Inventory Models
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Inventory Models. EOQ M odel with Planned Shortages. Assumptions. Assumptions of EOQ model. Shortages are allowed. ___________________________________________________________________________ Operations Research  Jan Fábry. Deterministic Inventory Models.

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Inventory Models

EOQ Model with Planned Shortages

Assumptions

  • Assumptions of EOQ model

  • Shortages are allowed

___________________________________________________________________________

Operations Research  Jan Fábry


Deterministic Inventory Models

EOQ Model with Quantity Discounts

___________________________________________________________________________

Operations Research  Jan Fábry


Inventory Models

EOQ Model with Quantity Discount

Assumptions

  • Assumptions of EOQ model

  • Purchase cost is NOT independent of the order quantity

  • Unit holding cost is NOT independent of the order quantity

___________________________________________________________________________

Operations Research  Jan Fábry


Inventory Models

EOQ Model with Quantity Discount

Example – Brewery

  • Monthly production of beer = 4 000 hl

  • Filling into glass bottles = 25% of production

  • Empty bottles stored in plastic cases (20 pcs.)

  • Ordering cost – transportation = 11 000 CZK per order – other = 1 000 CZK per order

  • Lead time = ½ of month

  • Objective: minimize total annual cost

___________________________________________________________________________

Operations Research  Jan Fábry


Inventory Models

EOQ Model with Quantity Discount

Example – Brewery

  • Unit purchase price – quantity discount schedule:

  • Annual holding cost per case = = 50% of unit purchase price

___________________________________________________________________________

Operations Research  Jan Fábry


Inventory Models

EOQ Model with Quantity Discount

Example – Brewery

  • Annual demand

Q = 120 000 cases

  • Purchase price

cq = 46/40/36 CZK per case

  • Annual holding cost

c1 = 23/20/18 CZK per case

  • Ordering cost

c2 = 12 000 CZK per order

  • Lead time

d = 1/2 of month = 1/24 of year

___________________________________________________________________________

Operations Research  Jan Fábry


Total annual PURCHASE cost

Total annual ORDERING cost

Total annual HOLDING cost

Inventory Models

EOQ Model with Quantity Discount

Example – Brewery

  • Total annual cost

___________________________________________________________________________

Operations Research  Jan Fábry


Inventory Models

EOQ Model with Quantity Discount

Example – Brewery

  • Total annual cost

___________________________________________________________________________

Operations Research  Jan Fábry


cq= 46

cq= 40

cq= 36

___________________________________________________________________________

Operations Research  Jan Fábry


Inventory Models

EOQ Model with Quantity Discount

Example – Brewery

  • Optimum order quantity for EACH CATEGORY

___________________________________________________________________________

Operations Research  Jan Fábry


cq= 46

4 999

11 191

cq= 40

cq= 36

___________________________________________________________________________

Operations Research  Jan Fábry


cq= 46

cq= 40

cq= 36

12 000

___________________________________________________________________________

Operations Research  Jan Fábry


cq= 46

cq= 40

cq= 36

15 000

12 650

___________________________________________________________________________

Operations Research  Jan Fábry


TC = 5 865546

TC = 5  040 000

TC = 4 551 000

___________________________________________________________________________

Operations Research  Jan Fábry


Deterministic Inventory Models

Economic Production Lot Size Model

___________________________________________________________________________

Operations Research  Jan Fábry


Inventory Models

Economic Production Lot Size Model

Assumptions

  • Assumptions of EOQ model

  • Inventory is NOT replenished through the single batch

___________________________________________________________________________

Operations Research  Jan Fábry


InventoryLevel

ProductionPhase

NonproductionPhase

Maximal

Inventory Level

Average

Inventory Level

0

t1

t2

Time

t

Inventory Models

Economic Production Lot Size Model

___________________________________________________________________________

Operations Research  Jan Fábry


Inventory Models

Economic Production Lot Size Model

Assumptions

  • Production phase

- production (production rate)

- demand (demand rate)

- replenishment

  • Nonproduction phase

- demand (demand rate)

- depletion

___________________________________________________________________________

Operations Research  Jan Fábry


Inventory Models

Economic Production Lot Size Model

Assumptions

Production rate  Demand rate

___________________________________________________________________________

Operations Research  Jan Fábry


Inventory Models

Economic Production Lot Size Model

Cost

  • Holding cost

  • Production setup cost

  • Objective: minimize total annual cost

___________________________________________________________________________

Operations Research  Jan Fábry


Inventory Models

Economic Production Lot Size Model

Example – Brewery

  • Monthly production of beer = 4 000 hl

  • Filling into glass bottles = 25% of production

  • Empty bottles are processed on the cleaning line (daily output = 8 000 bottles)

  • Setup cost – 12 000 CZK per one cleaning process

  • Annual holding cost per case = 20 CZK

  • Lead time (preparation of cleaning line) = ½ of month

  • Objective: minimize total annual cost

___________________________________________________________________________

Operations Research  Jan Fábry


Fillingbottles

Cleaning line

Store

Inventory Models

Economic Production Lot Size Model

Example – Brewery

Production phase

___________________________________________________________________________

Operations Research  Jan Fábry


Fillingbottles

Store

Inventory Models

Economic Production Lot Size Model

Example – Brewery

Nonproduction phase

Cleaning line

___________________________________________________________________________

Operations Research  Jan Fábry


Inventory Models

Economic Production Lot Size Model

Example – Brewery

  • What is the optimum LOT SIZE?

  • What is the maximum inventory level?

  • What is the minimum total annual cost ?

  • How long time does a cleaning run take?

  • When to start the preparation process for the cleaning run?

___________________________________________________________________________

Operations Research  Jan Fábry


Inventory Models

Economic Production Lot Size Model

Example – Brewery

  • Demand rate

h = 120 000 cases per year

  • Production rate

p = 146 000 cases per year

  • Annual holding cost

c1 = 20 CZK per case

  • Setup cost

c2 = 12 000 CZK per cleaning lot

  • Lead time

d = 1/2 of month = 1/24 of year

___________________________________________________________________________

Operations Research  Jan Fábry


Total annual SETUP cost

Total annual HOLDING cost

Inventory Models

Economic Production Lot Size Model

Example – Brewery

  • Total annual cost

___________________________________________________________________________

Operations Research  Jan Fábry


Inventory Models

Economic Production Lot Size Model

Example – Brewery

  • Production lot size – number of cleaned cases in a cleaning lot (within period t1)

  • Demand withinperiod t1 –

  • Maximum inventory level

___________________________________________________________________________

Operations Research  Jan Fábry


Inventory Models

Economic Production Lot Size Model

Example – Brewery

  • Average inventory level

  • Total annual HOLDING cost

___________________________________________________________________________

Operations Research  Jan Fábry


Inventory Models

Economic Production Lot Size Model

Example – Brewery

  • Number of production lots within a year

  • Total annual SETUP cost

___________________________________________________________________________

Operations Research  Jan Fábry


Inventory Models

Economic Production Lot Size Model

Example – Brewery

  • Total annual cost

___________________________________________________________________________

Operations Research  Jan Fábry


Inventory Models

Economic Production Lot Size Model

Example – Brewery

  • Optimum (economic) lot size

___________________________________________________________________________

Operations Research  Jan Fábry


Inventory Models

Economic Production Lot Size Model

Example – Brewery

  • Maximum inventory level

___________________________________________________________________________

Operations Research  Jan Fábry


Inventory Models

Economic Production Lot Size Model

Example – Brewery

  • Optimum total annual cost

___________________________________________________________________________

Operations Research  Jan Fábry


Inventory Models

Economic Production Lot Size Model

Example – Brewery

  • Optimum length of production period

___________________________________________________________________________

Operations Research  Jan Fábry


Inventory Models

Economic Production Lot Size Model

Example – Brewery

  • Optimum length of depletion period

___________________________________________________________________________

Operations Research  Jan Fábry


Inventory Models

Economic Production Lot Size Model

Example – Brewery

  • Optimum cycle

or

___________________________________________________________________________

Operations Research  Jan Fábry


InventoryLevel

InventoryLevel

Time

Time

  • Optimum starting setup point

___________________________________________________________________________

Operations Research  Jan Fábry


Inventory Models

Economic Production Lot Size Model

Example – Brewery

  • Optimum starting setup point

___________________________________________________________________________

Operations Research  Jan Fábry


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