Question

Using a level strategy with backorders, how many workers are required monthly for aggregate planning?

Answer 1

Using a level strategy with backorders, the number of workers required monthly for aggregate planning depends on the specific production requirements and demand fluctuations of the business.

Step-by-step explanation:

Aggregate planning involves determining the optimal production levels and workforce requirements to meet fluctuating demand efficiently. In a level strategy with backorders, the goal is to maintain a constant workforce level while allowing for backorders during periods of high demand. The number of workers required monthly will depend on the production rate necessary to meet the average demand and the company's policy regarding backorders.

Mathematically, the number of workers (W) required monthly can be expressed as:

`\[ W = (D + B - E) / \text{Working Hours per Worker per Month} \]`

Where:

- D is the average demand per month,

- B is the desired level of backorders,

- E is the existing inventory,

- Working Hours per Worker per Month is the number of working hours per worker in a month.

This formula takes into account the demand, desired backorders, and existing inventory to calculate the number of workers needed to meet production requirements. A level strategy with backorders aims to balance production capacity with demand variability, ensuring a consistent workforce level while managing fluctuations in customer orders. The actual number of workers required will be influenced by the specific parameters of the business, such as production efficiency, lead times, and the company's strategy regarding backorders.

Answer 2

The best production method when labor costs $100/unit and capital costs $400/unit is Method 1 with a cost of $9000. If the labor cost increases to $200/unit, Method 1 still remains the most cost-effective option at $14000. These cost calculations assist in determining the number of workers required for aggregate planning.

Step-by-step explanation:

To determine how many workers are required monthly for aggregate planning using a level strategy with backorders, it is essential to analyze the production technologies and understand the concept of marginal declines in production associated with overstaffing, as implied by the mention of Stage 3 producing in negative returns. However, the provided information does not give a specific production level or the desired quantity of output. Instead, various production methods with associated labor and capital units are presented, and we're asked to find the most cost-effective production method under different labor costs.

For example, the cost calculations for each method when labor costs $100/unit, and capital costs $400/unit would be:

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

The best production method, in this case, is Method 1 as it has the lowest cost. If the cost of labor rises to $200/unit, the new costs would be:

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

With the increased labor cost, Method 1 remains the most cost-effective. These costs should aid in making decisions about production levels and the number of workers to employ, integrating this information into aggregate planning.