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Case Study: The DVD Supply Chain Problem

Submitted: 31 Mar 2008

Operations Research Topics: NonlinearProgramming

Application Areas: Logistics

Contents

• Problem Description
• Problem Formulation
• Computational Model
• Results
• Conclusions

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 players using this manufacturing process costs dollars.

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

The storage of players costs DVDs-4-U .

DVDs-4-U estimate it costs customers

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

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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 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.

 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.

 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.

 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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