Tutorial_10

Tutorial_10 - IELM 202 Tutorial 10 1 Equipment Replacement...

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IELM 202 Tutorial 10 1/6/2011 1. Equipment Replacement Problem : N time periods (we must own a machine during each of the N time periods) y = age of machine at the start of year 1 c ( x ) = annual cost of operating a machine which is of age x at the start of the year p = price of a new machine t ( x ) = trade-in value of machine which is of age x at the start of the year s ( x ) = salvage value of machine which has just turned age x at the start of year N We need to decide when to replace the machine DP Formulation: (1) Define ) , ( x t f = the minimum cost of owning a machine from year t through year N , starting year t with a machine just turned age x (for N t , , 1 = ; 1 , , 1 - = t x and 1 - + t y ). (2) Recurrence relation: + + + + + + - = ) 1 , 1 ( ) ( : keep ) 1 , 1 ( ) 0 ( ) ( : replace min ) , ( x t f x c t f c x t p x t f (3) Optimal policy function: ) , ( x t P = R (replace) if line 1 on the right of the above recurrence relation yields the minimum;
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Tutorial_10 - IELM 202 Tutorial 10 1 Equipment Replacement...

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