You are the production manager overseeing three plants producing Li-ion batterie

Question

You are the production manager overseeing three plants producing Li-ion batteries. These are used in electric vehicles, and are made in three grades: light, medium and heavy. The unit profits, monthly demand and Li requirements per battery are given in the table below 4. Maximum demand (units/month) 7 000 9 000 4 000 Li Unit profit (per battery) Product Heavy $12 Medium $10 Light $7 requirements (kg/battery) 200 150 100 There are three plants where the batteries are produced. The maximum assembly capacities for any mix of battery grades are given below. The number of batteries that can be manufactured at a site is limited by the amount of Li the site can produce. The maximum Li production of each site is also given below Maximum Li production (kg/month) 100000 70 000 40 000 Assembly capacity (batteries/month) Plant Location Quebec City 5 500 Toronto 7 500 Seattle 2 200 Write a mathematical programming formulation that allocates production of the three battery grades among the three locations to maximize total profit. If the fraction of capacity must be the same for all plants (units scheduled/assembly capacity), modify your formulation to meet this constraint. The company negotiates a large ongoing order from Edison Motors, for their new electric sedan. The vehicle uses only Heavy batteries, and they need 10 000 units per month. This demand must be met each month, or the customer will be lost Modify your formulation to achieve this a. b. c.

Explanation / Answer

You are the production manager overseeing three plants producing Li-ion batteries. These are used in electric vehicles, and are made in three grades: light, medium and heavy. The unit profits, monthly demand and Li requirements per battery are given in the table below 4. Maximum demand (units/month) 7 000 9 000 4 000 Li Unit profit (per battery) Product Heavy $12 Medium $10 Light $7 requirements (kg/battery) 200 150 100 There are three plants where the batteries are produced. The maximum assembly capacities for any mix of battery grades are given below. The number of batteries that can be manufactured at a site is limited by the amount of Li the site can produce. The maximum Li production of each site is also given below Maximum Li production (kg/month) 100000 70 000 40 000 Assembly capacity (batteries/month) Plant Location Quebec City 5 500 Toronto 7 500 Seattle 2 200 Write a mathematical programming formulation that allocates production of the three battery grades among the three locations to maximize total profit. If the fraction of capacity must be the same for all plants (units scheduled/assembly capacity), modify your formulation to meet this constraint. The company negotiates a large ongoing order from Edison Motors, for their new electric sedan. The vehicle uses only Heavy batteries, and they need 10 000 units per month. This demand must be met each month, or the customer will be lost Modify your formulation to achieve this a. b. c.

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