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Public Operations Management by Mind Map: Public Operations
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Public Operations Management

The Waiting Time Formula

Waiting Time Formula for Multiple, Parallel Resources

U=FR/CAP, (1/a)/(m/p)=p/(a*m)


CV = Std Dev / avg

Utilization = process time / ( interarrival time * number of servers)

U= p/(a*m)


four dimensions

Productivity / costs, efficiency

variety, heterogeneity customer preferences

quality, product quality, how good, process quality, as good as promised

time, Responsiveness to demand, tradeoff, responsiveness vs. labor productivy, efficient forntier, line where industry has current froniter

performence measurements

cumulative inflow

cumulative outflow

cumulative flow, flow time ( horizontal), Inventory (vertical), example

flow unit (customer)

flowrate / throughput (Cust/h), flow unit / time

flow time, time from beginning to end

inventory, number of flow unit at a given moment

processing time / Activity time, Time / flow Unit

capacity, 1/processing time, unit/sec, units/h, m = number of parallel workers, capacity = m/procesing time

bottle neck, process with lowest capacity

process capacity, capacity of bottleneck, Min(all capacities)

flow rate, Min ( demand rate, process capacity), insufficient demand

utilization, Flow rate / capacity

process flow diagramm, triangle, waiting, buffer, box, processing time, multiple flow units, implied utilization, Dem / Cap, add up, generic flow unit ("Minute work"), advantage: units may have different times associated for different input types, process with attrition loss

cycle time, CT, 1/flow rate, direct labor content, sum all processing times, direct idle time, sum (all CT - p)

avg labor utilization, labor content / (labor content + direct idle time), = eff. process time / total time paying

cost of direct labor = total wages per unit of time / flow rate per unit of time


Little's Law, Inventory (I)[Units] = Flow Rate (R) [Units/h] * Flow Time (T) [h], Weakness: Averages, inventory turns, 1/T = COGS / Inventory, COGS = Cost of Goods sold, not revenue!, T = Time in Inventory, per unit inventory cost = Annual Inventory / Inventory turns (per year), example: 30%/4 = 7.5% "tax" for inventory, buffer or suffer, make to stock approach, + Scale economies of production, + Rapid fulfillment (short flow time for customer), make to order approach, + fresh preparation (flow time for the sandwich), + allows for more customization (you can't hold all versions of a sandwich in stock), + produce exaclty in the quantity demanded

Five reasons for inventory, pipeline inventory, you wil need some minimum inventory because of the flow time >0, I=RxT, seasonal inventory, driven by seasonal variation in demand and constant capacity, cycle inventory, economies of scale in production (purchasing drinks), safety inventory, buffer against demand (Mc Donalds hamburgers), decoupling inventory / buffers, buffers between several internal steps, where there is inventory there are supply / demand missmatches


process management

doing things repeatedly

!= project management

quartile analysis

compare top 25% with bottom 25% processing times

Flow Time Efficiency (or %VAT)

(Total value add time of a unit) / (Totla time a unit is in the process)


Units Output Produced / Input Used

example: 4 Units per labor hours (looks like processing time)

output: pruductive time

input: total time

Multifactor productivity

Output /(Capital$ + Labor$ + Materials$ + Services$ + Energy$)


key performance indicator

kpi tree, PROFIT, minus, REVENUE, multiply, FLOWRATE, min, DEMAND, CAPACITY, REVENUE/UNIT $, COST, plus, FIX, VAR, multiply, COST/UNIT $, FLOWRATE

break even point

Labor Productivity

Revenue / Labor Costs


7 sources of waste

overproduction, match supply with demand

transportation, relocate processes, then introduce standard sequences for transportation

rework, repetion or correction, analyse and solve root causes of rework -> more quality in module

over processing, provide clear, customer-driven standards for every process

motion, arrange people and parts around stations with work content that has been standardized to minimize motion

inventory, improve production control system and commit to reduce unnecessary "comport stocks"

waiting, understand the drivers of waiting

intellect, intelligence of workers

overall equipment effectiveness (OEE)

Downtime Losses

Availability Rate

Speed Losses

Performance Rate

Quality Losses

Quality Rate

Overall people effectiveness

100% total paid time

Takt Time

Time / #Units



1. Assign task so that total processing times < Takt time

2. Make sure that all tasks are assigned

3. Minimize the number of people needed (maximize labor utiilization)



Fit Based Variety, Horizontal Variety, distribution, examples, T-shirts, Shoes, Opening Hours, Departure Times for planes, trains

Perfomance Based Variety, Vertical, Customers differntiate on quality, distribution, examples, more features, better quality

Taste Based Variety, customers differ in their preferences or taste, distribution, examples, taste of food, art, colors

economic motives

performance based, Segment Market

Taste Based, Fit Based, Cater to heterogeneous customers

Variety seeking customers, example, food, lunch

avoid competition, varietion in a product can make it the lowest price, because none other is the same

Set Up


number of units between setups

capacity given batch size= Batch Size / (Setup Time + Batch size*Time per Unit)

with large batches, processing time approaches 1/processing time, set up becomes more and more irrelevant


SIngle Minute Exchange of Die, 6 stage approach

every set up can be broken up into, internal, external, set up that can be done in parallel before machine is standing still

mixed Module Production

large badges leads to large inventories


calculate batch size

B/(S+B*p) = Demand or Capacity (Units/t), B= Batch Size, S= Total Setup Time, p = Processing Time

Variability of Demand / pooling


mean, mü

standard deviation, sigma, s

Coefficient of Variation, CV=mü/s, doubling size leads to 2^(1/2) CV

positive correletion, when two things are positively correlated, it means two things: 1) a change in one of the two things directly leads to a change in the other thing. 2) both changes are similar in sign. take for example, temperature and ice melt. these two are positively correlated in that when temperature goes up, ice melt goes up. If temperature goes down, ice melt goes down.

random arrival times, a= average inter arrival time, CV = Coefficent of Variation, CVa = St-Dev ( inter arrival times)/(Avg(inter arrival times), Poisson ditribution, CVa = 1, Constant hazard times (no memory), Exponential inter arrivals, Exponential inter-arrivals



Delayed Differntiation

Modular Production

overwhelming of choice

priority rules

FCFS, = FIFO, easy to implement, fairness, lowest variance of waiting time

sequence based on importance

shortest Processing Time Rule (SPT), minimize average wiating time, Hard to hav true processing time


problem, no shows, solves wrong problem: shifts queue

waiting Problems, loss problems

Customers leaving while waiting.

due to limited buffers

impatient customers

Loss analyzation, Percentage of Lost Customers, r=p/a (p=processing time, a=interarrival time), lookup in Erlang Loss Table, Erlang forumla

Implied Utilization with Loss

1. Calculate Demand D, begin from the end of process

2. IU = effective Demand at step / Capacity


No Flexibility / Full Flexibility / Partial Flexibility

Partial Flexibility get almost all benefits of Full felxibilty with lower costs

Process Mapping

Yves Pigneur

Customer Actions

Onstage Actions

Backstage Actions

Value Stream Mapping




percentage according to specification

1 - defect probabilty

Swiss Cheese Model


ALL things have to go wrong




Cost of Defects, CATCH defects BEFORE bottleneck, costs before bottleneck: costs of goods used, costs after bottleneck: opportunity costs, full price charged!

Buffer or Suffer, Starved vs. Blocked, Starve = nothing recieved from up stream, Blocked = no place to put downstream, Buffers can reduce variability in Quality (prevent starving or blocking), Toyota: Inventory prevents quality problems from being reocognized, expose rocks!


Six Sigma

ppm, Parts Per Million, Defects Per Million Parts

Variation, assignable cause, Statistical Process Control, common cause

Process Capability / Capability Score, Cp = (USL - LSL)/6*std, USL = Upper Specification Limit, LSL = Lower Specification Limit, NORMDIST in excel

Manage Quality

The Three Enemies of Operatons

Toyota Production System

Inventory leads to longer "Inventory turnaround time" / feedback loops

Jidoka, Detect / Alert / Stop, Andon Cord

Manage Quality

Kaizen, Root Cause Analysis, Ishikawa Diagram, Fishbone Diagramm, 5 Whys, Pareto Chart, Map out assignable causes of a problem of the categories of the ishikawa diagram, Order root causes in decreasing order of frequency of occurence, 80-20 logic, interplay of reality and models, iterative problem solving

pull system / kanban

"buffers are as unlean as it can get"


original mindmap