Research Article

The Supply Chain Triangle: How Synchronisation, Stability, and Productivity of Material Flows Interact

Table 1

Notation list.

NotationTerm

i Index number of different parts
j Index number of different spaces
k Index number of different echelons
s Index number of disturbances
Trajectory of part i
n Number of parts
m Number of echelons
x Space variable
Length of supply chain echelon
Space vector
t Time variable
T Observation time
A Supply chain diameter in units of area
(t)Material inflow rate of echelon k at time t
(t)Material outflow rate of echelon k at time t
q( )Material flow rate at space x at time t
u( )Material density at space x at time t
(t)Echelon stock of supply chain echelon k at time t
S(t)Bounded total stock at time t
(t)Momentum velocity of part i at time t
Maximum velocity in echelon k
(u)Equilibrium velocity referred to the momentum material density
Maximum capacity of echelon k
Average maximum capacity of all echelons
Total maximum capacity
Throughput referred to echelon k to a certain observation time T
Averaged throughput per supply chain echelon to a certain observation time T
Throughput at to a certain observation time T
Standard deviation of internal capacities
Material flow productivity in %
Lead time echelon k
Total lead time
Disturbance s
Long-term demand
Midterm master schedule variation
Amplitude of rectangular function
Amplitude of sinusoidal oscillation of supply disruptions
Period/frequency of rectangular function
Period/frequency of sinusoidal oscillation of supply disruptions