf nnunetary h hEHf l HEB an rnnnetaryr benefits 393 First Cost gt The cost or total amount of investment required for getting an activity started I Occurs only once for any given activity I Typically used for capital land buildings tools equipment not operating expenses 393 Fixed Costs gt Costs that remain constant I Don t vary With level of production O 90 O 90 gt Examples I Depreciation maintenance taxes insurance lease rentals interest sales programs administrative expenses research heat light janitorial services gt Fixed costs are only relatively fixed Variable Costs gt Costs that vary with activity level I E g with number of units produced I Typically only direct costs I May or may not remain constant per unit of product I Examples 0 Materials costs direct labor direct electrical power Opportunity Costs gt The cost of forgoing the chance to earn interest or profit on investment funds gt The opportunity cost of an input is the value of that item if it were employed in its most valuable alternative use The opportunity cost of a good is the sum of the opportunity costs of the inputs used to make that good Sunk Costs gt Sunk cost is any cost that occurred in the past I Cannot be changed by a future decision or action gt Sunk costs are irrelevant for making decisions I Sunk costs should be ignored in your choise I Decisions should be made on the basis of differnces between choices I Identical factors can be canceled out gt How should you consider sunk costs I To learn what went wrong I So you can avoid that in the future decisions Interest gt What does the bank pay you when it uses your money for a period of time gt What does the bank charge you if you want to use its money gt Interest rate vs Interest Simple Interest gt I P n i where I P principal amount lent or borrowed I N number of interest periods e g years I I interest rate per interest period gt Example 10 interest on 1000 for 3 years I Total interest paid I 1000301 300 Compound Interest gt Interest charged for any period is based on the remaining principal amount plus any accumulated interest charges up to the beginning of that period O 9 rm aunt awed at and of Amuunt Interest awed at Amount fr heginn nl er of period 1 1 11 1121 2 1 1 111 1 1 3 1211 121 gt P 1000 gt How much do you have after 1 year given rate i I 1000 1000i 10001i gt After 2 years I 10001i 10001ii 10001i2 gt After 11 years I P1in general compound interest formula Notation gt i interest rate per time period gt n of time periods years months days seconds gt P money at present gt F money in future I After 11 time periods I Equivalent to P now at interest rate i gt A payment at end of each time period I E g annual Assumptions perid 1111 1111 1331 gt Assume all cash ow occurs at the end of each time period I For example all year 1 payments are due on December 31 of year 1 gt The present is the end of time period 0 gt NOTE unless otherwise states we will assume no in ation Converting from Present to Future gt To find F given P Inflowfreaceipt 39Iflbl l W FEM someone Else witllhtj rawal F Enmtpnund forward in time quot u u lowf pawm El lll loan TD among El 5a tiinvestime t 393 Derive by Recursion gt Invest an amount P at rate i I Amount at time 1 P1i I Amount at time 2 P1i2 I Amount at time n P1in gt So we know that F P1in Exponential growth I FP i n 1ir1 I Single payment compound amount factor 0 Fn P1ir1 0 Fn PFP i n 393 Example Present to Future gt Invest P 1000 n3 i10 gt What is the future value F 139 F I If you in wear P what WW you i ll 1 3 ha we in n years F v 39 I 39 tl lyear IF I3 Falng 13 i I Illa 39I i L33 W F It 33 ll LECTURE 11 INFLATION INTEREST RATES amp MARR 79 systems Analysis amp Economics Chapter 11 ineiass problems 2J26f2 15 maintmance and aperation M310 cost 0f frounteend Elaaders wnrking under harsh environmental conditions tends to increase by a constant 512130 per quotyear for the first 5 quotQ cuff operatmm Fur a leader that has a rst cost uf 39000 and rstyear MELO cost 5mm mmpar e the equ ivae lwent annual worth af a loader kept for 4 years with me 5 years at an interest rate of 096 per manth compounded quarter y The mime if as used Inacier is 23000 after 4 years and 13000 after 5 years Th 11 WhigMar 39 GJWI memM Tamra1 RIMe I M M Cnmgaum i Funpig Pgr gear x LWI Enun t mm 39 rni Mr Hm Freami uabe 1quot EomPMIEDM bumSe 39i he x 111V Wm b 3 F Qsam a 5 quot 7 quot39 g trtn v 11 3 635 2 PW 39withglsn ati n The loader will have a cost UfS 39l future cost six years from now Find the PW ofthe machine if the real interest rate is 10 per year and the in atinn rate is 5 per year using a conzsltantvaliue du ilars and in future dal lars 1 AF r H r mug t NAHUM E 55 spae w KWr J 133 A max 11
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