# Case Study: The DVD Supply Chain Problem

## 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 for players. The storage of players costs DVDs-4-U . DVDs-4-U estimate it costs customers dollars in petrol to visit their nearest DVDs-4-U 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. ## 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?