EOQ Answers the Question “How Much to Order?” Assumptions: zInstantaneous production zImmediate...
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Transcript of EOQ Answers the Question “How Much to Order?” Assumptions: zInstantaneous production zImmediate...
EOQ
Answers the Question “How Much to Order?”Assumptions:Instantaneous productionImmediate deliveryDeterministic demandConstant demand: D units/yearConstant setup cost: A $/setupIndependent products
EOQ view of Inventory
Time
Inve
ntor
y Order Quantity Q
Costs
• Setup Costs– A $/setup– How many setups if we make Q each time?
• Why not just make D units in one setup?
Inventory Cost
Usually billed as a “holding cost” Essentially interest on the money tied
up in inventory h $/unit/year
Example: Holding 100 units for 6 months costs: ?
Inventory holding Cost h*Average Inventory
A Model
Lot Size or Order Quantity: Q unitsAverage Inventory Level: Q/2unitsAnnual Demand: D units/yearOrder Frequency: every D/Q times per
yearAverage Variable Cost/Year: TVC = h*Q/2 +A*D/Q
The EOQ
Use Calculus to find the value of Q that minimizes TVC(Q)
Or...
Total Variable Cost
Order Quantity
TVC
Holding Costs
Transaction Costs
TVC
Total Variable Cost
Order Quantity
TVC
Holding Costs
Transaction Costs
TVC
Total Variable Cost
Order Quantity
TVC
Holding Costs
Transaction Costs
TVC
Total Variable Cost
Order Quantity
TVC
Holding Costs
Transaction Costs
TVC
The Economic Order Quantity
h Q/2 = A D/QQ2 = 2 A D/hQ = SQRT(2 A D/h)
CAVEAT: Make sure you use commensurate units!
An Example
Raw Material X Quarterly demand: 6,000 units Cost per unit: ~ $25/unit Holding Cost: say 10% per year Transaction Cost: $100/order
EOQ = SQRT(2 CT D/ CI)
= SQRT(2 * 100 * 6,000/(0.025*25)) ~ 1,385 units per shipment
Robustness of the EOQRobustness
-60%
-40%
-20%
0%
20%
40%
60%
80%
100%
% error in A*D
% error in Q
% error in TVC
RobustnessRobustness
-60%
-40%
-20%
0%
20%
40%
60%
80%
100%
%error in h
% error in Q
% error in TVC
EPQ Answers the Question “How Much to Produce?”Assumptions:Instantaneous production Constant production rate: P > D units/yearImmediate deliveryDeterministic demandConstant demand: D units/yearConstant setup cost: A$/setupIndependent products
EPQ view of Inventory
Time
Inve
ntor
y
Production Quantity Q
Max Inv. Level
Length of Prod. Run
A Model
Lot Size or Production Quantity: Q unitsAverage Inventory LevelProduction run lasts: Q/P Inventory grows at rate: (P-Q)So, max inventory is: (P-D)Q/P = (1-D/P)QAverage inventory is: (1-D/P)Q/2Order Frequency: every D/Q times per yearAverage Variable Cost/Year: TVC = h*(1-D/P)Q/2 +A*D/Q
The EPQ
Use Calculus to find the value of Q that minimizes TVC(Q)
Or use the previous answer... TVC = h*(1-D/P)Q/2 +A*D/Q = h’Q/2 +A*D/QSo, Q = SQRT(2 A D/h’) = SQRT(2AD/h(1-D/P))
An Example
Raw Material X Quarterly demand: 6,000 units Cost per unit: ~ $25/unit Holding Cost: say 10% per year Transaction Cost: $100/order Quarterly Production Rate: 8,000 units
EOQ = SQRT(2 CT D/ CI)
= SQRT(2*100*6,000/(0.025*25*(1-6/8)))
~ 2,771 units per run
A Model
Divide the planning horizon into time buckets t = 1, 2, ..., T
Dt = units of demand in period t
ct = unit production cost in period t
At = setup cost in period t
ht = inventory holding cost in period t
Qt = the lot size in period t
It = units in inventory at the end of period t
Heuristics
Lot-for-lot: Make what is required each period.
Fixed Order Quantity: Order the EOQ Period Order Quantity: Calculate the
EOQ, Q. Convert to order frequency: T = Q/D. Orders sized to last for time T.