Introduction Scientific inventory management Mathematical model describes system behavior Goal optimal inventory policy with respect to the model Computerized information processing system maintains inventory level records ID: 750922
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Slide1
Chapter 18
Inventory TheorySlide2
Introduction
Scientific inventory management
Mathematical model describes system behavior
Goal: optimal inventory policy with respect to the modelComputerized information processing system maintains inventory level recordsApply the inventory policy to replenish inventory
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Introduction
Demand
Number of units that will need to be withdrawn from inventory
Deterministic inventory modelUsed when demand is knownStochastic inventory modelUsed when demand cannot be predicted well
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18.1 Examples
Example 1: manufacturing speakers for TV sets
One speaker needed per TV set
Sets manufactured on continuous production lineSpeakers produced in batches$12,000 setup cost per batch$10 unit production cost of a single speaker
$0.30 per month holding cost per speaker
$1.10 per month shortage cost
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Examples
Example 2: wholesale bicycle distribution
Distributor purchases a specific bicycle model from the manufacturer and supplies it to various bike shops
Demand is uncertainOrdering cost includes administrative cost of $2000 and unit cost of $350 per bicycle$10 per bicycle holding cost
$150 per bicycle shortage cost
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Cost of ordering z units
Includes a static cost and a cost per unit
K
is the setup cost and c is the unit costHolding costRepresents all costs associated with holding a unit in inventory until it is sold or usedCost of tied-up capital
Space
Insurance
Protection
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18.2 Components of Inventory ModelsSlide7
Shortage costAlso called unsatisfied demand cost
Cost incurred when demand exceeds available stock
Backlogging: demand not lost but delayed
No backlogging: orders are canceled or met by priority shipmentRevenue may or may not be included in the model
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Components of Inventory ModelsSlide8
Salvage costNegative of the salvage value
Included in the holding cost
Discount rate
Accounts for the time value of moneyClassification of inventory model based on how often inventory is monitoredContinuous reviewPeriodic review
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Components of Inventory ModelsSlide9
18.3 Deterministic Continuous-Review Models
Economic order quantity (EOQ) model
Stock levels are depleted over time
Replenished by a batch shipmentBasic EOQ model assumptionsDemand rate is constant at d units per unit time
Order quantity
Q
to replenish inventory levels arrives all at once when inventory drops to 0
Planned shortages are not allowed
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Deterministic Continuous-Review Models
Reorder point equals demand rate times lead time
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Deterministic Continuous-Review Models
Components of total cost per unit time T
Production or ordering cost per cycle,
Holding cost per cycle,
Total cost per unit time
Value of
Q
,
Q
* that minimizes
T
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Deterministic Continuous-Review Models
Cycle time,
t*
For the speaker example:
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Deterministic Continuous-Review Models
The EOQ model with planned shortages
Third assumption of basic EOQ model is replaced:
When a shortage occurs, the affected customers will wait for the product to become available again. Backorders are filled immediately when order quantity arrives to replenish inventoryThe EOQ model with quantity discountsNew assumption:
Unit cost now depends on batch quantity
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Deterministic Continuous-Review Models
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Deterministic Continuous-Review Models
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Deterministic Continuous-Review Models
Different types of demand for a product
Independent demand
Bicycle wholesaler experiences this type of demandDependent demandIn the TV speaker example: speaker demand varies with TV set demandMaterial requirements planning (MRP)
Technique for managing inventory of dependent demand products
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Deterministic Continuous-Review Models
Just-in-time (JIT) inventory management
Emphasizes reducing inventory levels to the bare minimum
Providing items just as they are neededFocuses on finding ways to reduce setup costs so that order quantities can be small
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18.4 A Deterministic Periodic-Review Model
When demand varies from period to period
EOQ formula no longer ensures a minimum cost solution
Objective: minimize total cost over n periodsFixed costs are independent of the inventory policyMinimize total variable costs over the
n
periods
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A Deterministic Periodic-Review Model
Example given on Pages 815-817 of the text
An algorithm for an optimal inventory policy
An optimal policy produces only when the inventory level is zero
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18.5 Deterministic Multiechelon Inventory Models for Supply Chain Management
Echelon
Each stage in a multi-stage inventory system
Supply chainNetwork of facilities that take raw materials and transform them into finished goods at the customerIncludes procurement, manufacturing, and distribution
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Deterministic Multiechelon Inventory Models for Supply Chain Management
A model for a serial, two-echelon system
Seven assumptions in this model outlined on Page 822 of the text
Echelon stockStock physically on hand and downstream at subsequent echelons
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Deterministic Multiechelon Inventory Models for Supply Chain Management
Optimizing the two installations separately
A flawed approach
Choosing order quantities for installation 2 must account for the resulting costs at installation 1Optimizing the two installations simultaneouslyCorrect approachProcess outlined on Page 826-827 of the text
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Deterministic Multiechelon Inventory Models for Supply Chain Management
Model for a serial multiechelon system
Six assumptions outlined on Page 828 of the text
Difficult to solve for n > 2Simplifying approximations normally made to derive a solutionRoundy’s 98 percent approximation property
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Deterministic Multiechelon Inventory Models for Supply Chain Management
Extension of serial multiechelon model can be formulated for a distribution system
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18.6 A Stochastic Continuous-Review Model
Traditional method: a two-bin system
All units for a particular product held in two bins
Capacity of one bin equals the reorder pointUnits first withdrawn from the other binEmptying second bin triggers a new orderNewer approach: computerized inventory systems
Current inventory levels are always on record
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A Stochastic Continuous-Review Model
Inventory system based on:
Reorder point,
ROrder quantity, QInventory policy: whenever inventory drops to R units, place an order for
Q
more units
Ten model assumptions outlined on Page 839 of the text
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A Stochastic Continuous-Review Model
Choosing the order quantity,
Q
Use formula for EOQ model with planned shortagesd is the average demand per unit timeSee assumptions for definitions of
K
,
h
, and
p
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A Stochastic Continuous-Review Model
Choosing the reorder point,
R
Based on manager’s desired level of service to customersAlternative measures of service levelProbability that a stockout will not occur between the time an order is placed and when the order quantity is received
A
verage number of stockouts per year
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A Stochastic Continuous-Review Model
Alternative measures of service level
Average percentage of annual demand that can be filled immediately
Average delay in filling backorders when a stockout occursOverall average delay in filling ordersWhere delay without a stockout is zero
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A Stochastic Continuous-Review Model
Measure 1 is most convenient to use
Procedure for choosing
R under service level measure 1Choose L
Solve for
R
such that
Example given on Page 841 of the text
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18.7 A Stochastic Single-Period Model for Perishable Products
Stable product
Will remain sellable indefinitely
Perishable productCan be carried in inventory only a certain amount of timeSingle period model is appropriate in this caseTypes of perishable products
Newspapers, flowers, seasonal greeting cards, fashion goods, and airline reservations for a particular flight
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A Stochastic Single-Period Model for Perishable Products
Seven assumptions of the model
Given on Pages 846-847 of the text
Analysis of the model with no initial inventory and no setup costSimplest case to considerSee Pages 847-849Application to the bicycle example
Analysis extends to include setup cost and initial inventory levels
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18.8 Revenue Management
Airlines started using revenue management in the late 1970s
Overbooking
One of the oldest and most successful revenue management practicesRevenue management in the airline industry todayPervasive, highly developed, and effective
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Revenue Management
Model for capacity-controlled discount fares
Decision variable: inventory level that must be reserved for highest-paying customers
Key to solving: marginal analysisAn overbooking modelChoose overbooking level to maximize profitShortage cost (denied-boarding cost) is incurred if overbooking level is too high
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18.9 Conclusions
Models presented in this chapter illustrate the general nature of inventory models
EOQ models have been widely used
Stochastic single-period model is appropriate for perishable productsMultiechelon inventory models play an important role in supply chain management
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