BADM 375 Final Cheat Sheet
Kavin Chinnasamy
BADM 375 Cheat Sheet
Queues form due to variability in arrival times, service times & service availability. Impact of variability increases as utilization increases! (throughput goes up or capacity goes down).
Little’s Law: I = R x T (congestion = arrival rate x delay). Little’s Law is I = R*T (where I = avg inventory, r = throughput rate, t = avg flowtime). Delay explodes as the arrival rate approaches the system capacity: Delay ≈ 1/(capacity–arrival rate).
The utilization (per server): ρ = λ / (s μ). Where λ = arrival rate (also departure rate), s = servers & μ = service rate. For the servers to keep up, we must have ρ < 1.
Queuing models provide measures of approximate long-run performance. Queuing models do not typically provide information about start-up effects. Standard queueing models do not incorporate changes like rush hours – Different models are needed for different times of the day.
The “lost customer” rate = λ x Pb • Effective arrival rate = throughput rate = λ x (1-Pb). The key performance measure is Pb the probability that the system is full & arriving customers cannot get in.
If Cs is the cost per hour per server, & Cw is the cost per hour per customer waiting, then the cost per hour of running a queueing system with s servers is Cs(S) + Cw(i)
Safety Capacity - Capacity carried in excess of expected dem& to cover for system variability. Provides a safety net against higher than expected arrivals or services & reduces waiting time - MUST have it when variability too wild - It could be too costly.
Reasons to hold inventory: Safety Stock: Information Uncertainty & Supply/Dem& Uncertainty. Cycle/Batch Stock: Fixed Costs associated with batches, quantity discounts & trade promotions. Seasonal Stock: Seasonal Variability. Strategic Stock: Flooding/availability & acts as a sub for capacity.
Cost of overstocking (Co)● liquidation, obsolescence, holding.Cost of under-stocking (Cu)● lost sales & resulting lost margin
Physical
BADM 375 Cheat Sheet
Queues form due to variability in arrival times, service times & service availability. Impact of variability increases as utilization increases! (throughput goes up or capacity goes down).
Little’s Law: I = R x T (congestion = arrival rate x delay). Little’s Law is I = R*T (where I = avg inventory, r = throughput rate, t = avg flowtime). Delay explodes as the arrival rate approaches the system capacity: Delay ≈ 1/(capacity–arrival rate).
The utilization (per server): ρ = λ / (s μ). Where λ = arrival rate (also departure rate), s = servers & μ = service rate. For the servers to keep up, we must have ρ < 1.
Queuing models provide measures of approximate long-run performance. Queuing models do not typically provide information about start-up effects. Standard queueing models do not incorporate changes like rush hours – Different models are needed for different times of the day.
The “lost customer” rate = λ x Pb • Effective arrival rate = throughput rate = λ x (1-Pb). The key performance measure is Pb the probability that the system is full & arriving customers cannot get in.
If Cs is the cost per hour per server, & Cw is the cost per hour per customer waiting, then the cost per hour of running a queueing system with s servers is Cs(S) + Cw(i)
Safety Capacity - Capacity carried in excess of expected dem& to cover for system variability. Provides a safety net against higher than expected arrivals or services & reduces waiting time - MUST have it when variability too wild - It could be too costly.
Reasons to hold inventory: Safety Stock: Information Uncertainty & Supply/Dem& Uncertainty. Cycle/Batch Stock: Fixed Costs associated with batches, quantity discounts & trade promotions. Seasonal Stock: Seasonal Variability. Strategic Stock: Flooding/availability & acts as a sub for capacity.
Cost of overstocking (Co)● liquidation, obsolescence, holding.Cost of under-stocking (Cu)● lost sales & resulting lost margin
Physical