Term Definition / Symbol Cycle Time (time / unit) Average time for completion of a unit at a production step or process Throughput Rate (units / time) Average number of units processed over a time interval Bottleneck Process stage with the smallest throughput rate Capacity Effective Capacity Units per unit time that go through each step and entire process (overall process capacity; đ đ ) If there is an operational construct or constraint that necessitates correction in capacity calculation of a task, then đˇđˇđˇđˇđˇđˇđˇđˇđˇđˇđˇđˇ đļđļđļđļđļđļđļđļđļđļđļđļđļđļđļđļ effective capacity = đļđļđļđļđļđļđļđļđļđļđļđļđļđļđļđļđļđļđļđļ đšđšđšđšđšđšđšđšđšđšđšđš Remarks Capacity of process = Capacity of Bottleneck đđ; Average time that a unit takes to go Throughput Time through the entire process (including (time) waiting time) Work in Process (units) Little’s Law Utilization Arrival Rate (units / time) Average Interarrival Time Service Rate (units / time) Average Service Time Utilization of Queue’s Resources Level of Satisfaction (S) đŧđŧ; Average number of units in the system at a point in time đđđđđđđđ đđđđ đđđđđđđđđđđđđđ Throughput Time = đđâđđđđđđđđâđđđđđđ đ đ đ đ đ đ đ đ Time resource is active / total time Capacity of Bottleneck resource is available = Capacity of task (Lambda) īŦ; For M/M/x queues, it is the rate of the exponential distribution of inter-arrival times Also, termed as the expected time 1 between arrivals = đ¸đ¸(đđ) = đđ (Mu) µ; For M/M/x queues, it is the rate of the exponential distribution of service times Also, termed as the expected time taken to 1 process a service request = đ¸đ¸(đđ) = đđ đđ (Rho) ī˛ = đ đ đ đ , where s denotes number of servers = 1, 2, 3… = Perception (P) – Expectation (E) đŧđŧ = đ đ ∗ đđ Never exceeds 100% If inter-arrival times are exponentially distributed with rate īŦ, then number of arrivals follow a Poisson distribution (with rate īŦ) Stability Condition: đđ < 1; Idle Time = 1 − đđ The Psychology of Waiting OIM 305 – Spring 2019 – Useful Terms – Arora