Maximum Inventory Purchase Model Calculator

✖Demand per Year is the number of goods that consumers are willing and able to purchase at various prices during a given year.ⓘ Demand per Year [D]			+10% -10%
✖Order Cost is the expenses incurred to create and process an order to a supplier.ⓘ Order Cost [C₀]			+10% -10%
✖Carrying Cost is the total of all expenses related to storing unsold goods, and refers to the total cost of holding inventory.ⓘ Carrying Cost [C_c]			+10% -10%
✖The Shortage Cost is called the associate cost and is equal to the product's contribution margin.ⓘ Shortage Cost [C_s]			+10% -10%

✖The maximum inventory purchase model is based on the number of units you expect to sell during the replenishment lead time, and the demand and supply variation.ⓘ Maximum Inventory Purchase Model [Q_purch]

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Formula

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Maximum Inventory Purchase Model

Formula

`"Q"_{"purch"} = sqrt(2*"D"*"C"_{"0"}/"C"_{"c"}*("C"_{"s"}/("C"_{"s"}+"C"_{"c"})))`

Example

`"928.4767"=sqrt(2*"10000"*"200"/"4"*("25"/("25"+"4")))`

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Maximum Inventory Purchase Model Solution

STEP 0: Pre-Calculation Summary

Formula Used

Maximum Inventory Purchase Model = sqrt(2*Demand per Year*Order Cost/Carrying Cost*(Shortage Cost/(Shortage Cost+Carrying Cost)))
Q_purch = sqrt(2*D*C₀/C_c*(C_s/(C_s+C_c)))
This formula uses 1 Functions, 5 Variables

Functions Used

sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

Maximum Inventory Purchase Model - The maximum inventory purchase model is based on the number of units you expect to sell during the replenishment lead time, and the demand and supply variation.
Demand per Year - Demand per Year is the number of goods that consumers are willing and able to purchase at various prices during a given year.
Order Cost - Order Cost is the expenses incurred to create and process an order to a supplier.
Carrying Cost - Carrying Cost is the total of all expenses related to storing unsold goods, and refers to the total cost of holding inventory.
Shortage Cost - The Shortage Cost is called the associate cost and is equal to the product's contribution margin.

STEP 1: Convert Input(s) to Base Unit

Demand per Year: 10000 --> No Conversion Required
Order Cost: 200 --> No Conversion Required
Carrying Cost: 4 --> No Conversion Required
Shortage Cost: 25 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

Q_purch = sqrt(2*D*C₀/C_c*(C_s/(C_s+C_c))) --> sqrt(2*10000*200/4*(25/(25+4)))

Evaluating ... ...

Q_purch = 928.476690885259

STEP 3: Convert Result to Output's Unit

928.476690885259 --> No Conversion Required

FINAL ANSWER

928.476690885259 ≈ 928.4767 <-- Maximum Inventory Purchase Model

(Calculation completed in 00.004 seconds)

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Created by Suman Ray Pramanik

Indian Institute of Technology (IIT), Kanpur

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< 12 Manufacturing and Purchase Model Calculators

EOQ Manufacturing Model with Shortage

Go EOQ Manufacturing Model with Shortage = sqrt(2*Demand per Year*Order Cost*(Shortage Cost+Carrying Cost)/(Carrying Cost*Shortage Cost*(1-Demand per Year/Production Rate)))

Maximum Stock Out Manufacturing Model

Go Maximum Stock out Manufacturing Model = sqrt(2*Demand per Year*Order Cost*Shortage Cost*(1-Demand per Year/Production Rate)/(Carrying Cost*(Carrying Cost+Shortage Cost)))

Total Optimum Cost for Purchase Model

Go Total Optimum Cost for Purchase Model = sqrt(2*Demand per Year*Carrying Cost*Order Cost*Shortage Cost/(Shortage Cost+Carrying Cost))

Maximum Inventory Purchase Model

Go Maximum Inventory Purchase Model = sqrt(2*Demand per Year*Order Cost/Carrying Cost*(Shortage Cost/(Shortage Cost+Carrying Cost)))

EOQ Purchase Model with Shortage

Go EOQ Purchase Model = sqrt(2*Demand per Year*Order Cost/Carrying Cost*((Shortage Cost+Carrying Cost)/Shortage Cost))

Total Optimum Cost for Manufacturing Model

Go Total Optimum Cost for Manufacturing Model = sqrt(2*Demand per Year*Carrying Cost*Order Cost*(1-Demand per Year/Production Rate))

EOQ Manufacturing Model with No Shortage

Go EOQ Manufacturing Model No Shortage = sqrt((2*Order Cost*Demand per Year)/(Carrying Cost*(1-Demand per Year/Production Rate)))

Total Cost for Purchase Model with No Shortage

Go Total Cost for Purchase Model No Shortage = Demand per Year*Purchase Price+sqrt(2*Demand per Year*Carrying Cost*Order Cost)

Maximum Inventory Manufacturing Model

Go Maximum Inventory Manufacturing Model = (1-Demand per Year/Production Rate)*EOQ Manufacturing Model with Shortage-Maximum Stock out Manufacturing Model

EOQ Purchase Model with No Shortage

Go EOQ Purchase Model No Shortage = sqrt(2*Demand per Year*Order Cost/Carrying Cost)

Number of Order for Purchase Models with No Shortage

Go Number of Order Purchase Models no Shortage = Demand per Year/EOQ Purchase Model No Shortage

Maximum Stock Out Purchase Model

Go Maximum Stock out Purchase Model = EOQ Purchase Model-Maximum Inventory Purchase Model

Maximum Inventory Purchase Model Formula

Maximum Inventory Purchase Model = sqrt(2*Demand per Year*Order Cost/Carrying Cost*(Shortage Cost/(Shortage Cost+Carrying Cost)))
Q_purch = sqrt(2*D*C₀/C_c*(C_s/(C_s+C_c)))

What is maximum inventory purchase model?

The maximum inventory purchase model is based on the number of units you expect to sell during the replenishment lead time, and the demand and supply variation. the maximum level of inventory you should hold is equal to the sum of Expected sales, demand variation safety stock, and supply variation safety stock.

How to Calculate Maximum Inventory Purchase Model?

Maximum Inventory Purchase Model calculator uses Maximum Inventory Purchase Model = sqrt(2*Demand per Year*Order Cost/Carrying Cost*(Shortage Cost/(Shortage Cost+Carrying Cost))) to calculate the Maximum Inventory Purchase Model, The maximum inventory purchase model is based on the number of units you expect to sell during the replenishment lead time, and the demand and supply variation. Maximum Inventory Purchase Model is denoted by Q_purch symbol.

How to calculate Maximum Inventory Purchase Model using this online calculator? To use this online calculator for Maximum Inventory Purchase Model, enter Demand per Year (D), Order Cost (C₀), Carrying Cost (C_c) & Shortage Cost (C_s) and hit the calculate button. Here is how the Maximum Inventory Purchase Model calculation can be explained with given input values -> 928.4767 = sqrt(2*10000*200/4*(25/(25+4))).

FAQ

What is Maximum Inventory Purchase Model?

The maximum inventory purchase model is based on the number of units you expect to sell during the replenishment lead time, and the demand and supply variation and is represented as Q_purch = sqrt(2*D*C₀/C_c*(C_s/(C_s+C_c))) or Maximum Inventory Purchase Model = sqrt(2*Demand per Year*Order Cost/Carrying Cost*(Shortage Cost/(Shortage Cost+Carrying Cost))). Demand per Year is the number of goods that consumers are willing and able to purchase at various prices during a given year, Order Cost is the expenses incurred to create and process an order to a supplier, Carrying Cost is the total of all expenses related to storing unsold goods, and refers to the total cost of holding inventory & The Shortage Cost is called the associate cost and is equal to the product's contribution margin.

How to calculate Maximum Inventory Purchase Model?

The maximum inventory purchase model is based on the number of units you expect to sell during the replenishment lead time, and the demand and supply variation is calculated using Maximum Inventory Purchase Model = sqrt(2*Demand per Year*Order Cost/Carrying Cost*(Shortage Cost/(Shortage Cost+Carrying Cost))). To calculate Maximum Inventory Purchase Model, you need Demand per Year (D), Order Cost (C₀), Carrying Cost (C_c) & Shortage Cost (C_s). With our tool, you need to enter the respective value for Demand per Year, Order Cost, Carrying Cost & Shortage Cost and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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