COMM 398 FINAL EXAM

Define a blocked and a starved resource.

Blocked resource: resource is unable to release the flow unit is has just completed because the next downstream resource is unavailable Starved resource: when a resource is idle and the buffer feeding the resource is empty

Describe the bottleneck of a process. How do you determine a bottleneck with a product mix?

Defn: The resource with the lowest capacity rate (or the highest unit load). It determines the capacity rate of the entire process. A bottleneck is fully utilized while the other resources are not. How to determine a bottleneck when there is a product mix: - multiply the flow time for each unit by the number of each unit in the product mix for each step in the process

What is Utilization? What is the resource with the highest utilization?

Defn: a measure of how much a process actually produces vs how much it can produce. Utilization = (throughput rate/capacity rate)*100 Utilization can be calculated on 2 levels: the process level and the resource level The bottleneck is always the resource with the highest utilization (b/c throughput is the same for all resources but the bottleneck has the lowest capacity.) If the bottleneck step is used at 100% capacity, then the process is working at 100% capacity.

Define mass customization and provide some examples.

Defn: a risk-pooling method that aims to blend the efficiency of an assembly line with the flexibility of a job shop. Aims to merge the product fan-out point with the inventory-order interface. - examples of postponement and push-pull progression Example: - making all ice cream vanilla and mixing in flavours after the customer orders - make un-dyed sweaters and dye them when hot collars are apparent

Define forecasting. What is it often based on?

Defn: a statistical estimate of future demand that can be used to plan current activities Based on: - past sales - known trends (seasonality, trends, etc) - executive judgment (experience) - market research (surveys + interviews) - panel consensus

Define total quality management

Defn: managing the entire organization so that it excels in all dimensions of products and services that are important to the customer

Define operations management. What is the main aim of operations management?

Defn: methods for delivering value via proper execution of strategic goals. Aim: Help firms better match supply with demand. This can be a huge competitive advantage for a firm.

What is acceptance sampling. What variables are involved? How does it related to the operating characteristics curve?

Defn: sampling performed on goods that already exist to determine what percentage of product conforms to specifications. Variables: - AQL: max % defects before batch is rejected by producer - alpha, producer risk: prob of rejecting a good lot - LTPD: % defective for consumer rejection - beta, consumer risk: prob of accepting a bad lot - n: sample size - c = max # of defects before rejection The OCC brings these variables together for unique values of n and c.

Discuss six sigma quality. What are the steps used to drive the 6 sigma quality goals? What are 2 analytical tools used in 6 sigma?

Defn: statistical term to describe the quality goal of no more than 4 defects per million units. Uses the value of defects per million opportunities. DPMO = [# of defects/(# of opportunities for error per unit)(# of units)] * 1,000,000 How? The DMAIC cycle: 1. Define: customers + their priorities (mapping) 2. Measure: process performance 3. Analyse: causes of defects (fishbone diagrams) 4. Improve: remove causes of defects 5. Control: maintain quality (control charts) Analytical tools: a) Failure mode and effect analysis (FMEA): evaluate + prioritize risk of failure at each step b) Design of experiments (DOE): determines cause and effect relationships between variables and output

Define logistics. What are key components of logistics?

Defn: the design and administration of systems to control the movement and positioning of inputs (raw materials, labor, capital, energy), WIP, and finished good at the lowest cost. Logistics occurs OUTSIDE of factory walls! Components: order processing, inventory, transportation, sourcing, warehousing, handling and packaging. --> inventory and transportation management are the most important!!

Define supply chain synchronization. What does it seek to do?

Defn: the operational integration of multiple firms across a supply chain Seeks to: - coordinate flow of materials, products and information between supply chain partners - leverage overall supply chain capability rather than those of individual firms

Define lean production

Defn: the reduction of inventory to expose defects

Define execution.

Defn: the transformation of inputs into outputs. OM wants to make execution more efficient.

What is a fishbone diagram?

Defn: visualizton tool for categorizing the potential causes of a problem in order to ID root causes 4 elements: 1) specifications/information 2) people 3) machines 4) materials

What is the logistics performance index? Which 3 of the 6 are areas for policy? Which 3 of the 6 are areas for market regulation?

Has 6 core components: 1) Efficiency of customs and borders (NEXUS, NAFTA) 2) Quality of infrastructure (trade, transport) 3) Competence and quality of logistics services 4) Ease of arranging competitively priced shipments 5) Ability to track + trace consignments 6) Frequency of on-time delivery Areas for policy: 1,2,3 Areas for regulation: 4,5,6

What are time series plots? What types of trends can we see in a time series plot?

Shows demand over a period of time. Types of trends: - linear trend: overall demand is going up - seasonal variation: despite showing an overall trend demand varies seasonally

What is a swim-lane flow chart?

Shows the resources, activities and relative times of each step in a process.

What are the 2 review systems that are used in lead times?

a) Continuous review (aka fixed-order quantity model) - event triggered - ex, make an order for Q units every time inventory falls below the ROP b) Period review (aka fixed time period model) - time triggered - ex, count inventory every D days and order however much you need given the current inventory levels

What are some ways that you can: a) reduce variability b) manage variability

a) reduce variability - better demand forecasting - better scheduling - reduce variability within your own processes - increase quality b) manage variability - use risk pooling methods - building adequate inventory and/or capacity

Describe how to add Normal Distributions

Add the means: Mean3 = Mean1 + Mean2 Add the square root of the SD's squared: SD3 = sqrt(SD1^2 + SD2^2)

Describe the following quantitative method for forecasting demand: Weighted moving average.

A forecasting method that places greater weight on more recent observations. Ex, we can place more weight on more recent observations by multiplying averages by different weights that add to 1.

What are the advantages and disadvantages of using long vs short periods when forecasting?

Advantages of short periods: - more data points - effect of randomness reduced - when there is no trend in the data, more datapoint results in lower error Disadvantages of more periods: - too many obs can cause the moving average to respond slowly to permanent changes - when there is a trend, more obs will result in higher error

Describe the G/G/C Queue

Characteristics: G: inter arrivals follow a general distribution G: service time follows a general distribution c: C number of servers PK formula: Iq = p^{sqrt(2(c+1))-1}/(1-p) x Ca^2+Cs^2/2 where p = lambda/c*mu

Describe the operations frontier

A graph that shows the trade-off between quality and efficiency (ie cost) in a firm. Moving to any new point on the operations frontier requires trade-offs. Operations innovations shift the operations frontier to the right (higher quality for same cost). Operations management considers both: Tactical goals: ensure that you are on the operations frontier Strategic goals: choose the correct position on the operations frontier

Describe the classification of order process by customer interface.

*Short customer lead time* 1) Make to stock: - immediate delivery of goods based on predictable demand patterns - customer orders do not affect production process delivery - ex: toothpaste, candy 2) Assemble to order: - produce and stock a modular component which integrate as a whole - assemble finished goods according to components selected by customer - allows customization w/ standard production - ex: dell computers, omeletes 3) Make to order: - production starts after order is received from customer - goods produced to customer specification, customer is willing to wait, high product mix - ex: wedding cake, tailor made suit 4) Engineer to order - product is designed + engineered after order - ex: house building, industrial cranes *Long customer lead time*

What are the 4 methods to achieve centralization?

- Location pooling: serve demand with fewer locations, but moves inv away from the customer - Product pooling: serve demand with fewer products, but may limit functionality of products - Postponement/late customization: benefits of risk pooling without moving the product away from the customer - Commonality - Information pooling:

Describe the M/M/C Queue

Characteristics: M: M: arrivals follow exponential distribution M: service processing time follows exponential distribution c: C number of servers PK formula: Iq = p^sqrt(2(c+1))/1-p where p = lambda/c*mu

What are the 2 types of variation that lead to quality issues?

1) Common variation: random and inherent in the production process - ex, mould on cheese 2) Assignable causes: caused by factors that can be identified and possibly managed - ex, poorly trained employees

What are some important things to keep in mind regarding forecasts?

1) Forecasts are always wrong! 2) Long term forecasts are always less accurate than short term forecasts (ex, think about weather forecasts) 3) Aggregate forecasts (year/month/week) are always more accurate than disaggregate forecasts (day)

Describe the two types of bad inventory

1) Inv resulting from defects/rework 2) Inv resulting from the absence of smooth process flow

What are some reasons to not hold inventory?

1) Inventory hides defects 2) Cost of diluted return on investment 3) Holding costs

What are 3 performance metrics for operations?

1) Process efficiency = output/input 2) Process utilization = capacity used/total capacity 3) Quality: defect rate, time to completion, service level

What are 5 methods that can be used to forecast demand?

1) Simple moving average 2) Mean absolute deviation 3) Weighted moving average 4) Exponential smoothing 5) Linear regression

What are 5 reasons for holding inventory?

1) The time a flow unit spends in the process - having inventory in pipeline is a valid reason to hold inventory 2) Seasonal demand - when capacity is rigid but demand is stable, you plan in advance and hold inventory 3) Economies of scale - in order to get full truckloads (cheaper) order in pallets 4) Separation of steps in a process - having inventory between the steps can serve as a buffer 5) Stochastic demand - carrying safety stock for when actual demand differs from predicted demand

What are the 4 elements of strategy? Define a strategic fit.

1) Time: short, intermediate, long term 2) Evaluation: customer satisfaction, profitability 3) Focus: quality, technology, etc 4) Consistency: professionalism, achieving goals, proliferation Strategic fit: when business strategies and product design is compatible --> key for success

Describe two trade-offs regarding holding inventory. Which models are used for each trade-off?

1) Trade-off between inventory ordering costs (economics of scale) vs inventory holding costs - model: EOQ model 2) The cost of running out vs having excess inventory - model: Newsvendor model

What are the 2 different types of quality?

1) conformance quality: the degree to which product or service design specifications are met 2) design quality: the inherent value of the product in the market place

What is a Gantt chart?

A chart that allows for the visualization of a process' steps and their durations. Also shows the dependence of the tasks relative to other activities in the process (ex, some can occur at the same time). ** can also show resources next to activity

What is a linear flowchart?

A chart that shows the tasks of a process in sequence, along with the time for each task. Does now show resources.

What is a poisson distribution? What version of queueing theory uses this distribution?

A distribution where inter-arrival times are exponentially distributed. Note: the SD is equal to the mean, so CV=1 A M/M/1 queueing theory uses this distribution.

Describe the product-process matrix.

A matrix that shows that tradeoff between the variability of a product and the volume of it that can be produced. The different types of processes: *High variability, low volume, high equipment versatility, high labor skills* a) Project: one of a kind (ex, space shuttle) b) Job shop: variable manufacturing process (ex, print shop, mechanic) c) Batch: jobs pass through functional departments in lots (ex, bakery) d) Assembly/flow shop: repetitive production, assembly-line (ex, car assembly); low cycle time e) Continuous flow: non-discrete units like liquid, gas, or powder (ex, petroleum refining); low cycle time *Low variability, high volume, high equipment specialization, low labor skills* Note: if you are above or below the diagonal you have the wrong process: - above diagonal: too much flexibility - below diagonal: too little flexibility There is a tradeoff between the flexibility and efficiency of a process.

Define the kanban system

A pull method whereby the upstream replenishes what demand has withdrawn though use of an instruction card that is sent up the production line. - limits inventory and matches supply with demand

What is the delphi method of forecasting?

A systematic forecasting method with the following steps: 1) choose experts to participate 2) obtain forecasts + reasonings 3) summarize + distribute results/questions 4) summarize + refine + develop new questions 5) repeat 4 as needed and distribute final results

Describe the following quantitative method for forecasting demand: Exponential smoothing

Another forecasting method that puts more weight on more recent observations. We can assign different weights to previous actual demand and previous forecasted demand when calculating our new forecast by choosing certain values of alpha.

Define attributable control charts. When are they used?

Attributable control charts: when you want to measure the percentage of defective items in a sample. p = fraction of defects per sample p(bar)= total # of defects in all samples/(# of samples x sample size) sd = sqrt(pbar(1-pbar)/n) UCL = p(bar)+3sd LCL = p(bar)-3sd

Describe the M/M/1 Queue - characteristics - PK formula

Characteristics: M: arrivals follow exponential distribution M: service time follows exponential distribution 1: single server Note: because this is an exponential distribution, the mean = the SD, so both Ca=1 and Cs=1 and the entire second term cancels. PK formula: Iq = p^2/(1-p) where p = lambda/mu = D/S

What is implied utilization? Why and is it different than utilization?

By definition, utilization can never exceed 100%. Therefore, utilization does not provide any info when demand EXCEEDS supply, ie when there is a queue (it would just simply be 100%). *Implied utilization = Input rate / capacity rate* Unlike utilization, implied utilization can exceed 100%. It helps capture the idea that there may be excess demand in the short run.

What is the difference between capacity rate and throughput rate?

Capacity rate is the maximum possible output rate of a process (equal to the capacity rate of the bottleneck). Throughput rate is the actual output rate. The throughput rate is always less than or equal to the capacity rate.

Describe the M/D/1 Queue - characteristics - PK formula

Characteristics M: arrivals follow exponential distribution D: service time is CONSTANT 1: single server PK formula: Iq = p^2/(1-p) x (1/2) where p = lambda/mu = D/S note: since arrivals follows exponential distribution, Ca=1. But since service time is constant, Cs=1. This gives us the 1/2 term.

Describe the G/1/1 Queue - characteristics - assumptions - PK formula

Characteristics: G: arrivals follow general distribution G: service time follows general distribution 1: single server assumptions: single serve, single queue, no limit on queue length, all units in the queue stay until served, FIFO, units are independent PK formula: Iq = (p^2/1-p)x(Ca^2 + Cs^2)/2 where p = lambda/mu = D/S Ca = CV of inter-arrival times = (1/lambda)/SD of inter arrival times Cs = CV of service time = (1/mu)/SD of service time

What is the cycle service level and why is it important in the EOQ model?

Cycle service level: the probability of NOT stocking out during a cycle - i.e., it is the probability that DLT is less than or equal to ROP Why it's important: the desired level of service helps us determine the re-order point when demand is uncertain in the EOQ model!

What are the different dimensions of quality? What are the costs of quality?

Dimensions: performance, features, reliability, serviceability, aesthetics, perceived quality (brand name) Costs: 1) appraisal: measuring and monitoring of quality - ex, audits and inspections 2) prevention: incurred to prevent quality problems - ex, design + implementation of quality management sys 3) internal failure: - incurred to remedy defects that are discovered before the product gets to the customer - ex, reworks, scrapping 4) external failure: - incurred to remedy defects discovered by customers - ex, repairs, complaints, dissatisfaction, returns

Define a discrete random variable. Define a continuous random variable.

Discrete random variable: has a countable number of possible values (ex, rolling a dice) Continuous random variable: can take on any value between 2 specified values (ex, human height, or inter-arrival times)

What is the difference between the flow time and the cycle time?

Flow time: the average time for a unit to move through the system Cycle time: the average time between the completion of units. Flow time = 1/Cycle time

Describe the operations logistics strategy triangle.

In order to reach customer service goals, you must have good inventory, transportation and location strategies. Inventory strategies: forecasting, inventories levels, purchasing and supply decisions Transportation strategies: modes of transport, routes, scheduling Location: number, size, location of facilities, network planning

Describe the OM triangle for random demand. How do the values in the triangle relate to the PK formula?

If a firm is striving to meet demand, it can use capacity, inventory and information (ie, lower variability) to help mitigate. Note: trade-offs exist between these 3 so cannot do them all! Best one to do: increase information - inventory just covers problems! Iq = (p^2/1-p)x(Ca^2 + Cs^2)/2 Term 1: Iq = inventory Term 2: (p^2/1-p) = capacity Term 3: (Ca^2 + Cs^2)/2 = variability

Why is risk pooling beneficial?

Independent demand streams have inc variability than pooled demand streams. Pooling the demand streams therefore decreases variability. This is beneficial because: - allows you to hold less inventory - better service for same inv, or same service for smaller inv - costs are proportional to the square root of the # of locations pooled

Define: - inventory - flow time - unit load - throughput rate - capacity rate - bottleneck

Inventory: the number of flow units contained within a process Flow time: the time it takes a single unit to get through the process Unit load: the total amount of time the resource works to process each flow unit Throughput rate: the rate at which a process is delivering output (the lower of capacity rate and the input rate)*** Capacity rate: the maximum rate a process can generate Bottleneck: the resource with the lowest capacity rate

Describe the following quantitative method for forecasting demand: Linear regression analysis.

LR aims to determine whether there is a functional relationship between two or more correlated variables. Assumption: past data and future projections fall on a straight line. Y(t)= a + bx + Error Y(t) = regression forecasted value a = Y intercept b = slope of regression line E = error

Define lead time. Define re-order point. What is the re-order point equation?

Lead time (LT): the time between placing and receiving an order. Re-order point (ROP): the amount of inventory that is remaining at which point you should be making your next order. This ensures that you have sufficient inventory to satisfy demand during the lead time. ROP = D*LT

Define outsourcing and near-shoring.

Outsourcing: doing high value added activities in the home country and outsourcing low value added activities - ex, Apple does all of its design in cali (high value) and manufacturing in asia (low value) Near-shoring: moving outsources activities closer to the home country - ex, if apple were to move move outsourcing from asia to mexico

What is little's law?

Little's law: Inventory = Throughput rate * Flow time I = RT

What are long run and short run averages?

Long-run average input rate: MUST be less than the long run average capacity rate. --> ex, utilization must be less than 100% Short-run average input rate: can be greater than the short run average capacity rate (short term queue). --> ex, implied utilization can be higher than 100% Ex: going from the short run to the long run, the average inventory decreases.

Describe the following quantitative method for forecasting demand: Mean absolute deviation.

Looks at the errors between past forecasts and actual demands. Forecast error = forecasted D - actual D Mean absolute deviation (MAD) calculates the "average forecast error."

Describe the japanese approach to quality management. What is the over-arching theme? How does toyota achieve this?

Over-arching theme: ZERO non-value added activities (no breakdowns, no inventory, no setup, no defects) to increase time spent doing value-added activities Achieved by: 1) Just in time manufacturing (pull) - one unit at a time flow - produce at the rate of customer demand (forecasts) - implement pull systems (kanban + make to order) - smaller batches (mixed production) 2) Quality management - fool-proofing - detect-stop-alert (catch defect before product reaches customer) *1 and 2 lower inventory to expose defects --> lean production* 3) Flexibility - adjustment of capacity to meet variable demand 4) Standardization of work - low setups - standardized procedures - minimize setups 5) Worker involvement - worker autonomy (local/faster decision making) - continuous improvement + quality at the source (fixing the problem where it occurs is the cheapest)

What are some benefits of reducing inventory?

Philosophy: inventory is the physical embodiment of bad information, so substitute inventory for information. Benefits of reducing inventory: - higher inventory turns

What is pipeline inventory? What is the equation for pipeline inventory?

Pipeline inventory is inventory that is en route. Pipeline inventory = D*LT I = R*T --> fits with little's law! Note: it is the same equation as the re-order point!

What is the difference between a probability density function and a cumulative distribution function?

Probability density function: shows the probabilities of a certain event occurring at different values Cumulative density function: the integral of a probability density function (ie, the area under the graph).

Define process capability and the process capability index. When is this method used?

Process capability: describes the ability of a process to produce output (process limits) within its specification limits. Process capability index (Cpk): shows how well parts being produced fit into design limit specifications. The Cpk must be AT LEAST equal to 1 to be capable. Method is used when there is a single, measurable aspect of quality that you are interest in.

What is a process flow diagram? Describe the entities that you will likely see in a process flow diagram.

Process flow diagram: tool for understanding processes and making them more visible Entities in a process flow diagram: 1) Flow units: the items that flow through the process (homogenous or heterogenous) 2) Activities: the transformation of the steps in the process (takes time) 3) Resources: perform the activities (have capacities) 4) Buffers: storage units for flow units (finite size)

Describe some differences between products and services.

Products: physical + durable output, lower customer contact, large facilities, easy to measure quality Services: intangible + perishable output, cannot be inventoried, high customer contact, labor intensive, hard to measure quality, local markets, faster response time

Describe the difference between a push and a pull strategy.

Push strategy: when projected/forecasted demand determines what enters the process. Has nothing to do with actual demand. Pull strategy: products enter the supply chain when actual customer demand justifies it (just-in-time). Avoids costs of carrying inventory that won't sell.

What are the 3 outcomes when you use the EOQ model with uncertain demand?

ROP = re-order point DLT = demand during lead time 1) ROP = DLT - shortage = 0 - inventory = 0 2) ROP>DLT - inventory = ROP - DLT - shortage = 0 3) ROP<DLT - shortage = DLT-ROP - inventory = 0 **** BAD!

What comprises inventory?

Raw materials, WIP, finished goods, goods in transit, replacement parts, tools and supplies

How does the utilization of a resource impact queueing time in queueing theory? (describe graph) How is the graph impacted by variability?

Recall: Utilization = D/S The higher the demand, the higher the utilization and the longer the wait times (because queues). Increasing variability shifts the curve upwards towards longer queue lengths. This is why it is a VERY bad idea to work at max utilization when demand is variable.

What does the unit load tell us about how a process is organized?

Recall: unit load is the time a flow unit spends at a given resource in a process Higher unit load: higher labor skills, low equipment specialization, job shop Low unit load: low labor skills, high equipment specialization, flow shop

Describe the "minutes of work" approach.

Supply: (X # of workers)x(60 minutes/h) = 60X minutes of work per hour supplied Demand: (X # of flow units)x(Y flow time/unit) = Z minutes of work demanded Implied utilization = # of mins of work demanded/# of mins of work supplied The resource with the highest implied utilization is the bottleneck!

Describe the following quantitative method for forecasting demand: Simple moving average. How do the moving average plots change depending on period length?

Taking the average over a number of overlapping weeks of previous data. Ex, for a 3 week moving average: - take average of weeks 1,2,3 - take average of weeks 2,3,4 - take average of weeks 3,4,5 ... etc Moving averages become SMOOTHER (more linear) with LONGER periods.

What is the PK formula? What are some important variables in the PK formula and in queueing theory?

The PK formula allows us to measure the queue length of a given queue. Some important variables include: Iq = average queue length Is = average # of customers being served Tq = avg time spent in queue Ts = avg time spent being served I = Iq + Is = total avg inventory T = Tq + Ts = total avg flow time lamba = LR avg input rate = D 1/lambda - avg customer inter-arrival time mu = LR avg server processing rate = S 1/mu = avg processing time of a server utilization = p = lambda/mu = D/S k = buffer capacity C = # of servers safety capacity = mu - lambda = S-D

Define theoretical and effective capacity.

Theoretical capacity: the maximum possible capacity Effective capacity: takes maintenance, breaks, etc into account

Queueing theory tries to balance the trade-off between what?

Tradeoff between cost of service and cost of waiting.

Compare and contrast: - the traditional view on the cost of variability - Taguchi's view o the cost of variability

Traditional view is too binary, and doesn't recognize that it is on a spectrum. Taguchi's view is a much better representation of the costs of quality variability.

Differentiate between the traditional and current views on operations.

Traditional view: - a science of manufacturing, production and logistics - ex, demand forecasting, inventory management (note: still important for current view) Current view: - considers both manufacturing and service industries - the general study of business processes - ex, matching supply and demand, increasing value OM has shifted from purely tactical to strategic.

True or false: flow units can incur wait times even if utilization is less than 100%.

True! Even if utilization is less than 100%, implied utilization can be over 100% (ie, short term demand can exceed short term supply due to unpredictable variability). This means that there can be wait times, even if the long term demand is less than the long term supply.

What is the formula for inventory turnover? What about days of inventory?

Turns = Avg throughput rate (COGS) / Avg inventory = 1/Flow time Days of inventory = 1/Turns = Flow time = Inventory / Throughput rate

Compare and contrast Type 1 and Type 2 queues. Which has a longer wait time? Why?

Type 1: three G/G/1 queues Iq = 3 x [p^2/(1-p) x (Ca^2+Cs^2)/2] Type 2: one G/G/3 queue Iq = [p^2(sqrt2)]/1-p x (Ca^2+Cs^2)/2 Overall wait times are much shorter for type 2 queues due to risk pooling!

What are the 3 types of inventory and what are their relative proportions?

Type A: - 15% of items - 80% of orders Type B: - 35% of items - 15% of orders Type C - 50% of items - 5% of orders

What control limits do we use in quality management?

UCL = mean + 3SD LCL = mean - 3SD This means that 99.7% of values will fall within the acceptable range.

Where does variability come from in OM? What are the different types of variability?

Variability comes from: 1) Variable input 2) Variable capacity Different types of variability: a) Predictable variability: knowable changes in input and/or capacity rates - ex, pumpkin sales will go up at thanksgiving - can be controlled by making changes to the system (changing prices, inc staff) b) Unpredictable variability: unknown le changes in input and/or capacity rates - ex, supply of pumpkins will go down if crop fails - due to the lack of info - expressed by probabilities - can be reduced by gaining knowledge --> both types of variability exist simultaneously!

What are the 7 sources of waste:

Waiting Transport Inventory Overproduction Overprocessing Rework Motion (ergonomics)

What do we use as a general measure of variability?

We use the coefficient of variation! CV = SD/mean

When should you use an erlang loss function?

When you are dealing with variable demand and do not have a buffer.

What is the optimal utilization of a resource? How does this depend on the variability of a process?

With no variability: maximizing utilization is a good idea (besides time for maintenance/training). So, as close to 100% as possible. With variability: maximizing utility is a VERY bad idea. Note: the only resource that you want to work at 100% capacity is the artesian well.

What happens when an process faces variability and a buffer cannot be built? What happens when we add a buffer?

Without a buffer: - Some input will get lost, reducing the throughput rate. - This can result in lost revenue, lost/dissatisfied customers, and lower resource utilization. When we add a buffer: - Increased average inventory - Increased average flow time

If a given firm orders goods under the FOB shipping method, then what is their average inventory?

Your average inventory must take into account inventory in your warehouses, but also inventory in transit (pipeline inventory!) Avg inventory = cycle stock + pipeline inventory = Q/2 + D*LT