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Batch Size given Average Production Cost Formula

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Batch size refers to the number of identical parts produced in a single production run or cycle. Check FAQs

N b = N t \cdot \frac{C t \cdot t c + C t}{C pr - C t \cdot (t s + t m)}

N_b - Batch Size?N_t - Number of Tools Used?C_t - Cost of a Tool?t_c - Time to Change One Tool?C_pr - Production Cost of Each Component?t_s - Setup Time?t_m - Machining Time?

Batch Size given Average Production Cost Example

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Here is how the Batch Size given Average Production Cost equation looks like with Values.

Here is how the Batch Size given Average Production Cost equation looks like with Units.

Here is how the Batch Size given Average Production Cost equation looks like.

2 = 3 \cdot \frac{80 \cdot 0.5 + 80}{11400 - 80 \cdot (0.45 + 1.15)}

2 = 3 \cdot \frac{80 \cdot 0.5min + 80}{11400 - 80 \cdot (0.45min + 1.15min)}

2 = 3 \cdot \frac{80 \cdot 0.5 + 80}{11400 - 80 \cdot (0.45 + 1.15)}

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Batch Size given Average Production Cost Solution

Follow our step by step solution on how to calculate Batch Size given Average Production Cost?

FIRST Step Consider the formula

N b = N t \cdot \frac{C t \cdot t c + C t}{C pr - C t \cdot (t s + t m)}

Next Step Substitute values of Variables

∴

N b = 3 \cdot \frac{80 \cdot 0.5min + 80}{11400 - 80 \cdot (0.45min + 1.15min)}

Next Step Convert Units

∴

N b = 3 \cdot \frac{80 \cdot 30s + 80}{11400 - 80 \cdot (27s + 69s)}

Next Step Prepare to Evaluate

∴

N b = 3 \cdot \frac{80 \cdot 30 + 80}{11400 - 80 \cdot (27 + 69)}

LAST Step Evaluate

∴

N b = 2

Batch Size given Average Production Cost Formula Elements

Variables

Batch Size

Batch size refers to the number of identical parts produced in a single production run or cycle.

Symbol: N_b

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Batch Size

Number of Tools Used

The Number of Tools Used is the total number of tools used for manufacturing a batch of products.

Symbol: N_t

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Number of Tools Used

Cost of a Tool

Cost of a tool is a multifaceted consideration that includes the initial purchase price, maintenance costs, tool life, and the impact on overall production costs.

Symbol: C_t

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Cost of a Tool

Time to Change One Tool

Time to change one tool often referred to as tool change time, includes the duration taken to remove the used tool and install a new one.

Symbol: t_c

Measurement: TimeUnit: min

Note: Value should be greater than 0.

Formulas to find Time to Change One Tool

Production Cost of Each Component

Production cost of each component involves accounting for various factors, including material costs, labor, machine operating costs, tool costs, overhead, and other related expenses.

Symbol: C_pr

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Production Cost of Each Component

Setup Time

Setup Time of each component is the time required to load/unload the workpiece and position the tool for production for one component.

Symbol: t_s

Measurement: TimeUnit: min

Note: Value should be greater than 0.

Formulas to find Setup Time

Machining Time

Machining time refers to the total time required to complete a specific machining operation on a workpiece.

Symbol: t_m

Measurement: TimeUnit: min

Note: Value should be greater than 0.

Formulas to find Machining Time

Other formulas in Average Production Cost category

Go Number of Tools used given Average Production Cost

N t = N b \cdot \frac{C pr - C t \cdot (t s + t m)}{C t \cdot t c + C t}

Go Number of Tools used given Average Production Time

N t = N b \cdot \frac{t p - (t s + t m)}{t c}

How to Evaluate Batch Size given Average Production Cost?

Batch Size given Average Production Cost evaluator uses Batch Size = Number of Tools Used*(Cost of a Tool*Time to Change One Tool+Cost of a Tool)/(Production Cost of Each Component-Cost of a Tool*(Setup Time+Machining Time)) to evaluate the Batch Size, The Batch Size given Average Production Cost refers to the total number of components produced in a single production run or set. It is an important factor in manufacturing as it impacts production efficiency, costs, and scheduling. Batch Size is denoted by N_b symbol.

How to evaluate Batch Size given Average Production Cost using this online evaluator? To use this online evaluator for Batch Size given Average Production Cost, enter Number of Tools Used (N_t), Cost of a Tool (C_t), Time to Change One Tool (t_c), Production Cost of Each Component (C_pr), Setup Time (t_s) & Machining Time (t_m) and hit the calculate button.

FAQs on Batch Size given Average Production Cost

What is the formula to find Batch Size given Average Production Cost?

The formula of Batch Size given Average Production Cost is expressed as Batch Size = Number of Tools Used*(Cost of a Tool*Time to Change One Tool+Cost of a Tool)/(Production Cost of Each Component-Cost of a Tool*(Setup Time+Machining Time)). Here is an example- 2 = 3*(80*30+80)/(11400-80*(27+69)).

How to calculate Batch Size given Average Production Cost?

With Number of Tools Used (N_t), Cost of a Tool (C_t), Time to Change One Tool (t_c), Production Cost of Each Component (C_pr), Setup Time (t_s) & Machining Time (t_m) we can find Batch Size given Average Production Cost using the formula - Batch Size = Number of Tools Used*(Cost of a Tool*Time to Change One Tool+Cost of a Tool)/(Production Cost of Each Component-Cost of a Tool*(Setup Time+Machining Time)).

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Batch Size given Average Production Cost Formula

Batch Size given Average Production Cost Example

Batch Size given Average Production Cost Solution

Batch Size given Average Production Cost Formula Elements

Other formulas in Average Production Cost category

How to Evaluate Batch Size given Average Production Cost?

FAQs on Batch Size given Average Production Cost

Variable Name