Case Study: The DVD Supply Chain Problem

Submitted: 31 Mar 2008

Operations Research Topics: NonlinearProgramming

Application Areas: Logistics

Contents

Problem Description

This problem has been adapted from Supply Chain Network Economics: Dynamics of Prices, Flows and Profits by Anna Nagurney (2006)

DVD players are produced in Asia and bought by DVDs-4-U for sale throughout New Zealand.

The cost of producing DVD players comes from the setup cost and the production cost. To set up the manufacturing process costs $5 per player being produced. To produce $q$ players using this manufacturing process costs $q^2$ dollars.

The cost of performing DVDs-4-U's quality assurance test and then shipping the players to New Zealand is given by

\[q^2 + 2 q \]
for $q$ players.

The storage of $q$ players costs DVDs-4-U $2 q^2$.

DVDs-4-U estimate it costs customers

\[ (1 + q) q \]
dollars in petrol to visit their nearest DVDs-4-U retail store and buy $q$ DVD players. This gives a unit transaction cost of $1 + q$ dollars per player.

Their market research shows that the demand curve for the DVD players is given by

\[ d(\rho) = 100 - \rho \]
where $\rho$ is the effective price per player for the customers, i.e., retail price + unit transaction cost.

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Student Tasks

  1. The manufacturers in Asia are requesting $45 for each DVD player they send to DVDs-4-U. Given this price, solve the Manufacturer's Problem to find the amount of DVD players they want to ship to DVDs-4-U. Write a management summary of your solution.

    What to hand in Your AMPL files for solving the Manufacturer's Problem. Your management summary.

  2. Given the $45 cost for importing the DVD players from Task 1, DVDs-4-U have decided to sell them for $85. Given these prices, solve the Retailer's Problem to find the amount of DVD players they want to receive from Asia and sell in New Zealand. Write a management summary of your solution.

    What to hand in Your AMPL files for solving the Retailer's Problem Your management summary.

  3. Since DVDs-4-U have decided to sell the DVD players for $85, they have estimated the effective price for consumers in New Zealand to be $88. Given this price, solve the Consumer's Problem to find the amount of DVD players that are purchased in New Zealand. Write a management summary of your solution.

    What to hand in Your AMPL files for solving the Consumer's Problem. Your management summary.

  4. Given your solutions to Tasks 1, 2 and 3, what do you conclude about the prices in this supply chain?

    Variational inequalities suggest prices of $43.80 for sending a DVD player from Asia to DVDs-4-U, $80.60 for each player sold in New Zealand and an effective price of $90.80. How do these prices "fit" in this supply chain?

    What to hand in Your answers to the two questions along with reasons for these answers.

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Topic revision: r8 - 2018-11-23 - TWikiAdminUser
 
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