Question

Order backlog is allowed with a price. Each worker works 8 hours a day, 20 days a month. Initial workforce before the first month is 80 . Maximum allowed overtime workhour per worker per month is 10 hours. The inventory at the beginning of first month is 1000 , the inventory at the end of the last month is 500 . (1) How many units can each worker produce in each month with regular work hours? (2) Formulate a linear programming problem and solve it with CVX. You may choose to, but not required to apply the integer constraint. Hint: the decision variables include the workforce, hired workers, fired workers, production, inventory, backorder, subcontracts, and overtime workhours of each month. (3) With the optimal solution, what is the workforce management schedule? Is overtime workforce used? (4) With the optimal solution, how does inventory change between months and has backorder ever incurred? (5) Assume that the interest rates raises and it causes the inventory holding cost to become $3/ unit/month. Will the total cost increase? Will the production schedule change? (6) With the optimal solution, should the company delegate any orders to external subcontractor? If yes, how many orders will be produced by the subcontractor? Will the situation change if the subcontracting cost decreases to $25/ unit?

Answer 1

Method 2 is the best production method, but if the cost of labor rises, Method 3 would be the best production method.

Step-by-step explanation:

In order to determine the best production method, we need to calculate the cost of each method.

Method 1 requires 50 units of labor at $100/unit and 10 units of capital at $400/unit, resulting in a total cost of $9500.

Method 2 requires 20 units of labor at $100/unit and 40 units of capital at $400/unit, resulting in a total cost of $9000.

Method 3 requires 10 units of labor at $100/unit and 70 units of capital at $400/unit, resulting in a total cost of $11,000.

Therefore, Method 2 is the best production method.

If the cost of labor rises to $200/unit, the cost of Method 1 would be $15,000, the cost of Method 2 would be $14,000, and the cost of Method 3 would be $13,000.

Therefore, if the cost of labor rises, Method 3 would be the best production method.