Batch Size given Average Production Cost Solution

STEP 0: Pre-Calculation Summary
Formula Used
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)))
Nb = Nt*((Ct*tc)+Ct)/(Cpr-(Ct*(ts+tm)))
This formula uses 7 Variables
Variables Used
Batch Size - Batch Size is the count of similar kinds of products to be manufactured.
Number of Tools Used - The Number of Tools Used is the total number of tools used for manufacturing a batch of products.
Cost of a Tool - The Cost of a Tool is simply the cost of one tool being used for machining.
Time to Change One Tool - (Measured in Second) - Time to Change One Tool is the measure of time it takes to change one tool during machining.
Production Cost of Each Component - Production Cost of Each Component is the total amount that it takes to produce a single component from scratch.
Setup Time - (Measured in Second) - Setup Time of each component is the time required to load/unload the workpiece and position the tool for production for one component.
Machining Time - (Measured in Second) - Machining Time is the time when a machine is actually processing something. Generally, machining time is the term used when there is a removal of unwanted material.
STEP 1: Convert Input(s) to Base Unit
Number of Tools Used: 3 --> No Conversion Required
Cost of a Tool: 80 --> No Conversion Required
Time to Change One Tool: 0.5 Minute --> 30 Second (Check conversion here)
Production Cost of Each Component: 15000 --> No Conversion Required
Setup Time: 0.9 Minute --> 54 Second (Check conversion here)
Machining Time: 1.15 Minute --> 69 Second (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Nb = Nt*((Ct*tc)+Ct)/(Cpr-(Ct*(ts+tm))) --> 3*((80*30)+80)/(15000-(80*(54+69)))
Evaluating ... ...
Nb = 1.44186046511628
STEP 3: Convert Result to Output's Unit
1.44186046511628 --> No Conversion Required
FINAL ANSWER
1.44186046511628 1.44186 <-- Batch Size
(Calculation completed in 00.004 seconds)

Credits

Created by Kumar Siddhant
Indian Institute of Information Technology, Design and Manufacturing (IIITDM), Jabalpur
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13 Value of Production Calculators

Total Non-Productive Time using Average Production Cost
Go Non-Productive Time = (Batch Size*(Production Cost of Each Component-Cost of a Tool*Machining Time)-(Cost of a Tool*Number of Tools Used*Time to Change One Tool)-(Number of Tools Used*Cost of a Tool))/Cost of a Tool
Setup Time for Each Product given Total Production Cost
Go Setup Time = (Total Production Cost-Cost of a Tool*Batch Size*Machining Time-Number of Tools Used*(Cost of a Tool*Time to Change One Tool+Cost of a Tool))/(Cost of a Tool*Batch Size)
Machining and Operating Rate given Average Production Cost of each Component
Go Machining and Operating Rate = (Production Cost of Each Component-(Number of Tools Used*Cost of a Tool/Batch Size))/(Setup Time+Machining Time+(Number of Tools Used*Tool Changing Time/Batch Size))
Setup Time for Each Product given Average Production Cost
Go Setup Time = (Production Cost of Each Component-Cost of a Tool*Machining Time-(Number of Tools Used/Batch Size)*(Cost of a Tool*Time to Change One Tool+Cost of a Tool))/Cost of a Tool
Machining and Operating Rate given Total Production Cost
Go Machining and Operating Rate = (Total Production Cost-(Number of Tools Used*Cost of a Tool))/(Batch Size*(Setup Time+Machining Time)+(Number of Tools Used*Tool Changing Time))
Batch Size given Average Production Cost
Go 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)))
Number of Tools used given Average Production Cost
Go Number of Tools Used = Batch Size*(Production Cost of Each Component-Cost of a Tool*(Setup Time+Machining Time))/(Cost of a Tool*Time to Change One Tool+Cost of a Tool)
Number of Tools used given Total Production Cost
Go Number of Tools Used = (Total Production Cost- Batch Size*Cost of a Tool*(Setup Time+Machining Time))/(Cost of a Tool*Time to Change One Tool+Cost of a Tool)
Setup Time for Each Product given Individual Costs
Go Setup Time = (Total Production Cost-(Total Machining And Operating Cost+Total Tool Changing Cost+Total Cost of Tools Used))/(Cost of a Tool*Batch Size)
Machining and Operating Rate using Individual Cost
Go Cost of a Tool = (Total Production Cost-(Total Non-Productive Cost+Total Tool Changing Cost+Total Cost of Tools Used))/(Batch Size*Machining Time)
Total Non-Productive Time using Total Production Cost
Go Non-Productive Time = (Total Production Cost-(Total Machining And Operating Cost+Total Tool Changing Cost+Total Cost of Tools Used))/(Cost of a Tool)
Number of Tools used given Individual Costs
Go Number of Tools Used = (Total Production Cost-(Total Non-Productive Cost+Total Machining And Operating Cost+Total Tool Changing Cost))/Cost of a Tool
Batch Size given Total Production Cost
Go Batch Size = Total Production Cost/Production Cost of Each Component

Batch Size given Average Production Cost 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)))
Nb = Nt*((Ct*tc)+Ct)/(Cpr-(Ct*(ts+tm)))

Average Production Cost of each component

The average Production Cost of each component is usually determined by taking an average over a defined batch of products. The reason for this is the extended costs such as the cost of tools and operating costs etc. This makes the Average Production Cost becomes quite higher for a single product than when measured over batch size.

How to Calculate Batch Size given Average Production Cost?

Batch Size given Average Production Cost calculator 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 calculate the Batch Size, The Batch Size given Average Production Cost is a method to determine the maximum that component that can be produced in a batch when the maximum allowed expense on one component is given. Batch Size is denoted by Nb symbol.

How to calculate Batch Size given Average Production Cost using this online calculator? To use this online calculator for Batch Size given Average Production Cost, enter Number of Tools Used (Nt), Cost of a Tool (Ct), Time to Change One Tool (tc), Production Cost of Each Component (Cpr), Setup Time (ts) & Machining Time (tm) and hit the calculate button. Here is how the Batch Size given Average Production Cost calculation can be explained with given input values -> 1.44186 = 3*((80*30)+80)/(15000-(80*(54+69))).

FAQ

What is Batch Size given Average Production Cost?
The Batch Size given Average Production Cost is a method to determine the maximum that component that can be produced in a batch when the maximum allowed expense on one component is given and is represented as Nb = Nt*((Ct*tc)+Ct)/(Cpr-(Ct*(ts+tm))) or 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))). The Number of Tools Used is the total number of tools used for manufacturing a batch of products, The Cost of a Tool is simply the cost of one tool being used for machining, Time to Change One Tool is the measure of time it takes to change one tool during machining, Production Cost of Each Component is the total amount that it takes to produce a single component from scratch, Setup Time of each component is the time required to load/unload the workpiece and position the tool for production for one component & Machining Time is the time when a machine is actually processing something. Generally, machining time is the term used when there is a removal of unwanted material.
How to calculate Batch Size given Average Production Cost?
The Batch Size given Average Production Cost is a method to determine the maximum that component that can be produced in a batch when the maximum allowed expense on one component is given is calculated using 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 calculate Batch Size given Average Production Cost, you need Number of Tools Used (Nt), Cost of a Tool (Ct), Time to Change One Tool (tc), Production Cost of Each Component (Cpr), Setup Time (ts) & Machining Time (tm). With our tool, you need to enter the respective value for Number of Tools Used, Cost of a Tool, Time to Change One Tool, Production Cost of Each Component, Setup Time & Machining Time and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
How many ways are there to calculate Batch Size?
In this formula, Batch Size uses Number of Tools Used, Cost of a Tool, Time to Change One Tool, Production Cost of Each Component, Setup Time & Machining Time. We can use 1 other way(s) to calculate the same, which is/are as follows -
  • Batch Size = Total Production Cost/Production Cost of Each Component
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