Operations Notes – Waiting and Service Quality


Notes from core MBA Operations class, these focused on waiting and service quality.
Subject: Operations
  • Waiting can significantly increase throughput time
  • Same duration of wait may mean different things to customers in different environments
  • Unoccupied time feels longer than occupied time
  • ⇒ Pre-process time longer than in-process time

  • Anxiety makes the wait seem even longer
  • Uncertain waits are worse than certain waits (How long will the wait be?)
  • Unexplained waits are worse than explained waits (What is the cause of the wait?)
  • Unfair waits are longer than equitable waits
  • More valuable service allows longer acceptable waits (Queue specialization)
  • Solo waits are longer than group waits

Variability causes waiting
⇒ When variability is present, a queue will result even if avg. arrival rate (λ) < avg. service rate (μ)

λ = average arrival rate
μ = average service rate
ρ = flow intensity of the system
Wq = average waiting time
Lq = average queue length
L = average number in the system
W = average time in the system
U = utilization (1-U = idle time)
M = the number of service providers

ρ = λ/μ
Wq = Lq
Lq = Wq * λ
L = Lq + ρ
W = Wq + 1/μ = Lq/λ + 1/μ
U = λ/Mμ

There is a trade-off between cost and waiting times. Returns from adding capacities are significantly higher when utilization is brought down from 95% to 90% than from 85% to 80% (set Utilization to less than or equal to 90%):

Good News: initial improvements are easy
Bad News: diminishing marginal returns

Decision variables when designing a queuing system:

  • target waiting time
  • number of stages
  • queue discipline
  • level of worker training

Channels are the number of parallel windows open (M)
Lines are the number of waiting lines
Stages are the number of windows a customer gets serviced at

Reduce/Improve waiting times by:

  • hiring more workers
  • training workers or taking other steps to improve productivity
  • shaping customer demand
  • use psychology principles to lower perceived waiting times

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