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Breadco Bakeries is a new bakery chain that sells bread to customers throughout the state of Indiana. Breadco is considering building bakeries in three locations: Evansville, Indianapolis, and South Bend. Each bakery can bake as many as 900,000 loaves of bread each year. The cost of building a bakery at each site is $5 million in Evansville, $4 million in Indianapolis, and $4.5 million in South Bend. To simplify the problem, we assume that Breadco has only three customers, whose demands each year are 700,000 loaves (customer 1); 400,000 loaves (customer 2); and 300,000 loaves (customer 3). The total cost of baking and shipping a loaf of bread to a customer is given in Table 1.

Breadco Bakeries is a new bakery chain that sells bread to customers throughout the state of Indiana. Breadco is considering building bakeries in three locations: Evansville, Indianapolis, and South Bend. Each bakery can bake as many as 900,000 loaves of bread each year. The cost of building a bakery at each site is $5 million in Evansville, $4 million in Indianapolis, and $4.5 million in South Bend. To simplify the problem, we assume that Breadco has only three customers, whose demands each year are 700,000 loaves (customer 1); 400,000 loaves (customer 2); and 300,000 loaves (customer 3). The total cost of baking and shipping a loaf of bread to a customer is given in Table 1.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Formulate an optimization model
Breadco Bakeries is a new bakery chain that sells bread to customers throughout the state of Indiana. Breadco is considering building bakeries in three locations: Evansville, Indianapolis, and South Bend. Each bakery can bake as many as 900,000 loaves of bread each year. The cost of building a bakery at each site is $5 million in Evansville, $4 million in Indianapolis, and $4.5 million in South Bend. To simplify the problem, we assume that Breadco has only three customers, whose demands each year are 700,000 loaves (customer 1); 400,000 loaves (customer 2); and 300,000 loaves (customer 3). The total cost of baking and shipping a loaf of bread to a customer is given in Table 1. From To Evansville Indianapolis South Bend Customer 1 Customer 2 16¢ 40¢ 45¢ 34¢ 30¢ 45¢ Customer 3 26¢ 35¢ 23¢ Table 1: Production & shipping costs Assume that future shipping and production costs are discounted at a rate of 11%per year. Assume that once built, a bakery lasts forever. 1. Formulate an integer optimization model to minimize Breadco's total cost of meeting demand (present and future). (Hint: You will need the fact that for x < 1, a + ax + ax² + ax³ + ... = a/(1-x).) 2. Obtain an optimal solution to the problem using AMPL. 3. How would you modify the formulation if either Evansville or South Bend must produce at least 800,000 loaves per year?
Transcribed Image Text:Breadco Bakeries is a new bakery chain that sells bread to customers throughout the state of Indiana. Breadco is considering building bakeries in three locations: Evansville, Indianapolis, and South Bend. Each bakery can bake as many as 900,000 loaves of bread each year. The cost of building a bakery at each site is $5 million in Evansville, $4 million in Indianapolis, and $4.5 million in South Bend. To simplify the problem, we assume that Breadco has only three customers, whose demands each year are 700,000 loaves (customer 1); 400,000 loaves (customer 2); and 300,000 loaves (customer 3). The total cost of baking and shipping a loaf of bread to a customer is given in Table 1. From To Evansville Indianapolis South Bend Customer 1 Customer 2 16¢ 40¢ 45¢ 34¢ 30¢ 45¢ Customer 3 26¢ 35¢ 23¢ Table 1: Production & shipping costs Assume that future shipping and production costs are discounted at a rate of 11%per year. Assume that once built, a bakery lasts forever. 1. Formulate an integer optimization model to minimize Breadco's total cost of meeting demand (present and future). (Hint: You will need the fact that for x < 1, a + ax + ax² + ax³ + ... = a/(1-x).) 2. Obtain an optimal solution to the problem using AMPL. 3. How would you modify the formulation if either Evansville or South Bend must produce at least 800,000 loaves per year?
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