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Case Study: The DVD Supply Chain Problem
Submitted: 31 Mar 2008
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 DVDs4U 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 players using this manufacturing process costs dollars.
The cost of performing DVDs4U's quality assurance test and then shipping the players to New Zealand is given by
for players.
The storage of players costs DVDs4U .
DVDs4U estimate it costs customers
dollars in petrol to visit their nearest DVDs4U retail store and buy DVD players. This gives a unit transaction cost of dollars per player.
Their market research shows that the demand curve for the DVD players is given by
where is the effective price per player for the customers, i.e., retail price + unit transaction cost.
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Problem Formulation
The formulation...
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Computational Model
The computational model...
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Results
The results...
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Conclusions
In conclusion...
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 The manufacturers in Asia are requesting $45 for each DVD player they send to DVDs4U. Given this price, solve the Manufacturer's Problem to find the amount of DVD players they want to ship to DVDs4U. Write a management summary of your solution.
What to hand in Your AMPL files for solving the Manufacturer's Problem. Your management summary.
 Given the $45 cost for importing the DVD players from Task 1, DVDs4U 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.
 Since DVDs4U 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.
 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 DVDs4U, $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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*FORM FIELD ProblemDescription*ProblemDescription*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 DVDs4U 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 players using this manufacturing process costs dollars.
The cost of performing DVDs4U's quality assurance test and then shipping the players to New Zealand is given by
for players.
The storage of players costs DVDs4U .
DVDs4U estimate it costs customers
dollars in petrol to visit their nearest DVDs4U retail store and buy DVD players. This gives a unit transaction cost of dollars per player.
Their market research shows that the demand curve for the DVD players is given by
where is the effective price per player for the customers, i.e., retail price + unit transaction cost.

*FORM FIELD StudentTasks*StudentTasks
 The manufacturers in Asia are requesting $45 for each DVD player they send to DVDs4U. Given this price, solve the Manufacturer's Problem to find the amount of DVD players they want to ship to DVDs4U. Write a management summary of your solution.
What to hand in Your AMPL files for solving the Manufacturer's Problem. Your management summary.
 Given the $45 cost for importing the DVD players from Task 1, DVDs4U 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.
 Since DVDs4U 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.
 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 DVDs4U, $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.
 