U max

Maximal production rate

α ( . )

Continuous time and finite state Markov process

Θ ( )

System state

ξ ( )

Stochastic process of machine states

Ω

Set of system modes

B ( )

Set of admissible production capacities for each

Q ( )

Transition matrix

π ( )

Probability limit

ρ

Discount rate

g ( )

Instantaneous cost

J ( )

Total cost function

z j

Optimal inventory level of product type j

c +

Inventory cost

c

Shortage cost

c r

CM cost

c L O T O

LOTO cost

c α

Operation cost under CM at state α ( . )

q α β

Rate of transition from state α ( . ) to β ( . )

r 21

CM rate without human error (CM - WOHE) with demand d1

r 31

CM rate with human error (CM - WHE) with demand d1

r 54

CM rate without human error (CM - WOHE) with demand d2

r 64

CM rate with human error (CM - WHE) with demand d2

h x

Increment of the variable x

ϑ x ( )

Value function of inventory x

ϑ h ( )

Approximation of the value function for h x increment