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Each day you own 0 or 1 stocks of certain commodity. The price of the stock is a stochastic process that can be modeled as a Markov chain with transition rates as follows
day n+1
100
200
day n
0.5
0.25
0.75
At the start of a day at which you own a stock you may choose to either sell at the current price, or keep the stock. At the start of a day at which you do not own stock, you may choose to either buy one stock at the current price or do nothing. You have initial capital of 200.
Your target is to maximize the discounted value of the profit over an infinite horizon, use discountfactor 0.8 (per day).
a) Define the states and give for each state the possible decisions.b) Formulate the optimality equations.c) Carry out two iterations of value iteration.d) Formulate the L.P.-model to solve this problem. Describe how you can obtain the optimal policy from the LP formulation.e) Choose a stationary policy and investigate using the policy iteration algorithm whether or not that policy is optimal.f) Give the number of stationary policies. Motivate your answer by using the definition of stationary policy.
Problems based on LPP when feasible region is a line segment or it does not exist. 1. Maximize z = 2x+3y subject to the constraints X + y ≤ 1 X + y ≥ 3 X, y ≥ 0
solve the LPP using simple method, maximize z= 3x1+2x2 subject to constraints
A Paper mill produces two grades of paper viz. X and Y. Because of raw material restrictions, it cannot produce more than 400 tons of grade X paper and 300 tons of grade Y paper in
Select five Operations Research techniques and describe in detail the real world application of such techniques in business decision making.
Question A The basic characteristic feature of Operations Research is that it employs mathematical representations or models to analyse problems. Explain the methodology of Operat
A paper mill produces two grades of paper viz., X and Y. Because of raw material restrictions, it cannot produce more than 400 tons of grade X paper and 300 tons of grade Y paper i
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maximize z=3x1+2*2 subject to the constraints x1+x2=4 x1-x2=2 x1.x2=0
This assessment aims to provide students with the opportunity to hone their analytical and decision- making skills. It also aims to help students develop their ability to think cre
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