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Stochastic model - Coggle Diagram
Stochastic model
Shortage
= stockout
SS = Safety Stock
= additional stock absorbing the demand variability during the vulnerability perdio (lead time L)
Decision variables
Q
= the order lot size
ROP
= Rorder Point =
(D*L) + SS
= demand during lead time + safety stock
Objectives
Minimize the costs
Optimize the service
Method 1 - Marginal analysis
TSL
= Target Service Level =
(1 - P(stockout))
If TSL ↗
SS ↗
Holding cost ↗
Stockout cost ↘
Method 2 - Maximum stockout frequency f
Maximum stockout probability per cycle α
= f / (D/Q)
P (DLt ≤ ROP) = (1 – α)
ROP = µ + SS
SS = z * σ
SS depends on the demand variability σ & the lead time Lt
Lead time variability
Previous models = only 1 source of
variability = Demand D
Here = 2nd source of
variability = LeadTime Lt
DLt composed of 2 sources of variability
Demand
Lead time
Pooling effect
= square root effect = centralization
µ = n*µ
σ = √(n.σ)
Centralized demand = sum of n decentralized demands
n decentralized demands
normally distributed + independents & identically distributed
Global demand addressed to the centralized warehouse =
normally distributed