n Problem 4. Let Dn denote the demand for Canon Rebel cameras at Lenox Photo on day
Fantastic news! We've Found the answer you've been seeking!
Question:
n
Transcribed Image Text:
Problem 4. Let Dn denote the demand for Canon Rebel cameras at Lenox Photo on day n. Suppose that D1, D2,... are independent and identically dis- tributed with P(D₁ = 0) = 0.3, P(D₁ = 1) = 0.3, P(D₁ = 2) = 0.4, and P(D₁ = m) = 0 when m > 2. Suppose that Lenox Photo uses an (s,S) inventory policy with s = 1 and S = 3 (i.e., when inventory is lower than 1, order up to 3). Orders must be placed at the end of each business day; they are filled before the store opens the next morning. If Lenox Photo does not have a Canon Rebel camera in stock when a customer arrives to purchase such a camera, then the customer will go to a different store and purchase the camera, and so the sale is lost. The cost of lost profit and loss of customer satisfaction associated with losing a customer is $40. Placing an order for m cameras costs $50+10 x m ($50 is a fixed cost regardless of the size of the order, and $10 is the cost per ordered camera). Finally, the cost of storing Canon Rebel cameras is $5 per day per camera. (a) Model this situation as a Markov chain. (b) Determine the steady-state probabilities. (c) Determine the long-run average cost per unit time. Problem 4. Let Dn denote the demand for Canon Rebel cameras at Lenox Photo on day n. Suppose that D1, D2,... are independent and identically dis- tributed with P(D₁ = 0) = 0.3, P(D₁ = 1) = 0.3, P(D₁ = 2) = 0.4, and P(D₁ = m) = 0 when m > 2. Suppose that Lenox Photo uses an (s,S) inventory policy with s = 1 and S = 3 (i.e., when inventory is lower than 1, order up to 3). Orders must be placed at the end of each business day; they are filled before the store opens the next morning. If Lenox Photo does not have a Canon Rebel camera in stock when a customer arrives to purchase such a camera, then the customer will go to a different store and purchase the camera, and so the sale is lost. The cost of lost profit and loss of customer satisfaction associated with losing a customer is $40. Placing an order for m cameras costs $50+10 x m ($50 is a fixed cost regardless of the size of the order, and $10 is the cost per ordered camera). Finally, the cost of storing Canon Rebel cameras is $5 per day per camera. (a) Model this situation as a Markov chain. (b) Determine the steady-state probabilities. (c) Determine the long-run average cost per unit time.
Expert Answer:
Answer rating: 100% (QA)
a To model this situation as a Markov chain we need to define the states transition probabilities and the corresponding cost associated with each stat... View the full answer
Related Book For
Thomas Calculus Early Transcendentals
ISBN: 9780321884077
13th Edition
Authors: Joel R Hass, Christopher E Heil, Maurice D Weir
Posted Date:
Students also viewed these mathematics questions
-
The following additional information is available for the Dr. Ivan and Irene Incisor family from Chapters 1-5. Ivan's grandfather died and left a portfolio of municipal bonds. In 2012, they pay Ivan...
-
Managing Scope Changes Case Study Scope changes on a project can occur regardless of how well the project is planned or executed. Scope changes can be the result of something that was omitted during...
-
The Crazy Eddie fraud may appear smaller and gentler than the massive billion-dollar frauds exposed in recent times, such as Bernie Madoffs Ponzi scheme, frauds in the subprime mortgage market, the...
-
Write a program that takes three double command-line arguments x, y, and z, reads from standard input a sequence of point coordinates (xi, yi, zi), and prints the coordinates of the point closest to...
-
A millipede sits 1.0 m in front of the nearest part of the surface of a shiny sphere of diameter 0.70 m. (a) How far from the surface does the millipede's image appear? (b) If the millipede's height...
-
What is a low-code development platform? What are its advantages and disadvantages?
-
When parties must arbitrate their disputes?
-
Your roommate, Matt Mikan, contends that accounting contributes to most of the steps in managements decision- making process. Is your roommate correct? Explain.
-
In the context of geotechnical engineering, discuss the application of advanced numerical methods such as finite element analysis in simulating the behavior of soil-structure interaction for complex...
-
During the boom years of 2010-2014, ace mutual fund manager Diana Sauros produced the following percentage rates of return. Rates of return on the market are given for comparison. Calculate the...
-
Why is it important for policymakers to consider both the direct and indirect effects of public policies?
-
Discuss some of the ways you can conserve electrical energy. Include in your discussion the possible changes that you can bring about in the use of electricity at home.
-
1. Suppose you are analyzing Firm X, which currently has total assets of $650M, 35% of which is debt. The company resides in an industry with an average levered beta of 1.8 and an industry average...
-
Sportsman Shoes has been a leader in the shoe industry for more than 30 years. Sportsman manufactures and sells athletic shoes for all types of sports. The company has pursued a low-cost strategy to...
-
Video Example Find f'(x) if f(x) = Solution Since In (18x1). f(x): = [In(8x) In(-8x) it follows that f'(x) = if x > 0 if x < 0 1 (8x) if x > 0 = dx d -(-8x) = = if x < 0 dx Thus, f'(x) = for all x 0.
-
Jane is on her 3rd placement. She must answer the engagement of the skate holders in the service/ 1.Engaging educators a) How do educators contribute to the QIP on a regular, ongoing basis? b)How are...
-
Which three of the following scenarios represent a deviation from a project plan? a. A production facility goes out of business b. A project team hits a major milestone on schedule c. A company...
-
What is removed during each of the three stages of wastewater treatment: primary, secondary, and tertiary? During which state would you expect items to be recovered that were accidentally flushed,...
-
Determine from its graph if the function is one-toone. f(x) = 3-x, x <0 (3, x 0
-
Graph each function (x) over the given interval. Partition the interval into four subintervals of equal length. Then add to your sketch the rectangles associated with the Riemann sum 4 k =1 (c k ) x...
-
Let D be the region bounded by the paraboloids z = 8 - x 2 - y 2 and z = x 2 + y 2 . Write six different triple iterated integrals for the volume of D. Evaluate one of the integrals.
-
What is thermodynamics?
-
Explain the scope and limitations of thermodynamics.
-
An astronaut weighs \(800 \mathrm{~N}\) on the earth's surface where the acceleration of gravity is \(g=9.83 \mathrm{~m} / \mathrm{s}^{2}\). The mass and the radius of the moon are \(7.4 \times...
Study smarter with the SolutionInn App