TO 302

time to serve the person arriving at time T

= T*([Demand/Capacity] - 1) the higher the implied utilization, the longer customers need to wait the greater the demand exceeds supply

Standard normal distribution

A normal distribution with a mean of 0 and a standard deviation of 1. Q=u+ z*o

Newsvendor Model

A single-period inventory control model that aims to define optimal order quantities so as to minimize expected overstock costs. key inputs; cost of ordering too little or too much, demand forecast

how many customers are waiting

Iq=R*Tq=Tq/a Iq is the average number of customers waiting Tq is the time in queue arrival rate = 1/a Ip is the average number of customers in service Ip=R*p*p/a

Poisson Distribution

Probability distribution often used to describe the number of arrivals during a given time period inter arrival time is exponentially distributed

time to serve the Qth person in the queue

Q/capacity the higher the growth rate for a queue the linger it will be at time T

VUT Equation

Tq= (CVa + CVp) / 2 * u/(1-u) * p a; inter arrival time p; service time caveats; -yields long term steady state average waiting time -apples only when u<1, otherwise system is unstable and we can't apply VUT (use inventory build instead) -assumes infinite buffer size (if buffer is small, use computer simulation) -good approximation, exact equation when m=1 and arrivals are "poisson" demand must be less than or equal to capacity (if not use inventory build up diagram)

normal distribution

a bell-shaped curve, describing the spread of a characteristic throughout a population one sigma, 34%, the middle is 68%

density function

a function that returns the probability a given outcome occurs for a particular statistical distribution

queue

a line of people or vehicles unstable queue; demand rate (1/a) exceeds capacity (m/p) stable; demand is less than capacity the higher the growth rate for a queue, the longer it will be at time T growth rate is positive when demand exceeds capacity

Single-server queuing system

a service system with one line and one server assumes that demand is less than capacity

Multiple-server queuing system

a service system with one waiting line but with several servers p is the servers average processing time a is the average inter arrival time of customers capacity of each server is 1/p utilization= p/a*m minimum number of servers > p/a number of agents has no influence o the number of people in service determining average number of customers in service does not depend on whether there are multiple servers different in single and multiple; capacity and utilization, not variability

pooled queue

all demand is shared across all servers. each customer served by the first available and they don't know who that will be

Variability

any departure from absolute uniformity think about heights of people, speeds of car, the food/service industry, etc

Peak load pricing (aka congestion pricing)

charging more during the times that you know are busiest some will choose not to pay, lowering demand higher price will hopefully offset the lost revenue

overage cost

cost of ordering one unit too many Co

underage cost

cost of ordering too few Cu cost of under ordering by one unit

Three drivers of waiting time in a queue

decrease utilization, increase capacity, or decrease variability the average waiting time grows at an increasing rate as utilization grows.

separate queue

demand is immediately divided among the servers and a customer is only served by her designated agent ie dr office, you always have the same doctor

implied utilization

demand rate/ capacity may exceed 100%

process capacity

determines max flow rate a process can provide per unit of time determines max supply capacity constrained; when demand exceeds supply demand constrained; when capacity exceeds demand

order winners

dimensions that can differentiate one firm price, quality, speed, flexibility can't be good at everything strategic trade off and efficient frontier

Bottleneck

everything has a bottle neck limits capacity resource with lowest capacity highest utilization resource can be 100% utilized, might not be the bottleneck of the entire process improving non bottleneck processes can still improve performance

economies of scale

factors that cause a producer's average cost per unit to fall as output rises efficiency of the system increases as it gets larger bigger queuing systems work better the challenge is to get demand to have a large operation

Resource

help the flow units move from being a unit of input to be a output i.e. employees shown as rectangular boxes

Effect of utilization on wait time

high u, higher wait time High u makes system slow to recover from periods of higher than normal demand or service times -must maintain capacity in excess of average demand if cannot tolerate long waits -rule of thumb; keep utilization lower than 80%

Sources of uncertainties

input Predictable: supply seasonality Unpredictable: supplier disruptions, natural disasters, global tariffs transition process predict: scheduled down time unpredict: worker absence, cyber attacks, plant fire, machine break down output to demand side predict: demand seasonality unpredict: random demand, weather, macro economic conditions (i.e. 2008 crash)

what is a process

inputs (raw material, customers) transformation process; creating something outputs; goods, served customers ie input rate units/hr; hungry customers process; serving customers output; satisfied customers WIP; work in progress beginning of flow is upstream end is downstream

Littles law

inventory = throughput rate x flow time

capacity

max output rate when working at full speed Rate NOT a number maximum flow rate

inventory

mismatch between supply and demand

Off peak discount

offering a discount during non busy period in the hope that some customers will arrive during this time instead of the peak time reduce demand at peak time

operations management

organization and control of fundamental business activities that provide goods and services to customers don't focus on stock price but controllable inputs

round up rule

probability between two entries, choose the larger

coefficient of variation

ratio of standard deviation to the average less than one- suggests some consistency greater than one- work is inherently uncertain better way to measure variability any amount of variability, a queue forms at least some of the time if CV=0 then Tq=0gs

pre-processing strategy

reducing the amount of work needed to process a customer during the peak time period by moving some of the work to an off-peak time; increase process's capacity to serve customers ex. asking customers to fill out a form online instead of in store

Excess supply and excess demand

surplus, wasted resources ex. call agents idle and wait for call shortage, lost revenue ex. customers wait for representative

arrival and service process

the flow of customers arriving to the system -inter-arrival time; time between customer arrivals to the system the flow of customers when they are being served -processing time; time a customer spends with a server

throughput rate

the output rate that the process is expected to produce over a period of time

Coefficient of Variation (CV)

the standardized measure of the risk per unit of return; calculated as the standard deviation divided by the average inter arrival time sigma/a measures variability relative to the mean steady vs. bursty

salvage value

the value that can be obtained per unit of inventory left over at the end of the season

actual utilization

throughput rate (how much does it produce)/ capacity (how much can it produce always less than 100%

flow time

time a unit takes from entering to leaving the process flow rate and throughput are the same

cycle time

time between consecutive units leaving process

lead time

time interval between ordering and receiving the order aka flow time

Buffer inventory

waiting flow units, depicted as triangles inventory can build infront of a non bottleneck