Jones Bakery sells bread throughout the New England region. Jones is considering

Question

Jones Bakery sells bread throughout the New England region. Jones is considering building bakeries in 3 locations. Each bakery can bake up to 900,000 loaves per year. The cost of building each bakery and the total cost of baking and shipping a load of bread is given in the file below. Assume that Jones only has 3 customers and their demands each year are; Customer 1 – 700,000 loaves, Customer 2 – 400,000 loaves, and Customer 3 – 300,000 loaves. Assume that future shipping and production costs are discounted at 12% per year. Assume that once built a bakery last forever. How would you minimize the company’s total cost of meeting demand, present and future?

Unit Production and shipping costs per loaf

Customer 1 Customer 2 Customer 3 Factory Cost

Boston $0.16 $0.34 $0.26 $5 million

Providence $0.40 $0.30 $0.35 $4 million

Hartford $0.45 $0.45 $0.23 $4.5 million

Explanation / Answer

Solution:

Here, we need to understand that the given problem is a transportation problem. To solve it, transportation problem must be balanced transportation problem. i.e. Total supply ( Bake Capacity here) must be equal to Total market demand ( Demand by 3 customers).

Here, Total Supply or Capacity = 3 * 9,00,000 = 27,00,000 Loaves

and Total Customer Demand = 7,00,000 + 4,00,000 + 3,00,000 = 14,00,000 Loaves

So, this is unbalanced transportation problem. To convert it into balanced T.P. we have to add Dummy Customer having demand of 13,00,000 Loaves ( = 27,00,000 - 14,00,000 ). Considering 3 Bake Factories and 4 Markets ( Customers) we will solve the given numerical. Also, we will consider given data in the form of Fixed Cost (Factory cost ) and Variable Costs ( Unit production and shipping costs).

We assume that, unit cost of prodcution and shipping to dummy customer is highest . i.e. More than biggest unit cost in the matrix given in question. Lets consider it as $1 required to produce and ship from any factory to dummy customer.

Then, numerical can be solved by using Transportation Problem Method or By using Solver in Microsoft-EXCEL.

If you need detailed answer , please comment below.

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