# hw3 - x> 0 and time t< N consider the diﬀerence...

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EE 292E Analysis and Control of Markov Chains Spring 2008 Prof. Ben Van Roy April 17, 2008 Homework Assignment 3: Due April 24 Dynamic Pricing Consider the dynamic pricing model discussed in class. Suppose that there are 1000 time periods and we start with 20 units of inventory. In each period, a customer arrives with probability 0 . 1. Each customer’s expected reservation price is \$400. Compute and plot the optimal price and optimal future revenue as a function of remaining time and inventory (use the ”mesh” command in Matlab to plot a function of two variables). For a positive inventory level
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Unformatted text preview: x > 0 and time t < N , consider the diﬀerence between the optimal price and what it would be if we had x + 1 units of inventory on hand. Call this the sensitivity of price to inventory. What is the maximal sensitivity, and at what x > 0 and t < N does this occur? Correlated Demands Do problem 4.7 from the textbook. Capacity Expansion Do problem 4.11 from the textbook. Item Decomposition Explain why an optimal item-based strategy as discussed in class results in an order-up-to strategy for each echelon of the system....
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