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Inventory ControlInventory Control

Operations ManagementFor Competitive Advantage, 10th edition

CHASE, JACOBS & AQUILANO

Tenth edition

Chapter 14

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Chapter 14

Inventory ControlThe reasons to hold inventory

The reasons for not holding inventory

Inventory Costs

Independent vs. Dependent Demand

Basic Fixed-Order Quantity Models

Basic Fixed-Time Period Model- we will omit.

Quantity Discounts-also known as price break

models.

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Purposes of Inventory1. To maintain independence of operations.

2. To meet variation in product demand.

3. To allow flexibility in production scheduling.

4. To provide a safeguard for variation in raw material delivery time.

5. To take advantage of economic purchase-order size.

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Inventory CostsHolding (or carrying) costs.

Costs for storage, handling, insurance, etc.

Setup (or production change) costs.Costs for arranging specific equipment setups, etc.

Ordering costs.Costs of someone placing an order, etc.

Shortage costs.Costs of canceling an order, etc.

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Independent vs. Dependent Demand

Independent Demand (Demand not related to other items or the final end-product)

Dependent Demand

(Derived demand items for

component parts,

subassemblies, raw materials,

etc.)

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Classifying Inventory ModelsFixed-Order Quantity Models Event triggered (Example: running out of

stock)

The sale of an item reduces the inventory position to the re order point.

Fixed-Time Period Models Time triggered (Example: Monthly sales call by sales representative)

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Fixed-Order Quantity Models:Model Assumptions (Part 1)

Demand for the product is constant and uniform throughout the period.

Lead time (time from ordering to receipt) is constant.

Price per unit of product is constant.

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Fixed-Order Quantity Models:Model Assumptions (Part 2)

Inventory holding cost is based on average inventory.

Ordering or setup costs are constant.

All demands for the product will be satisfied. (No back orders are allowed.)

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Basic Fixed-Order Quantity Model and Reorder Point Behavior

R = Reorder pointQ = Economic order quantityL = Lead time

L L

Q QQ

R

Time

Numberof unitson hand

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Cost Minimization Goal

Ordering Costs

HoldingCosts

QOPT

Order Quantity (Q)

COST

Annual Cost ofItems (DC)

Total Cost

By adding the item, holding, and ordering costs together, we determine the total cost curve, which in turn is used to find the Qopt inventory order point that minimizes total costs.

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Basic Fixed-Order Quantity (EOQ) Model Formula

H 2

Q + S

Q

D + DC = TC

Total Annual Cost =Annual

PurchaseCost

AnnualOrdering

Cost

AnnualHolding

Cost+ +

TC = Total annual costD = DemandC = Cost per unitQ = Order quantityS = Cost of placing an order or setup costR = Reorder pointL = Lead timeH = Annual holding and storage cost per unit of inventory

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Deriving the EOQ

Cost Holding Annual

Cost) Setupor der Demand)(Or 2(Annual =

H

2DS = QOPT

Reorder point, R = d L_

d = average daily demand (constant)

L = Lead time (constant)

_

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EOQ Example Problem Data

Annual Demand = 1,000 unitsDays per year considered in average daily demand = 365Cost to place an order = $10Holding cost per unit per year = $2.50Lead time = 7 daysCost per unit = $15

Given the information below, what are the EOQ and reorder point?

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EOQ Example Solution

Q = 2DS

H =

2(1,000 )(10)

2.50 = 89.443 units or OPT 90 units

d = 1,000 units / year

365 days / year = 2.74 units / day

Reorder point, R = d L = 2.74units / day (7days) = 19.18 or _

20 units

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Special Purpose Model: Price-Break Model Formula

Cost Holding Annual

Cost) Setupor der Demand)(Or 2(Annual =

iC

2DS = QOPT

Based on the same assumptions as the EOQ model, the price-break model has a similar Qopt formula:

i = percentage of unit cost attributed to carrying inventoryC = cost per unit

Since “C” changes for each price-break, the formula above will have to be used with each price-break cost value.

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Price-Break Example Problem Data (Part 1)

Order Quantity(units) Price/unit($)0 to 2,499 $1.202,500 to 3,999 1.004,000 or more .98

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Price-Break Example Solution (Part 2)

units 1,826 = 0.02(1.20)

4)2(10,000)( =

iC

2DS = QOPT

Annual Demand (D)= 10,000 unitsCost to place an order (S)= $4

First, plug data into formula for each price-break value of “C”.

units 2,000 = 0.02(1.00)

4)2(10,000)( =

iC

2DS = QOPT

units 2,020 = 0.02(0.98)

4)2(10,000)( =

iC

2DS = QOPT

Carrying cost % of total cost (i)= 2%Cost per unit (C) = $1.20, $1.00, $0.98

Interval from 0 to 2499, the Qopt value is feasible.

Interval from 2500-3999, the Qopt value is not feasible.

Interval from 4000 & more, the Qopt value is not feasible.

Next, determine if the computed Qopt values are feasible or not.

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Price-Break Example Solution (Part 3)

Since the feasible solution occurred in the first price-break, it means that all the other true Qopt values occur at the beginnings of each price-break interval. Why?

0 1826 2500 4000 Order Quantity

Total annual costs

Because the total annual cost function is a “u” shaped function.

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Price-Break Example Solution (Part 4)

iC 2

Q + S

Q

D + DC = TC

TC(1826)=(10000*1.20)+(10000/1826)*4+(1826/2)(0.02*1.20) = $12,043.82

TC(2500) = $10,041

TC(4000) = $9,949.20