Linear Prog COP4355_Part_38

Linear Prog COP4355_Part_38 - Chapter 14 Dynamic...

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156 Chapter 14 Dynamic Programming 14.7 (continued) STAGE 3 1st Month ____________________________________________________________ Units Available Units Total Revenue to Sell (X 1 ) Sold (S 1 ) TR 1 * X 2 * TR 2-3 * TR 1-3 * ___________________________________________________________ 8 0 0 8 723 723 1 99 7 641 740 2 196 6 556 752 3 291 5 470 761 4 384 4 380 764 * 5 475 3 289 764 * 6 564 2 195 759 7 651 1 98 749 8 736 0 0 736 ___________________________________________________________ Solution: Month(i) X i S i X i+1 TR i ___________________________________________ 1 8 4 4 $384 2 4 2 2 192 3 2 2 0 188 ___ Total Profit: $764 ___________________________________________ or Month (i) X i S i X i+1 TR i _____________________________________________ 1 8 5 3 $475 2 3 2 1 192 3 1 1 0 97 ___ Total Profit: $764 _____________________________________________
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157 14.8 X i+1 = X i - S i NI i = TR i - HC i Total net income NI i * = MAX {NI i + NI i-1 *} STAGE 1 March __________________________________________________________ Units Available Units to Sale (X 3 ) Sold (S 3 ) S 3 X 4 * NI 3 * _________________________________________________________ 1 1 1 0 44 * 2 2 2 0 86 3 3 3 0 126 __________________________________________________________ *Because all tractors are on hand at the beginning of Jan, the number of tractors entering this stage X 3 will incur holding costs of $5 ($3 for Feb-Mar plus $2 for Jan-Feb). S 1 S 2 S 3 Jan. Feb. Mar. X 2 X 3 X 4 = 0 X 1 = 5 HC = $2 HC = $3
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158 Chapter 14 Dynamic Programming 14.8 (continued) STAGE 2 February ____________________________________________________________ Units Available Units Total Income to Sale (X 2 ) Sold (S 2 ) NI 2 * X 3 * NI 3 * NI 2-3 * ____________________________________________________________ 2 1 25 1 44 69 * ------------------------------------------------------ 3 1 23 2 86 109 * 2 50 1 44 94 ------------------------------------------------------ 4 1 21 3 126 147 * 2 48 2 86 134 3 73 1 44 117 ____________________________________________________________
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Linear Prog COP4355_Part_38 - Chapter 14 Dynamic...

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