Week 3-4 Flashcards
Random Variation
Controllable Variation - direct result of decision (setup time)
Random Variation - Beyond immediate control and unable to avoid (Customer demand, machine fail)
How to deal with random variation
Develop good probabilistic intuition
Develop robust control policy
Problem with variability
Causes on flow of production line, causes starvation and blockage
Upstream: high variability of processing time
- > Downstream: high variability of arrival rate
- > Inflates CT and WIP of other WS
Variability
Anything that causes the system to depart from regular, predictable
behavior
Sources of Variability
Natural: work piece variation
Preemptive: machine failures
Non-preemptive: setups
Preemptive outage and Availability
Unscheduled downtime which occur in the middle of processing
effective production rate:
𝐴 = MTTF / (MTTR + MTTF)
Effective Processing Time and Rate
𝑟𝑒 = 𝐴*𝑟0 𝑡𝑒 = 𝑡0/𝐴
Effective Variability
σ𝑒^2 = (𝜎0/𝐴)^2 + (𝑚𝑟^2+𝜎𝑟^2)(1−𝐴)𝑡0 / 𝐴
𝑐𝑒^2 = 𝜎𝑒^2 / 𝑡𝑒^2
Non preemptive outage
Controllable Outage that may take place between processing of two consecutive parts
Variability of non preemptive outage
𝑡𝑒 = 𝑡0 + 𝑡𝑠/𝑁𝑠
Propagation of Variability
High Utilization WS: flow variability out determined primarily by process variability
Low utilization WS: ow variability out determined primarily by flow variability variability into
Queuing parameters
5 parameters to describe station
𝑟a = the rate of arrivals in jobs per unit time (𝑡a = 1/𝑟a the average time
between arrivals)
𝑐a = the CV of inter arrival times
m = the number of machines
𝑟𝑒 = m/𝑡𝑒 the rate of the station in jobs per unit time
𝑐𝑒 = the CV of effective process times
Queuing Measures
CTq = the expected waiting time spent in queue
CT = the expected time spent at the process center, i.e. queue time plus process time
WIP = the average WIP level (in jobs) at the station
WIPq = the expected WIP in jobs in queue
CT =CTq + 𝑡𝑒
WIP = 𝑟aCT
WIPq = 𝑟aCTq
