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Deterministic Inventory Theory
Professor Stephen R. LawrenceLeeds School of BusinessUniversity of Colorado at BoulderBoulder, CO 80309-7058
EOQ
Economic Order Quantity
EOQ Assumptions Demand rate deterministic and constant (no
variation); No quantity discounts; Cost factors do not change appreciably with time; All items treated independently of other items; Constant replenishment leadtime; No shortages/backorders allowed; Entire order quantity is delivered at same time.
EOQ Inventory Pattern
time
Inventory Level
t t t t
Q
Q /2average inventory
EOQ Problem Structure Each order is for quantity Q A stocking cost of S is incurred every time an
order (outside vendor) or setup (internal production) is incurred
Cost of a single item is C The annual holding cost fraction is h The holding cost per unit is H=hC Annual demand is D
EOQ Costs Annual holding costs:
(Q/2)H Annual stocking costs:
D S / Q Total inventory costs:
holding + stocking costs
TCQ
HD
QS
2
EOQ Cost Trade-offs
TotalCosts
Stocking Costs
HoldingCosts
min TC
Q*
Costs
Quantity Q
QH /2
DS /Q
TC
EOQ Cost Trade-offs Trade-off between stocking and holding costs Minimum cost where holding = stocking cost Note that Total Cost curve is “flat” near Q* Lesson! total cost is relatively insensitive to
small errors in optimal order quantity Q*.
Intuitive Solution for Q*
Total costs minimized when holding costs = stocking costs
QH
D
QS
2
Solving for Q gives optimal order quantity Q*
H
SDQ
2*
Exact Determination of Q*
Total costs minimized when
02 2
SQ
DHTC
Q
Solving for Q gives optimal order quantity Q*
H
SDQ
2*
EOQ Example Consider a product with the following
parameters: D = 10,000 units per year h = 24% per year S = $2,500 C = $1,000
What is the Economic Order Quantity?
Other EOQ-type Models Economic Production Quantity (EPQ) EOQ with quantity discounts Backorder and stockout (lost sales) Special sale price Known price increase Multiple item Maximum order size Inflation Quality deterioration
Inventory Spreadsheet
Utility of EOQ Models Offer good insights Conceptually elegant Robust
Good results even when assumptions are violated Very useful despite shortcomings
