Lecture10

2z 105105 p 273 time periods markov decision

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Unformatted text preview: +0.5(1+0.5~,*) p,* = 2.73 (time periods) Markov Decision Model Markov Reward Model Mail Order Company Given: l Markov Process with a known stationary dlstrlbution (Steady State Vector) l Set of values reflecting the net effect of each outcome (Reward Vector) The long run expected value for the system can be estimated A mail order company is studying the reliability of its order entry computer l Using a series of 10 minute samplings of the current system, it was found that the computer behaves as follows: . If the computer was observed in the UP condition, 5% of the time it was DOWN at the next observation l If it was DOWN, it had been brought back UP by the next sampling 90% of the time l EM-602 / QM-710 (NJ) Lecture IO Page 10-4 Example (cont’d) Example (cont’d) Mail Order Company Mail Order Company A proposed expansion of the computer maintenance department will improve the situation so that: if in the UP condition, it will be DOWN at the next observation 4% of the time if it is DOWN, it can be brought back UP by the next sampling 95% of the time Evaluate the current and proposed systems Current System l UP DOWN 0.95 0.05 UP 0.10 I DOWNI 0.90 l l For which we can compute the Steady - State Vector x = [0.947 0.053] Example (cont’d) Example (cont’d) Mail Order Company Mail Order Company *Proposed System Determine whether the company should implement the proposal if: The net revenue when operatify is $4000 I day The net loss when down is $5000 I day The net cost of implementing the maintenance plan is $300 per day UP DOWN l l l For which we can compute the new Stead! -State Vecctor ?l = [0.95% o.O.Ku] Example (cont’d) Example Mail Order Company Barber Shop Problem Calculate the expected monetary value (EMV) of each state under each plan Current System EMV = + 4000 (0.947) - 5000 (0.053) = 53523 Proposed System EMV = +4000 (0.9596) - 5000 (0.0404) 300 = $3336 l l l l l l l A barber shop has one barber chair and 3 chairs for waiting A haircut always takes 15 minutes Customers arrive according to some (known) empirical distribution if a customer arrives and there is a place to sit, they wait and get a haircut if a customer arrives and the shop iS full, they immediately leave EM-602 / QM-710 (NJ) Lecture 10 Page 10-5 ,. Example (cont’d) Example (cont’d)...
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This document was uploaded on 03/31/2014 for the course MS 602 at NJIT.

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