Question

ABC Co. is to plan its workforce and production levels for next year. Forecast demands for the next 4 quarters are 1160, 960, 1150,1380 units. Ending inventory of last year is expected to be 60, and the ABC would like to have a minimum of 50 units in inventory at the end of next year. The cost of holding one unit in inventory for one quarter is $190.

There are currently 200 workers. The cost of hiring one worker is $700, and the cost of firing one worker is $1500.

In the past, the plant manager observed that over 60 workings days and with the workforce level constant at 200 workers, ABC produced 1200 units.

The number of working days for the next 4 quarters are respectively 61, 62, 65, and 58.

Assume that ABC plans to adopt a level strategy (constant workforce plan) for next year.

Same as Problem 1, except that the forecast demands for the next 4 quarters are 1160, 1260, 1150,980 units.

Determine the level of workforce for next year such that all quarterly demands will be met (no backlogging and no lost sales).

Answer 1

To choose the best production method, the total costs of each method are compared. Method 1 is the most cost-effective with a labor cost of $100/unit, and even as the labor cost rises to $200/unit, Method 1 remains the cheapest option.

Step-by-step explanation:

To determine the best production method based on the costs of labor and capital, we need to calculate the total cost for each method. Let's consider the original labor cost of $100/unit and the capital cost of $400/unit.

• Method 1: The cost is (50 units of labor × $100) + (10 units of capital × $400) = $5000 + $4000 = $9000.
• Method 2: The cost is (20 units of labor × $100) + (40 units of capital × $400) = $2000 + $16000 = $18000.
• Method 3: The cost is (10 units of labor × $100) + (70 units of capital × $400) = $1000 + $28000 = $29000.

With initial labor cost of $100/unit, Method 1 is the cheapest.

However, if the cost of labor rises to $200/unit:

• Method 1: The cost is (50 units of labor × $200) + (10 units of capital × $400) = $10000 + $4000 = $14000.
• Method 2: The cost is (20 units of labor × $200) + (40 units of capital × $400) = $4000 + $16000 = $20000.
• Method 3: The cost is (10 units of labor × $200) + (70 units of capital × $400) = $2000 + $28000 = $30000.

With the increased labor cost of $200/unit, Method 1 remains the cheapest production method.