Chapter 9 : Management of Quality
~Quality: Ability of product to consistently meet/exceed customer expectations
~Quality control: Monitoring, testing and correcting quality problems after they occur, 1930’s,
foremen and full-time quality inspectors checked quality mostly at end
~Quality assurance: Ensuring product quality will be good by preventing defects, 1950’s,
operators during production
~Quality management system (QMS): Structured/documented system describing policy,
responsibilities and implementation plan for quality, 1970’s
~Total quality management (TQM): Renamed QMS, emphasis on customer satisfaction
involving all management/workers
~Dimensions of quality of goods: Performance, aesthetics, special features, conformance,
reliability, durability, perceived quality, service after sale
~Dimensions of service quality: Tangibles, convenience, reliability, responsiveness,
timeliness, assurance, courtesy/empathy
~Determinants of quality: Product design (technical characteristics
translated to process characteristics/specifications), production
process design, production, use
~Conformance to design specification during production: Degree
a good is defect-free. Determined by documentation of processes and
procedure, skills/training of operators, stability/monitoring of processes, taking corrective
actions, staff communication/meeting, record keeping/verification, good quality suppliers
~Cost of quality: Methodology to determine resources used to prevent poor quality, appraise
quality of products, deal with internal/external failures
~Categories of cost quality:
1. Internal failure costs: Part/product failures during production, caused by defective
material from suppliers, incorrect machine settings, faulty equipment/material
handling/procedures, incorrect methods/processing. Cause loss of production time, scrap and
rework, possible equipment damage/employee injury
2. External failure costs: Part/product failures after delivery, include handling of
complaints, recall, replacement, liability/litigation, payments to
customers or discounts to offset quality, loss of customer goodwill,
opportunity costs due to lost sales
3. Appraisal (detection) costs: Inspection, testing, activities to
uncover defective products. Costs of inspectors, testing, test
equipment, labs, quality audits
4. Prevention costs: Attempts to prevent defects. Costs of market
research, product design verification, quality planning/admin, statistical
process control, working with suppliers to improve quality of purchased materials/parts,
standard operating procedures, training
~Spending $1 on prevention can save $10 on detection and $100 on fixing failures
~Taguchi quality loss function: Quality worsens at a faster rate
the further measurement deviate from target
~Deming stated cause of inefficiency/poor quality is system not
employees and management’s responsibility to correct. Suggested
reduce variation output by distinguishing special causes of variation and common causes. He
didn’t name “total quality management” but started the movement of quality is a “total field”.
Foundation of statistical process control (SPC), promoted plan-do-study-act (PDSA) cycle
of problem solving. Believed management’s greatest challenge in achieving quality was in
motivating workers and that workers wanted to create/learn but management unintentionally did
things to inhibit motivation
~Deming’s 14 points (needed to achieve quality):
~Juran believed 80% of quality defects are controllable and management has responsibility
to correct deficiencies. “Quality is fitness for use” Quality trilogy: Quality planning necessary
for processes capable of meeting quality standards, quality control necessary to know when
corrective action is needed, quality improvement helps find better way to do things
~Feigenbaum recognized quality was more than collection of tools/techniques, “total field”
aka quality control. Introduced quality at the source: Avoiding passing defective products
and fix problem
~Crosby: Believed any level of defects is too high, management must install programs to move
towards zero.
~Concept of zero-defects:
1. Top management must demonstrate commitment to quality/willingness to give support to
achieve good quality
2. Management must be persistent in efforts to achieve good quality
3. Management must spell out what it wants in terms of quality and what workers must do
4. Make it (or do it) right the first
~Crosby’s “quality is free” concept: Cost of poor quality are much greater than recognized,
and costs of quality efforts should be viewed as way to reduce costs
~ISO 9001: International standard for quality management system. Firms must document
processes and undergo external on-site assessment by auditors to achieve standard. Must be
recertified every 3 years, ISO is reviewed every 5 years. Three types of documents created;
quality control manual, procedures manual, detailed work instructions and supporting
documents
~Summary requirements for ISO 9001 page 313
~ISO 14002: International standard for assessing company’s environmental performance, what
firm should do to minimize harmful effects of operations on environment
~HAACP: Quality management system designed for food processors. Inspects
construction/sanitary aspects of plant/equipment/personnel. Ensures regular system of work
instructions/inspection/prevention
~Product/process background info required:
1. Describe product, source of raw material, product characteristics, ingredients,
packaging, how product is used, shelf life, where product will be sold, labelling instructions,
distribution control
2. Draw process flow diagram and number steps, draw plant layout identifying operations
by number and material flows by arrows
3. Identify all regulatory action points (RAP) (points where safety control is mandated by
gov). Usually include receiving points of raw materials/shipping points of products/critical points.
SOP’s are usually provided, if not need to define one. Specifies control measures, inspection
procedures and corrective actions
~Main HACCP steps:
1. Perform hazard analysis: For each ingredient/processing step identify potential
hazards, determine if is significant with justification, provide preventative measures for
significant hazards
2. Determine critical points (CCPs): For every ingredient/processing step with on ot more
significant hazards, if there is not a subsequent step to eliminate hazard, step is CCP.
3. Establish HACCP plan: For each significant hazard determine control/preventative
measure, critical limits, monitoring procedure, corrective action, documentation and
record-keeping procedure, verification procedure
~Canada Awards for Excellence (CAE) and Total Quality Management (TQM): Excellence
in areas like quality, mental/health, innovation
~Criteria for award:
1. Leadership and governance: Creating culture, values, overall direction for success.
Showing good governance/innovation and fulfilling legal/ethical.social obligations
2. Strategy and planning: Developing business/improvement plans across all drivers,
monitoring/evaluating/reporting progress in meeting goals
3. Customer experience: Engages customers for satisfaction and success,
listening/acting/reporting
4. People engagement: How workers are treated, encouraged, supported, enabled to
contribute to success, physical/mental wellness of employees/families and safe environment
5. Process and project management: Disciplined/common approach toward
analyzing/solving process problems/project management. Facilitates prevention-based
approach to process management
6. Partners and suppliers: External relationships with others critical to meet strategic
goals
~Requirements/outcomes for levels of quality:
Level 1, Bronze: Clear commitment to quality, early stages of implementing long-term
strategic focus on quality that promotes good principles as outlined.
Commitment to continuous improvement with awareness/education
on standard and using internal/external assessment to assist
process of establishing priorities for improvement. Outcomes:
Broad support of vision/mission/values, recognition of importance
of embedding quality principles in decision making, policy
statements related to quality.
Level 2, Silver: Builds on commitment/foundation established in bronze, solid
methodology based on standard and implemented in key areas. In transition from a focus on
“reacting” to issues to a more “proactive” approach. Positive results being achieved from
improvement efforts. Outcomes: Wider understanding by employees of organization’s strategic
approach to quality, having strategic/operational plans, establishment of baseline
indicators/measures/related goals for quality
Level 3, Gold: Builds solid implementation of quality established in silver.
Organization-wide implementation of strategic focus on quality through
understanding/application of standard. Sounds, systemic approach to quality. Outcomes:
Positive achievements in meeting/exceeding strategic goals, organization-wide quality issues,
positive results across al drivers/departments, widespread quantifiable improvement as a result
of moving from reactive to proactive approaches
Level 4, Platinum: Builds on achievement/outcomes from previous three levels focus on
establishing sustainable practices. Organization achieved good to excellent results and positive
trends from efforts for overall improvement in quality. Can clearly identify sustained
improvements against specific objectives. Outcomes: Sound/systemic approach to quality,
continuous improvement as a “way of life” with full integration into culture/systems, sustained
positive improvements in all areas over at least three years, organization viewed as leader
within its sector regarding quality in terms of knowledge sharing/industry, benchmark leadership,
best practices.
~Total quality management (TQM): Approach to quality management that involves everyone
in firm in quality management and continual effort to improve quality/customer satisfaction.
Three features: Never-ending push to improve quality (continuous improvement), involvement of
everyone in firm in quality management, goal of ever-increasing customer satisfaction
~TQM approach :
1. Find out what customers want (surveys, focus groups, interviews…)
2. Design product that will meet/exceed customers want
3. Design processes that facilitates doing job right the first time (quality of source),
determine where mistakes are likely to occur and try to prevent, incorporate process design
elements that prevent mistakes. When mistakes occur find out why and implement corrective
actions so less likely to occur again.
4. Keep track of results and use to guide improvement in system, never stop trying to
improve
5. Extend concepts to suppliers/partners
~Process improvement steps: Map, analyze, redesign, acquire resources,
implement/communicate change, review process.
~Process improvement goals: Optimize performance, meet best practice standards, improve
quality, improve user experience, reduction of waste
~Plan-do-study-act (PDSA) cycle (Deming cycle): Testing a
change by developing plan to test change, carrying out test,
observing/learning from consequences, determining
modifications. Circle of plan -> do -> act -> study ->
~Six sigma: Statistical approach to problem solving/quality
improvement. Five steps: Define, measure, analyze, improve,
control. Best employees trained to become full-time change
agents (black belts) who act like internal consultants with
considerable power/resources. More coordinated that
improvement projects of TQM/continuous improvement. Each
project should increase value for customers/shareholders/employees. Refers to having very
capable and precise processes that make only 3-4 defects per million parts produced.
~Seven basic quality tools:
1. Process flow diagram (process map): Steps in a process and
movement of material between steps. Variations: Flowchart, service blueprint, swim lane
diagram. Can help identify possible points where problems/opportunities for improvement occur
2. Check sheet: Paper that provides format for recording/organizing data
that facilitates collection analysis. Designed on basis of what users are
attempting to learn. Many different formats.
3. Histogram: Chart of frequency distribution of observed values. Can
see if distribution is symmetrical, range of values and if unusual values.
4. Pareto analysis: Technique for focusing attention on most important
problem or opportunity for improvement, shows number of occurrences
/category. Few factors account for large percentage of total problems. 80%
of problems are from 20% of types of problems. Sometimes each defect
type has different consequence and firm assigns different weight to each.
5. Scatter diagram: Plot of pairs of observations of two variables that
show correlation.
May point to cause of problem. The higher the correlation the less scatter.
6. Control chart: Line plot of time-ordered values of sample statistic
with control limits. Can be used to monitor process to see if if output is stable or detect presence
of assignable/correctable causes of variation, or to indicate when a problem occurred.
7. Cause-and-effect diagram (fishbone, Ishikawa diagram): Used to organize possible
causes of problem, usually four M’s; machine, method, manpower, materials, are categories.
Often used in brainstorming.
8. Run chart: Time plot used to track values of a variable over time. Can aid in identifying
trends/patterns
~ Methods for problem solving/continuous improvement:
1. Brainstorming: Generating free flow of ideas on finding causes/solutions and
implementing in a group of people, no single member dominating or criticism
2. Affinity diagram: Show relationship among large numbers of ideas. Each participant
writes ideas on sticky note. All are posted on wall and moved around to form similar groups
3. Quality circle: Group of workers in same department who meet to discuss ways of
improving products/processes. Can motivate workers by demonstrating management interest in
worker ideas. Less structured, more informal than quality improvement teams. Usually have little
authority to implement only minor changes
4. Interviewing: Used to collect info on a problem or opportunity, sometimes employees for
internal and customers/suppliers for external
5. Benchmarking: Measuring a firm’s performance against best firm in same or other
industry. To establish standard against which performance is judged and to learn how to
improve. Goal is to meet/exceed standard
~5W2H: Asks questions about a problem that begin with 5 W’s 2 H for cause and improvement
~5 Whys: Asking “why” five times to ask logical questions summarizing observations from
earlier questions. If more than one answer per why, should be subjected to another “why”
question.
~Reaching consensus methods:
1. List reduction applied to list of possible solutions, clarifies/reduces list of items by asking
questions about affordability/feasibility/likelihood of solving problem or improving quality
2. Balance sheet lists pros and cons of each item
3. Paired comparison has each item on list compared with every other item. For each pair
team members select preferred item, best when list is small
Chapter 10: Statistical Quality Control
~Statistical quality control: Statistical techniques/sampling in monitoring and testing of
products
~Acceptance sampling: Relies primarily on inspection of previously produced items
~Statistical process control: Occurs during production
~Inspection: Appraisal activity that compares quality of
product to standard. Vital but unappreciated.
~Statistical process control planning process:
1. Define quality characteristics important to customers (only ones that can be measured
are valid) and how each is measured (must have standard used to evaluate)
2. For each characteristic, determine quality control point (for goods usually at beginning,
end, or at operation where characteristic of interest to customers is first determined, for services
usually where personnel and customers interact and parts of facility customer sees), plan how
inspection is to be done/how much to inspect (low-cost high-volume items need little inspection
because cost associated with defective items is low and processes are usually reliable and
v.v.)/whether centralized or on-site (if advantages of specialized lab tests are worth
time/interruption), plan corrective action
~Operations with high human involvement need more
inspection than mechanical. Stable process will require few
checks and v.v. Small lots require more samples because it
is important to obtain sample data from each lot and v.v. High
volume repetitive operations, computerized automatic
inspections at critical points are cost effective
~Statistical process control (SPC): Statistical evaluation of product in production process
(operator takes periodic samples and compares with predetermined limits). Main task is to
distinguish assignable from random (usually taking a sample of two or more observation and
calculating sample statistic). Goal is to assure output is random so future output is random
~Random/Chance variation (Deming’s common variability of process): Inherit variability
created by combined influences of countless minor factors so unimportant that effect is
negligible
~Assignable variation (Deming’s special
variation): Nonrandom, mains source of variability
can usually be identified and eliminated
~Sampling distribution: Variability of sample statistic, theoretical distribution of values of
statistic for all possible sample of given size from process
~99.7% of values fall between +- 3 stdevs, 95.5% between +- 2 stdevs,
~Type 1 error (alpha/producer’s risk): Value falls outside
given stdevs, insinuating process shift when it has not
~Type 2 error (consumer’s risk): When looks process
hasn’t shifted when it has
~Averaging in sample means: High and low values tend to offset
each other resulting in less variability
~Central limit theorem: As sample size increases, distribution of
sample averages approaches a normal distribution. The larger the
sample size the narrower the distribution (chances sample statistic is
close to true value is high in large samples)
~If a sample falls outside limits (usually 2 or 3 stdevs) small
probability it is random variation and is usually a shift in process
~Control chart: Time-ordered plot of sample statistic with limits, used to distinguish between
random/assignable variation. Has upper/lower (control) limits. Used to monitor process output to
see if random. Necessary condition for process to be in control is for all data points to fall
between upper and lower limits. Basis is sampling distribution, but extends in either direction to
infinity so any value is theoretically possible, even one that is considerable distance from mean.
~Designing control charts:
1. Determining sample size, n, usually between 2-20. Depends on cost of inspection vs
expected cost of Type 2 error (larger n smaller possibility)
2. Obtain 20-25 samples of n. Compute sample statistic for each
3. Establish preliminary control limits and graph them
4. Plot sample statistic values on chart, note points falling outside limits
5. If no points outside limits, assume no assignable cause and process is stable/in control,
if not, investigate and correct, repeat from step 2
~Sample mean (x̄) control chart: Monitors/processes mean, center line is process mean. Take
few samples, compute mean, average means. Used to ensure process is stable/in control.
Average of means is mean of all observations in sample (grand mean).
~Upper control limit (UCLx̄) = ⩢ + z σ x̄
Lower control limit (LCLx̄) = ⩢ - z σ x̄
σ x̄ = st dev of sampling distribution of sample mean = σ / √n z = st normal deviate (usually 3)
⩢ = avg of sample means = grand mean
~Upper control limit (UCLx̄) = ⩢ + A2Ṝ
Lower control limit (LCLx̄) = ⩢ - A2Ṝ
A2 comes from table
Ṝ = Avg of sample ranges of a few samples
~Sample range (R) control chart: Used to monitor process dispersion/spread.
~UCLR = D4Ṝ
LCLR = D3Ṝ D3,4 from table
~If stdev of process is not known but average of sample ranges Ṝ is known, equate two
UCL’s, substitute 3 for z and simplify
~Sample mean controls are sensitive to shifts in process and sample range control
charts are sensitive to changes in dispersion
~Individual unit (X) control chart: When rate of production is low, testing is expensive or no
reason to expect additional info, only one unit is used for inspection.
~UCLx = x̄ + z σ
LCLx = x̄ - z σ
x̄ = mean of few individual observations
~Moving range (MR) control chart: Differences between consecutive observations used to
control dispersion
~UCLMR = 3.27Ṝ
LCLMR = 0Ṝ = 0
Ṝ = average of moving ranges (absolute value of difference between two consecutive
observations)
~Control charts for attributes: Used when process characteristic is counted rather than
measured. One type for fraction of defective items in sample, and one for number of
defects/unit. P chart is appropriate when data consists of two categories of items. C-chart is
appropriate when can count number for one category and not for other.
~Use p-chart when observations can be placed into one of two categories, ex: Good or bad,
pass or fail, operate or don’t, or when data consists of multiple samples of n observations each
~Use c-chart when only number of occurrences/unit of measure can be counted,
non-occurrences can’t be counted, ex: scratches/item, cracks/distance, tears/area, calls/time
~P-chart is control chart for sample proportions of defectives, used to monitor defective
proportion of items generated by process, theoretical basis is binomial distribution but for large
sample sizes normal distribution is good.
~Centre line: Average proportion of defectives in population. St dev of sampling distribution
­
of sample proportion is σ p = √(p(1 p))/n
UCLp = p + z σ p
LCLp = p - z σ p
~If p is unknown can be estimated from few samples. If LCLp is negative, use zero as LCLp
~C-chart: Goal is to control number of occurrences of defects per unit of product. Only
occurrences may be counted. Underlying Poisson distribution.
~Poisson distribution assumes defects occur over continuous region and probability of more
than one defect at any spot is negligible. Mean number of defects/unit product is c and st dev is
LCLc = c - z √c
If c is unknown, average number of
√c . UCLc = c + z √c
defects/unit product from a few samples, C̅, is used. When LCL is negative, set to zero.
~Decisions about control charts:
1. At what point in process to use: Focus on aspects of process that have a tendency to
go out of control and are critical to success
2. What size samples: Important because cost/time are functions of sample size (greater
the size the greater the cost and time), and smaller samples are more likely to show change in
process because change is more likely to take place in large sample but between small
samples. Sample statistic could combine before-change and after-change observations, but in
two smaller samples they could be seperate
3. What type of chart: Must weigh time/cost against info
4. How often samples should be taken
~Patterns in data can suggest nonrandom process (trend, cycles, level shift, bias (too many on
one side), too much dispersion
~Run test: Checks for patterns in sequence because means not in state of control
~Run: Sequence of observations with a certain characteristic followed by 1+ observations with
a different characteristic (can be anything observable). Two useful run tests involve number of
runs up/down and runs above/below median. Data transformed into series of Us/Ds and As/Bs
(first value doesn’t receive a label because nothing precedes it). Runs easily counted fro plot
~These runs must be compared with number of runs would be expected in random
series. Expected number of runs is
E(r)med = (N/2) +1
E(r)u/d = (2N-1)/3
N = # observations
Chance variability = σ med =
√(N ­ 1)/4
= σ u/d =
√(16N
­ 29)/90
~If observed numbers of runs falls beyond limits, suspect patterns are present. Too
many/few shows nonrandomness.
~ztest = (Observed # of runs - Expected # of runs)/Standard deviation of # of runs
Median: z = (r-(N/2 +1))/ √(N
­ 1)/4
Up and down: z = (r-((2N -1)/3))/ √(16N
­ 29)/90
N = total # of observations r = observed # of runs
~Usually easiest to calculate # of stdevs, z, which observed # of runs differs from
expected, and compared with value of 2 or 3 stdevs. If test z exceeds desired limits patterns
are present. Desirable to run both tests
~Procedure for tests:
1. Determine type of control chart, compute control limits ( if no probability given use z = +3), if any sample statistics fall outside limits process is not in control
2. Conduct median/up/down run tests. Use z = +- 3 for comparing test scores if no other
values given. If either or both scores are not within limits output is probably not random
3. Plot sample data and check for patterns. If pattern, output is probably not random.
Otherwise conclude process is in control
~Design specification: Range of values into which product must fall to be acceptable
~Process variability: Actual variability for product. Usually measured with +-3 stdevs. Compare
this to acceptable range of variation (assuming process mean is centered at midpoint). Can also
compare six stdevs of process with design specification width
~Control limits based on sampling distribution variability, sampling distribution
variability function of process variability (control limits & process variability directly related)
~Process capability: Ability to meet design specifications. Measuring is called capability
analysis
~Case C solutions: Redesign process or
reduce variability, use alternative process, retain
current process but attempt to eliminate
unacceptable output using 100% inspection, examine design specification to see whether could
be relaxed without affecting customer satisfaction
~Process capability ratio (Cp) = Design specification width/Process width (or 6 σ )
For process to be capable must at least have ratio of 1.00, implies 99.74% of output is
expected within limits.
~If process is not centered between design specification limits or no limit on one side, use Cpk
(difference between each specification limits and process mean). Cpk = smaller ratio between
(Upper design specification - Process mean)/3 σ AND
(Process mean - Lower design specification)/3 σ
~Six Sigma quality: Advanced version of problem
solving/continuous improvements. Goal of achieving
process variability so small half-width of design
specifications = six stdevs of process. Process capability ratio = 2.00
~Six Sigma improvement methodology (DMAIC):
1. Define: Determine customers and critical-to-quality products
2. Measure: Identify/measure quality problem, determine baseline Sigma and possible
influencing factors
3. Analyze: Test influencing factors and identify vital few
4. Improve: Select solution method, prove effectiveness, implement
5. Control: Develop process control plan
~Design of experiments: Performing experiments by changing levels of factors to measure
influence on output/identifying best levels-for each factor. If done by changing level of one factor
at a time and keeping levels of others constant, extremely large number of experiments
required. Fractional factorial design suggests more concise experiments by changing level of
more than one factor at a time
Chapter 12: Inventory Management
~Independent demand: Unknown demand and has to be forecasted
~Dependent demand: Demand depends on production schedule for finished goods
~Inventory: Material/part/idle product kept for use/sale
~Stock keeping unit (SKU): Unique item stored and accounted for separately from others
~Work-in-process (WIP): Partially finished items
~Inventory management: Planning/controlling inventories
~Typical firm has half of current assets in inventory
~Return on assets (ROA): Profit after tax divided by total assets. Reduction in inventory can
cause increase
~Cost of good sold (COGS): Sum of material (sum of value of inventory at start of year + total
cost of material purchase during year - value of inventory at end of year), direct/indirect labour
costs
~Inventory methods: First-in-first-out (FIFO), last-in-first-out (LIFO) and weighted average cost
~In-transit inventory: Items being transported
~Purposes of inventory:
1. To wait while being transported: Raw materials/parts and finished goods heading to
market need to be transported, freight could take up to a month.
2. Protect against stock-outs: Delayed deliveries/unexpected increases in demand
increase risk of stock-outs. Risk can be reduced by holding safety stock (in excess of average
demand)
3. Take advantage of economic lot size or to avoid future price increase: Minimize
purchasing/receiving/material handling/accounts payable costs by buying in quantity that
exceeds immediate requirements (economic order quantity), sometimes due to
discount/avoiding future price increase. Usually economical to produce in large quantities
(economic production quantity). Order cycle occurs. Resulting inventory (cycle stock) is
replenished cyclically and gradually depleted.
4. To smooth seasonal demand/production: Manufacturers will seasonal demand build
up inventory during off season to meet high demand during peak season. May keep some of
products for later sale (seasonal inventory)
5. Decouple operations: Decoupling inventory (WIP inventory) between successive
operations to create independence between two operations if one temporarily breaks down.
Fluctuation similar to water in a tank. Average supply/demand rate should be equal or tank will
be empty/overflow. Average WIP inventory = Avg time unit spends waiting in inventory X avg
supply/demand rate
6. To meet anticipated above-average demand: Build up goods inventory (anticipation
inventory), or in anticipation of plant shutdown.
~Concerns of inventory management: Level of
customer service (item availability/fill rate), costs of
ordering/holding inventory
~Objective is to achieve satisfactory levels of customer service while minimizing
inventory costs
~Item fill rate: Percentage demand filled from stocks on hand
~Inventory turnover: Ratio of annual COGS to average inventory investment. Indicates how
many times/year inventory is sold/used. The higher the better. Can compare with others in
industry
~Warehouse management system (WMS): Software that controls movement/storage of
materials in warehouse and processes associated transactions (receiving/put-away/
replenishment/picking/shipping)
~Inventory position: Quantity on hand + on order (received by supplier but not arrived) back-ordered (shortage customer agreed to wait for)
~Requirements for effective inventory management:
1. Safe storage/handling of inventories:
● Usually stored indoors to protect from environment.
● Heavy/fast moving items are kept on floor. Warehouses use vertical space and high
ceilings with forklifts. Uncluttered stock room, sometimes conveyors/carousel storage systems.
● WMS generates bar code label once pallet is received. Large warehouses usually have
two locations, bulk (reserve) high up, individual-item pick location (reachable by person no
equipment). When customer order arrives is assigned to oper picker on pallet jack and item is
retrieved in sequence that minimizes distance travelled while picking heavy cases first.
● Orders picked moved to wrapping station, label printed/attached and moved to shipping.
● Can also use automated storage and retrieval system (ASRS).
● Ownership of a warehouse provides control but demand should be high to be
economical, renting is for short-term needs with no capital or personnel
● Outdated items should be removed or sold
2. Tracking inventory levels and using inventory control models:
● If not continually tracked must be periodically reviewed/counted to determine inventory
position
● ~Fixed-interval/order-up-to level model: Estimates how much item will be demanded
from now until next delivery (order-up-to-level) and bases order quantity on difference between
order-up- to-level and inventory position. Also used when computer keeps track of inventory
continually. Items from same supplier are ordered at same time (economies in
ordering/shipping/receiving/ paying). Disadvantage is possibility of stock-out between reviews
● ~Perpetual/continual tracking: Keeps track of removals/additions to inventory on
continuous basis so system can provide info on current inventory position for each item at any
time (bank accounts)
● ~Economic order quantity/reorder point model (EOQ/ROP): Only works with
perpetual tracking. When inventory position of an item drops down below predetermined
minimum called reorder point (ROP), fixed economic quantity of item is ordered. Usually
computer keeps track. Advantage is probability/expected shortages can be controlled, order
quantity is fixed (management can determine optimal order quantity and use it for a few months
provided no seasonality/trend. Disadvantage is added cost of individual ordering
● Min/Max model: Inventory position drops to/below min, order equal to max is placed.
Can approximate min by ROP and max by ROP + EOQ without large penalty cost, slightly
underestimates
● EOQ/ROP and min/max can carry over unused items into subsequent periods and
used/sold. Single-period method is appropriate when items can’t be carried over
● Two-bin system: EOC/ROP model with no perpetual inventory tracking. Items
withdrawn from first bin until contents are exhausted, then time to reorder. Second bin contains
enough stock to satisfy expected demand until order is filled plus safety stock. When order
arrives second bin is topped off and remainder is placed in first bin. Sometimes order card is at
bottom of first bin
● Bar code: Unique number assigned to item/location made of group of vertical
black/white bars read by scanner. Standard grocery bar code is universal product code (UPC),
has 12 digits. Zero on left of bar code identifies a regular grocery item, next five numbers
indicate manufacturer, next five indicate specific item, last two digits is check-digit used by
computer to check validity of first 11 digits. Each digit made of seven black/white bars. Color of
bar depends on whether digit is on left or right of centre guard
3. Forecasting demands and lead times:
● Purchase lead time: Time interval between ordering/receiving order. Similar for
manufacturing lead time with items produced in house, how long will take to be produced.
Greater potential variability in times greater need for additional safety stock to reduce risk of
stock-out between deliveries
● Point-of-sale (POS) system: Electronically records actual sales at time/location of sale
● Exponential smoothing commonly used as forecasting technique for large # of SKU’s
4. Estimating inventory costs:
● Holding cost: Physically having items in storage, include warehousing
(rent/building/labour/light…) and opportunity costs associated with funds tied up in inventory.
Others are insurance, obsolescence, spoilage, theft, breakage. Items easily
concealed/expensive are prone to theft. Stated either as percentage of unit cost or as
dollar/unit. Typical annual holding cost rates are 20-40% of cost of an item
● Ordering cost: Cost of placing an order, receiving and paying for it. Includes time of
purchasing/inventory control staff determining how much is needed, periodically evaluating
sources of supply, preparing purchase orders and fixed-cost portion of
transportation/receiving/inspection and moving goods to storage. Also includes cost of time
spent paying invoice. Generally fixed dollar amount/order. Cost of machine is analogous to
ordering cost, fixed charge/production run regardless of size, when company produces its own
parts.
● Shortage cost: When demand exceeds supply on inventory on hand. Can include
opportunity cost of not making sale/loss of customer goodwill/late charges/expediting costs. If
shortage occurs in item carried for internal use cost of lost production/downtime is shortage cost
5. Performing A-B-C classification:
● Groups inventory into three classes according to measure of importance usually annual
dollar value, and allocates inventory control efforts accordingly. Class A 15-20% of inventory
and 70-80% of annual dollar value (ADV) (very important), B (moderately important), and C
50-60% of SKU’s and 5-10% of ADV (least important). Usually small number of items account
for large share of ADV and should receive greater share of inventory control. Factors to change
classification are risk of obsolescence/consequence of stock-out/distance of supplier/lead time...
● Cycle-counting: Counting items in inventory on cyclic schedule. Reduces discrepancies
between records and actual quantities and investigates cause of inaccuracy and fixes them. Ask
how much accuracy is needed, how frequently should count, and who should do it.
● APICS recommended inventory accuracy: +-0.2% for A, +-1% for B, 5+- for C. A should
be counted most frequently
● Physical inventory: Determination of inventory quantity by actual count
~Economic order quantity (EOQ): Order size that minimizes total annual inventory control
cost
~Basic economic order quantity: Minimizes sum of annual
costs of holding/ordering inventory. Annual purchase price
not included because assumed unit purchase price is
unaffected by size
~Cycle starts with receipt of shipment used at constant rate
over time, when quantity is just sufficient to satisfy demand
during purchase lead time another purchase is submitted. Shipment is received at instant
inventory on hand equals zero. Orders are timed to avoid excess/shortage.
~Reflects trade-off between total annual holding/ordering costs. If order size is small
average inventory will be low with low annual holding cost but will require frequent orders driving
up ordering cost and v.v. Solution is to order size not too big/small
~Annual holding cost = Q/2 X H Q = Order quantity
H = Holding cost/unit/year
Is linear function but annual ordering cost is inversely and nonlinearly related. Total annual
inventory cost is u-shaped and minimum annual holding = annual ordering cost
~Annual ordering costs decrease as quantity increases, = D/Q X S
D = Demand S = Ordering cost/order
~Total annual inventory = Annual holding cost + Annual ordering cost =
Q/2 X H + D/Q X S
~Optimal order quantity = EOQ = Q0 = √(2D)S /H , substitute Q0 for Q to find minimum cost
~Length of order cycle = Q0/D
~Annual demand usually estimated by multiplying next month’s forecast of demand by 12 or
next week’s by 52. If seasonality lot sizing technique is better
~Economic production quantity (EPQ): Production lot
size that minimizes total annual production setup and
inventory holding cost. Units received incrementally
~During production phase inventory builds up at rate
equal to difference between production and usage
rates. If production continues inventory will grow. Inventory on hand will be max when
production ceases. When inventory on hand is done production is resumed and cycle repeats
itself. Avg inventory on hand is 0.5Imax.
~No ordering costs, but setup cost are analogous to ordering costs because independent of
lost quantity. Treated same way, S. Larger the run, fewer number of runs and lower setup cost.
Number of runs s D/Q and annual setup cost = (D/Q) X S
~Total annual inventory control cost = Annual holding cost + Annual setup cost =
(Imax/2)H + (D/Q)S
Imax = Max inventory Q = production run quantity s = setup cost/run
~Cycle length = Q/d
Production run length = Q/P
p = production rate d = usage/demand rate
­
~Imax = Q - d(Q/P) = (Q/P)(p-d)
Q0 = √(2D)S /H √p/(p d)
~EOQ with quantity discount: Price reduction for large orders. Identify order quantity that will
represent lowest total annual cost
~All-unit discount case: Price of every unit is price/unit given for order quantity. Buyer must
weigh benefits of reduced purchase price and fewer orders against increase in holding cost with
higher average inventory
~Total cost = annual holding cost + annual ordering cost + annual
purchase cost = (Q/2)H + (D/Q)S + RD
R = unit price
~Seperate U-shaped total cost curve for each unit price. Smaller unit
prices will raise total cost curve less than larger ones. Each curve applies
only to portion of range
~Applicable/feasible total cost is initially on curve at highest unit price then drops down
at break quantities. Lower prices lead to lower holding costs and larger EOQ’s. As each price
decreases each curve’s minimum point will be to right of previous curve’s minimum point
~Best purchase quantity by beginning with lowest unit price, calculating EOQ for each unit
until price find feasible EOQ, and if so is optimal. If not compare total cost at all break quantities
larger than feasible EOQ with total cost of feasible EOQ. Quantity yielding lowest total cost is
optimum
~EOQ with planned shortage: When holding cost/unit is large and customer can wait. Assume
will be back-ordered but will incur shortage cost proportional to length of time unit is
back-ordered
B = back-order cost/unit/year
Qb= Quantity back-ordered/order cycle
T = length of order cycle
t = time period when inventory position is non-negative
Tb = time period when inventory position is negative
~When next order arrives back-order is satisfied first.
Inventory after order arrival = Q - Qb = d X t
~t = (Q - Qb)/d
tb = Qb/d
T = t + tb = Q/D
t/T = ((Q-Qb)/d)/(Q/d) = (Q-Qb)/Q tb/t = (Qb/d)/(Q/d) = Qb/Q
~Average inventory on hand = (Q-Qb)/2 X t/T + 0(tb/T) =
(Q-Qb)2/2Q Average level of back-orders = Qb/2 X tb/T + 0(t/T) = Q2b/2Q
Total inventory control cost = Annual ordering cost + annual holding cost + annual
back-order cost = (D/Q)S + ((Q-Qb)2/2Q)H + (Q2/2Q)B
Qb = Q(H/(H+B))
Q=
√(2DS /H)((H + B )/B)
~Reorder point (ROP): Inventory position (on hand + on
order - back ordered) at/below order should be issued
ROP = d X LT
d = demand rate
LT = lead time
~When variability creates possibility actual demand during lead time will exceed demand
during lead time. Necessary to carry additional inventory (safety stock) to reduce risk of running
out or reduce number of units short. Reorder point is increased by amount of safety stock
~Amount of safety stock depends on demand and lead time variability and desired service
level
~Lead time service level: Probability demand will not exceed inventory on hand during lead
time (no shortage). Equal to fraction of cycles with no shortage
~Annual service level: Proportion of annual demand filled from stocks on hand (fill rate)
~Safety stock = z X σdLT z = safety factor; # of stdevs above expected demand
σ dLT = stdev of demand during lead time
~Stockout risk = 1 - lead service time level. Smaller desired
stock-out, greater the z.
~If only demand is variable σ dLT = √LT σ d
and
ROP = d̅LT + z √LT σ d
d̅ = average demand
σ d = stdev of demand
LT = lead time
~If demand and lead time are variable
σ d LT =
√LT σ
2
ROP = d̅ LT + z
d
+ d­2 σ 2 LT
√LT σ
2
d
+ d­2 σ 2 LT
LT = Avg lead time
σ LT = stdev of lead time
~Avg demand usually estimated using forecast demand and
stdev of demand usually estimated using stdev of forecast error
~When desired annual service level SLannual, calculate standardized expected number of units
short during order cycle = E(z) = (Q(1-SLannual))/ σ d LT, use table to find associated z value,
use z to find ROP = Expected demand during lead time + z σd LT
~Periodic review model: Inventory position reviewed periodically. When demand is variable
Min = d̅(LT + RP) + z σd√LT + RP Max = Min + EOQ
RP = review period
~Can-order model: When item’s inventory position drops to/below ROP all related items are
investigated to see if inventory position is at/below can-order level. If so, are ordered too to bring
inventory up to max
~Fixed-interval/order-up-to level model used when orders are at fixed item intervals and
inventory position is brought up to order-uo-to level. Used by wholesalers/distributors/retailers
where all items from same supplier are ordered at same time with varying order sizes
~Order interval: Determined by minimizing total annual holding/ordering costs of SKU’s from
supplier. Two components, cost of issuing purchase order and cost of ordering each line item
~Purchase order ordering cost: Fixed ordering cost/purchase excluding line items
~Line item ordering cost: Variable ordering cost/SKU included in purchase order
~OI = order interval S = purchase order ordering cost
Rj = unit cost of SKUj
n = number of SKU’s bought from supplier
i = Annual holding cost rate
s = line item ordering cost (assume is same for every SKU)
Dj = annual demand of SKUj
Total annual inventory cost control (TC) = Σ ((DjOI)/2)Rji + (S + ns)(1/OI)
For each SKU will purchase enough to last until next order time = Qj = DjOI
Optimal order interval (OI*) =
√(2(S + N S))/iΣD R
j
j
~Order-up-to level should be enough so item lasts until next shipment arrives (order interval
+ time lead). With demand and lead time variability, need for safety stock. Fixed interval model
must have stock-out protection until next order arrives (larger amount), EOQ/ROP model needs
protection only during time lead
~Order-up-to level (Imax) = Expected demand during order interval pulse lead time + safety
stock
~When demand is variable and lead time case is constant
Imax = d̅(OI + LT) + z σ d √OI + LT
d̅ = Average demand
OI = Order interval
LT = Lead time
Z = safety factor, # of stdevs above expected demand
σ d = stdev of demand
~Q = Imax - inventory position
~Imax does not have to be re-calculated at each order time unless trend/seasonality. Avg
demand estimated using forecast of demand and stdev of demand usually estimated using
stdev of forecast error (sqrt MSE or 1.25 MAD)
~In fixed-interval model might cost less to order items at more order intervals than every
interval because holding cost may be less than line-item ordering cost
~Coordinated periodic review model: Determines common order interval OI for reviewing
every SKU and multiple of mi of OI for ordering stock keeping unit i. Inventory position of each
SKU is compared with forecast demand for next OI plus lead time plus safety stocks and if
inventory position is less, quantity that will bring inventory up to SKU’s order-up-to level is
ordered (should cover forecast demand during next mi order intervals plus lead time plus safety
stocks for next order interval plus lead time)
~To calculate optimal value: Find SKU with largest annual dollar value DiRi. For every other
√(sD R )/(D R (S + s)) and round to nearest integer greater than or
OI* = (2(S + s Σ(1/m ))/( Σm D R )
√
SKU calculate mj =
equal to 1.
k
k
j
j
j
j
j
j
~Common variation of fixed-interval/order-up-to-level model is when order is placed at
review time only if order quantity is larger than minimum Q.
Imax = d̅(OI + LT) + z σ d √OI + LT + Qmin
~Single period (news-vendor problem) method: Used for ordering perishables and other
items with limited useful life. Period for spare part is lifetime, and unsold/unused goods are not
usually brought over to next period at least not without penalty.
~Shortage cost: May include charge for loss of customer goodwill and opportunity cost of lost
sale (unrealized profit/unit). Assume Cs≽0 Cshortage = Cs = Revenue/unit - purchase cost/unit
If shortage/stock-out is item used in production/part, shortage cost is of lost production
~Excess cost: Items left over at end of period. If cost associated with disposal of excess items,
salvage value will be negative and will increase excess cost/unit. If salvage value is larger than
purchase cost, Ce will be negative. Cs + Ce > 0 because salvage value/unit must be less than
revenue/unit
Cexcess = Ce = Purchase cost/unit - Salvage value/unit
~Goal of single period model is to identify order quantity/stocking level that will minimize
long-run total excess/shortage costs
~General categories of problems to consider: Those
which demand can be approximated by continuous vs
discrete distributions
~Service level (SL): Probability demand will not exceed stocking level. SL = Cs/(Cs + Ce)
So is point in demand distribution that satisfies Probability
(demand<So) = SL
~Optimal stocking level when stocking levels are discrete is the
higher level, where cumulative probability equals or just exceeds ratio
~Multi-echelon supply chain: Demands are dependent on such so methods of single
inventory location models cannot be used in this case. Decentralized control causes total orders
from downstream facilities to be overwhelming.
~Multi-echelon control: Distribution network usually like a tree on its side. Retailers transmit
POS data to warehouse.
~Warehouse determines inventory control by looking at
demand forecasted based on total POS data, echelon lead time
equal to sum of lead time from supplier to warehouse
(warehouse lead time) and lead time of warehouse to retailer
(retailer lead time), and echelon inventory position is that total
inventory at all retailers/warehouse/en route - back orders
~Warehouse echelon level is warehouse/retailers it feeds.
~Distribution requirements planning (DRP): Planning method that determines time-phased
replenishment schedules between manufacturer’s facility and DC’s or DC and store. For
distribution planning.For each SKU, DRP starts with forecast demand at DC’s and works
backward in time offsetting for replenishment lead times.
~DRP requires forecast of demand at each DC, current inventory on hand and on order, order
quantities/batch size, lead times
~Solutions to not meeting orders due to capacity limitations: Overtime, outsourcing, putting
retailers on allocation (retailers will not receive all of order, often fair share which is bases
allocation on actual sales - inventory on hand, not order quantities)
~Inventory optimization: Determines location and optimal level on inventory in supply chain,
described as given customer-promised LT, probability distribution of demand at each inventory
location, cost of holding inventory at each location, transport times, determine committed LT and
amount of inventory to be kept at each location to maximize total inventory holding cost.
~If location does not hold inventory, committed LT has to be met within incoming
raw-materials lead time and processing item. Fixed-interval inventory used at each stacking
location. Dynamic programming (optimization method) used to solve problem.