man 2 test Flashcards
3 main characterizations of the supply chain process
processing
assembly
distribution
principles of manufacturing systems
- little’s law
- matter is conserved
- more components = less reliability
- exponential growth in complexity - N^M possible states
- system components appear to behave randomly
- limits of human rationale
USA Principle
Understand existing processes
Simplify the process
Automate the process
Prescriptive vs Descriptive Models
Prescriptive - model determines how to set decision variables to optimize system performance
Descriptive - given a set of values for the decision variables, model estimates systems performance - rely on these for detailed decision making
heuristic procedures - definition and evaluation of
- rational method that attempts to find a good solution to a model
- evaluation: Quality of solution (“distance” from optimal and bounds), and effort expended generating solution
Computational Time: empirical vs. theoretical
- empirical: run heuristic on a sample of “representative” problems
- theoretical: worst-case running time based on # of computations required, classification of problem in terms of # computations (P polynomial vs NP) - you can solve vs you cant solve
Queuing
analysis of system behavior based on long-run avg performance
Simulation
- experimental model that mimics events that occur in real system
- allows experimentation by running model with different operating parameters or control logic: sensitivity analysis, robustness
- requires verification and validation of model
verification and validation
verification - model does what you want it to do - implemented correctly
validation - model correctly represents real system
Modeling Loss
- don’t necessarily want to minimize these losses - simply want to build the simplest model that answers your question
- Losses:
- perception and measurement
- model simplification
- solution approximation
- implementation
Tc for single unit
Tc = Tm + Ts
Tc for storage cell
Tc = max(Tm,Ts) + Tr
if Ts > Tm, you have forced idle time
Fundamental imbalance law
you cant buffer against fundamental imbalance (b/c speed is always dictated by max(Ts,Tm)), but you can buffer against variability (adding a machine helps variability of setup)
Tm for machine clusters
Tm = NTr + (n-1)Ts
how many machines 1 person can handle in a cluster
n = (Tm + Ts) / (Tr + Ts)
Capacity
= (n * AT) / Tm
= 1 / (Tc1 + Tc1 + …)
Suppose you want to find minimum W - how?
M/G/1
set Var(service time) = 0
Solve for L
Solve for W
Sequencing vs Scheduling
Sequencing - permutation of the job set (order)
scheduling - assigning start/end/preemption times to individual jobs on each machine
Regular vs. Non-regular measures of performance
-regular: non-decreasing in job completion times (if any job is made to finish later, the measure will stay the same or increase) - flowtime, makespan, tardiness, etc
non-regular - lateness and earliness penalties (the larger the deviation, the larger the penalty)
Non-Delay Schedules
no machine is kept idle when there is an operation available for processing
active schedules
no operation can be completed earlier by altering processing sequences on machines and not delaying any other operation - Never make a job in queue wait when it can be completely processed before the next job is scheduled to start
semi-active schedules
No operation can be completed earlier without altering the processing sequence on any of the machines
single machine scheduling: SPT vs EDD
- SPT minimizes mean flow timed
- EDD minimizes max lateness
makespan and mean flow time in single machine scheduling
Makespan is independent of sequence
mean flow time is dependent on sequence
Single Pass Construction Heuristic
Minimize Mean flow time with respect to Max Lateness = 0
Single Machine Scheduling with non-zero ready times
Makespan DOES depend on sequence b/c ri is not equal to zero
Single Machine Scheduling: Setup Times
- sequence - independent setup times: doesn’t matter what you did before - makespan is independent of sequence - just add setup times to process times
- sequence-dependent setup times: makespan is no longer independent of sequence - solve using TSP
TSP formulation
Min sum sum (Cij) * (Xij)
s.t.
sum Xij = 1 ("enter" each city once)
sum Xij = 1 ("exit" each city once)
no subtours
Xij = 0,1closest insertion algorithm
- maintains a partial sequence throughout entire procedure
- is a TSP algorithm
