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Ops Class

is the ability to hold, receive, store, absorb, process or transform inputs.
Output measures
‘units’ or resources exiting a process or system
Input measures
‘units’ or resources that are put into or enter the process or system
Measures of Capacity
Always a unit of measure over some time period

Restaurant: number of meals / day
Amusement Park: number of customers who visit / day
Delivery Company: number of packages delivered / hour
Customer Service Center: calls answered / hour
Auto Manufacturer: vehicles built / day

Capacity Time Measurements
Long range: >1year & strategic, some resources take a long time to source, acquire or put in place.

Intermediate range: 6-18 months, take some time to implement but there is some flexibility

Short range: <1month and tactical, easy to implement, relatively low cost adjustments

capacity cushion
purposeful reserve of capacity. It is the difference between average utilization and 100% utilization of capacity.
Capacity Cushion Measurement
= 100% ? Utilization Rate (%)
Improving Capacity
Increase Utilization
Increase up-time
Reduce changeovers and set-up times
Improve scheduling/sequencing

Improve Efficiency
Improve layout
Manage bottlenecks
Reduce or buffer variation
Increase labor productivity & flexibility

Increase Yield
Voice of the customer (VoC)
Increase process capability and control
Improve in-coming materials quality

mistake-proofing methods aimed at designing fail-safe systems that minimize human error
Voice of the customer
planning technique used to provide products, services and results that truly reflect customer requirements by translating those customer requirements into the appropriate technical requirements for each phase of project product development
Peak or maximum attainable capacity
the maximum rate that a process or system can achieve in the short term under ideal conditions with maximum effort.
Best operating level or Effective capacity
the most economically sustainable output under normal conditions for an extended time period.
Utilization rate
available time that the resource is used (how much a resource is being used) compared to best operating level

output rate/maximum capacity

the ratio of outputs over inputs (how well a resource is being used)
usable output from input
Peak vs. Best Operating Level of Capacity
Difference is due primarily to assumptions usually included in estimates of maximum capacity:

Equally skilled workers that are available and fully productive
100% yield rates; processes yield no defects
No loss of time to product changeovers or differences in products
No loss of capacity due to equipment breakdowns or worker problems
No loss of capacity for preventive maintenance or planned downtime
No lack of available orders (work) or materials (resources)
No variation in set-up or change over times

Economies of scale
occur when the average unit cost of a service or good can be reduced by spreading fixed costs over a larger volume.
Diseconomies of scale
occur when the average cost per unit increases as the volume changes
Capacity strategy
refers to several aspects of capacity management, including:
the timing of expansion or contraction
the amount of capacity cushion
the size of facilities
the linkage with marketing/business plans
the linkage with competitive priorities
Capacity Changes
Size of Changes:
Small, frequent changes
Large, infrequent changes

Timing of Changes:
Changes lag behind need
Changes in anticipation of need

strategy typically involves postponing commitments to building or expanding facilities, or acquiring equipment or personnel until after demand has already exceeded capacity

Advantage: large investments are postponed
Disadvantage: very low (or no) cushion, risk of losing sales, and possibly compromising quality, flexibility and responsiveness

This strategy fits best in fairly slow growth industries where unused capacity is expensive

Aggressive expansion
facilities where capacity exceeds projected demand in the short term.

Economies of Scale
Higher service, volume flexibility and possibly quality
Installed capacity can be much higher than actual demand
Technological obsolescence
This strategy occurs primarily in growing markets, where excess capacity allows an organization to capture market-share through first mover advantages. Good when lost sales are expensive or the firm competes on attributes of delivery.

Wait-and-See vs. Aggressive
An expansionist strategy fits well in situations where a company is in a growing industry, market-share leader, or wants to maintain a high level of service, flexibility and responsiveness.
Organizations that compete primarily based on low cost or where capacity is expensive to acquire are more likely to follow a wait-and-see strategy
Additional Capacity Strategies
NEUTRAL- a blend of Expanionist & Wait-and-See

FOLLOW THE LEADER- Action (and in some cases even Location) follow a move by the acknowledged industry leader. Example- A Pizza Hut opens in the vicinity of a McDonald’s

Accelerate the completion schedule

Make up lost time to avoid penalties
Finish earlier to earn incentives

HOW to Crash a Project
Start with the Project network
What criteria determine which Activities to Crash?
Activity MUST be on Critical Path. (WHY?)
Prioritize by Lowest Crash Cost per Week
Re-determine the Critical Path
Repeat the process
Cost to Crash per Period
Crash Cost ? Normal Cost/
Normal Time ? Crash Time
the physical items (stock) used by the firm to transform and provide goods and services to customers.
Why have Inventory?
The only good reason to have inventory beyond immediate needs is when it costs less to have it than to not have it
Independent Demand Inventory
Items for which demand is influenced by market conditions and is not related to production decisions for any other item held in stock.
Dependent Demand Inventory
Items required as components or inputs to a product or service and depends on (can be calculated from) independent demand.
Cycle Inventory
(Lot Size or Batch Inventory)
Inventory that results from the replenishment process of a fixed order quantity (Avg ? Q/2)
Safety Stock
Extra held due to uncertainties in demand or supply
Increases with higher variation in demand or supply
Should be determined by customer service level goals
Anticipation Stock
(can be Seasonal Stock)
Items stocked in anticipation of a known event
Hedge Stock (Speculative Stock)
Inventory of items for possible events
Financial reasons or supply reasons
Pipeline Inventory (In-Transit Inventory )
Items that are enroute from one location to another
Considered part of on-hand inventory, even though it is not available (Avg DL)
Work in Process (WIP)
inventory undergoing transformation
Inventory Costs
Item Cost
Holding or Carrying Holding Costs
Ordering or Set-up Cost
Stock Out Costs
Holding or Carrying Holding Costs
A percent of the per unit dollar value of inventory per unit of time (generally one year) OR fixed value/ unit
Carrying costs can vary from 10-35% annually, depending on the firm and type of industry
Ordering or Set-up Cost
Includes creating and issuing a purchase order or build order, paperwork processing, receiving, set-up, invoice payment, order tracking, etc. OR production set-up
Stock Out Costs
Costs of expediting backorder or lost business
Average Inventory
Steady-state demand (i.e. no variability)
Absolute reliability in Lead Time for replenishment
There are no “stock-outs” or backorders; all demand is satisfied
No changes in costs
Pressures for High Inventories
Ordering Cost: The cost of preparing a purchase or a production order.
Set-up Cost: The cost involved in changing over a machine to produce a different item.
Customer Service: Reduces the potential for stock-outs and backorders.
Labor and Equipment Utilization: (use with caution!)
Transportation Costs: Full truck (FTL) or container loads.
Quantity Discount: Lower price per unit for a sufficiently large order.
Pressures for Low Inventories
Inventory holding cost: the sum of the cost of capital and the variable costs of keeping items on hand, such as storage and handling, taxes, insurance, and shrinkage.
Storage and Handling
Cost of Capital (often the largest portion of holding costs)
Taxes, Insurance
‘Loss’ (shrinkage), Obsolescence and Spoilage (shelf life)
Placement (Location) of Inventories
The positioning of a firm’s inventories supports its competitive dimensions (priorities).
Inventory can be held at a single or multiple locations to meet firm and customer needs.
Service levels
Risk management
Cost considerations
Single-period inventory model (perishables)
One time purchasing decision (Example: vendor selling t-shirts at a football game)
Seeks to balance the costs of inventory overstock and under stock
Multi-period inventory models
Fixed-order quantity models
Event triggered (Example: running out of stock)
Fixed-time period models
Time triggered (Example: Monthly sales call by sales representative)
Single Period Inventory Model (Newsvendor Problem)
Newsvendor problem: a technique that determines how much inventory to order when handling perishable products or items that have a limited life span
Shortage cost: the lost profit from not being able to make a sale, plus any loss of customer goodwill
Excess cost: the different between the purchase cost of an item and its salvage or discounted value
Multi-Period Inventory Models
Fixed Order Quantity or Q System
Quantity is fixed
Order can be placed at any time

Periodic Order Quantity or P System
Any quantity (including none) can be ordered
Order interval is fixed

Key Differences single/Multi Inventory
To use the fixed-order quantity model, the inventory remaining must be continually monitored
In a fixed-time period model, counting takes place only at the review period
The fixed-time period model
Has a larger average inventory
Favors more expensive items
Is more appropriate for important items
Requires more time to maintain
Fixed-Order Quantity Models
Demand for the product is constant and uniform throughout the period
Lead time (time from ordering to receipt) is constant
Price per unit of product is constant
Inventory holding cost is based on average inventory
Ordering or setup costs are constant
All demands for the product will be satisfied
Economic Order Quantity (EOQ)
D = Annual demand or usage of product (units/year§)
S = The ordering or set-up cost ($/order)
H = Holding cost one unit per year§ (or C*h)
C = Average price or value ($ per unit)
h = Annual holding rate§ (as a % of product cost or value)
Q = Order quantity, batch or lot size (units)

Ordering Cost = (D/Q)*S
Holding Cost = (Q/2)*H or (Q/2)*(C*h)
Total Cost (IC) = (D/Q)*S + (Q/2)*H + DC (no SS at this point)

Fill Rate
Common measure of the customer service performance of inventory
Often presented as the percentage of units available when requested by the customer
A 96% Fill Rate means that 4% of requested units were unavailable when ordered by the customer

Trade-off between service level and costs
Theoretically, 100% service is impossible
Each additional unit of safety stock earns a diminishing return on service level improvement
Not all customers are equally sensitive to stock-outs
Not all stock outs are equally expensive
Not all items are equally variable in demand or supply

Price Break Models
Price varies with Order size
We choose the correct order Quantity based on lowest Total Cost, which may NOT always = the greatest discount
Inventory accuracy
refers to how well the inventory records agree with physical count
Cycle counting
a physical inventory-taking technique in which inventory is counted on a frequent basis rather than once or twice a year
External Causes of Supply Chain Disruption
Variable delivery lead time
Incorrect shipment quantities
Volume changes
Service and product mix changes
Internal Causes of Supply Chain Disruption
Service or product promotions
Information errors
New service or product introductions
Engineering changes
Internally generated shortages
bullwhip effect
occurs when distorted product-demand information ripples from one partner to the next throughout the supply chain
Tactics for Reducing the Bullwhip Effect
Design to deal with uncertainty
Appropriate when a firm cannot influence its customers or other firms

Seek to reduce uncertainty
Appropriate when other partners’ actions can be influenced

Safety Stock: use of inventory to protect from unexpected variations in demand or supply
Safety Lead Time: increase of the delivery lead time that is promised to the customers in order to cope with unexpected internal delays
Safety Capacity: Idle capacity that accomodate unplanned changes in orders.
Delay of an action until associated uncertainties are resolved.
Info Sharing
Uncertainty is reduced when forecasts, sales data, production schedules and future plans are shared.
Going beyond information sharing, coordination requires commitment to certain actions
Efficient Supply Chain
focus on cost, economies of scale and higher capacity utilization
DemandUncertainty:: Low Supply Uncertainty: Low
Risk-hedging Supply Chain
pooling/sharing risk, sharing inventory, real-time data is needed
Demand Uncertainty: Low Supply Uncertainty:: High
Responsive Supply Chain
flexible to changing customer needs

Demand Uncertainty: High Supply Uncertainty: Low

Agile Supply Chain
combine risk hedging and responsiveness, respond to front-end changes with less back-end disruptions

Demand Uncertainty: High Supply Uncertainty: High

Why Globalize?
It offers access to cheaper labor and operational costs from locating production facilities overseas.
Locating facilities in another country allows companies to get access to the knowledge and skills of people in that country.
Certain parts of the world are rich in natural resources.
Globalization allows companies access to new markets.
Facilities at strategic international locations can reduce logistics and distribution costs.
Internationally located facilities take advantage of tax and financial incentives provided by local governments.
International locations may have political and industry-specific reasons behind the choice.
Challenges of Going Global
Time differences
Cultural differences
Lead time
Hidden costs
Language differences
Returns and repairs of defective products
Political risks
Differences in units of measurement
Globalized SCM Functions
Maintenance and Monitoring
Logistics and Distribution Services
Customer Service and Support
Knowledge-Based Processes
Product Development and Innovation
a supply chain strategy that involves moving processes to another country.
Factors that influence the offshoring decision include:
Comparative labor costs
Logistics costs
Labor Laws and Unions
Skill shortages
Tariffs and Taxes
Pitfalls of offshoring include:
Pulling the plug too quickly by not making a good- faith effort to fix the existing process
Technology transfer
Difficulties integrating processes
Make-or-buy decisions
Make = more integration
Backward integration: acquisition of upstream entities
Forward integration: acquisition of downstream channels

Buy = more outsourcing
Outsourcing of non-core processes allows a firm to concentrate efforts on those processes it does best
Skills and knowledge of the outsourced process are often lost and difficult to bring back into the firm

SCM Metrics
Business Cycle or Cash-to-Cash Cycle
Total Delivered Cost
Inventory Measures
average aggregate inventory value
weeks/days/hours of supply
inventory turnover
Process Measures
customer relationship
order fulfillment
supplier relationship
receiving, storing, shipping and moving the right stuff to the right places, in the right quantity, at the right time, at the right cost
3rd Party Logistics (3PL): using another company to do your logistics (outsourcing)
Service Location Strategy
Usually lower investment than manufacturing
Proximity and purchasing power of customer drawing area
Compatibility with local demographics and with competition and complementary services
Uniqueness of offering (order winners)
Physical qualities of facilities and area
Ease of access (customers and employees)
Process Capability
The ability of an in-control process to meet the design specification of a product/service
Consists of two bits of information:
The width or spread of the process in comparison to the allowable spread (Cp)
The ‘centeredness’ of the process on the nominal or target value (Cpk)
Process Distributions
A process is said to be in statistical control when the location, spread, and shape of its distribution does not change over time.
After the process is in statistical control, managers use SPC procedures to detect the onset of assignable causes so that they can be eliminated.
Six Sigma Quality
a set of principles and practices whose core ideas include understanding customer needs, doing things right the first time, and striving for continuous improvement 3.4 per million.
Conformance to customer specifications and expectations.

Quality is defined by the customer.
Quality has a key role in customer perception of value.

Customer Loyalty and Quality
The cost of acquiring a new customer is much higher than the cost of retaining a current one (up to x10).
Customer retention results from the customer having good experiences.
A positive relationship can lead to more revenue.
As the customer becomes more loyal, retention costs less.
A very loyal customer may become a company advocate.
WHERE does this Profit come from?
Better use of Raw Materials (yield) through less scrap or waste
Less failure (internal, external) and the resulting cost consequences
Less downtime (ongoing maintenance is a critical element of TQM)
Better processes (reduced set-up time)
Less inspection
Potential for increased sales
Total Quality Management (TQM
“An effective system for integrating the quality development, quality maintenance, and quality improvement efforts of the various groups in an organization so as to enable production and service at the most economical levels which allow for full customer satisfaction.”
—Armand Fiegenbaum

Organizational management for excellence on the factors that are important to customers:
Careful design of products & services
Managing systems & processes

Malcolm Baldrige National Quality Award (MBNQA)
Awarded to high-performing organizations within the United States (established in 1987)
Small business
Key Elements for TQM:
Quality is defined by the customer
Management is ultimately responsible for quality
Continuous improvement (CI)
Employee involvement
Prevention, not inspection
Drive out variability for process control (SPC)
Remove barriers that prevent quality
An ongoing process, not a one time program
Zero defects or cost/benefit analysis
Team effort, both cross-functional & -organizational
Quality Specifications
Design Quality
Conformance Quality
Quality at the source
Dimensions of quality
Dimensions of Product Quality
What are the desirable operating characteristics of the product?
What additional characteristics are included or available?
Is the product dependable? Does it accomplish what it promises? Does it work when needed?
How long will the product last? How ‘rough’ can it be used?
Can the product be easily and inexpensively repaired?
Dimensions of Both Product & Service Quality
Does the product satisfy subjective requirements?
Is the interaction between the customer and the product provider pleasant and appropriate?
What does information on past performance say about the company?
Does the business keep its promises?
Does it promptly respond to the needs of its customers?
Do the physical facilities, equipment, and written materials show care and attention?
Dimensions of Service Quality
Can the employees generate customer trust and confidence?
Are employees approachable and sensitive to individual customers? Do they seem to care?
Can there be TOO MUCH Quality?
Products or Services over-designed for their intended use (customers won’t pay for it!)
Unnecessarily high costs = lost business
Capability- does operations (for either goods or services) have the capability to achieve such high quality?
Quality Affects Profitability
If a business provides too much quality, beyond what customers value, costs may be higher than necessary, and/or sales may be lost.
The perception of value, or high quality for the price, improves profitability in several ways:
+ Creates more demand
+ Earns customer loyalty
+ May command a higher price
+ Savings from reduced scrap, rework, warranty claims
An Historical Viewpoint Quality
Early Thinking
Improving the QUALITY implies increasing costs (particularly of Prevention and Appraisal).

Current Thinking
But what if improving QUALITY also improved processes (Deming’s view)? This allows Quality to go up AND costs to go down!

Costs of Quality: Four Sources
Prevention Costs
Costs associated with preventing defects and limiting failure and appraisal costs (e.g., training, improvement projects, data gathering, analysis)

Appraisal Costs
Costs associated with discovering the condition of products and raw materials (e.g., inspection)

Internal Failure Costs
Costs from defects found before delivery to the customer (e.g., rework, scrap)

External Failure Costs
Costs associated with defects found after delivery to customer (e.g., warranty, recall)

Six Sigma Quality
A philosophy and set of methods companies use to eliminate defects in their products and processes
Evolution of “Total Quality Management” movement
Adopted by General Electric, Motorola, Cardinal Health, Riverside Hospital, U.S. Military, etc., as a means of focusing effort on quality using a methodological approach
Overall focus of the methodology is to understand and achieve what the customer wants
Seeks to reduce variation in the processes that lead to product defects
DPMO (Defects Per Million Opportunities)
# of Observed Defects/
# of Opportunities for Defect
X 1,000,000 = DPMO
Goals of SIX SIGMA
To reduce process variation to the point that no more than 3.4 defects per million opportunities (DPMO) parts produced in a high volume manufacturing or service environment
This is equivalent to a quality objective of 99.9997%

Organizations that succeed in implementing these programs can expect to see meaningful profit improvement.

When 99.9% Quality is Not Enough
Two million documents would be lost by IRS each year
20,000 incorrect drug prescriptions written per year
17,000 unsafe cars built each year
1,314 phone calls would be misrouted each day
12 babies would be given to the wrong parents each day
Two plane landings daily at O’Hare would be unsafe
107 incorrect medical procedures performed today
22,000 checks would be deducted from the wrong bank account in the next hour
18,322 pieces of mail mishandled in the next hour
When GOOD quality gets better…
Defects at 99.9997% (or 6.0 Sigma standards) =

MAIL DELIVERY- 7 lost articles/ hour
DRINKING WATER- 2 minutes/yr of unsafe drinking water
SURGERY- 2 incorrect procedures/ week
AIR TRAVEL- 1 abnormal landing every 5 years

Six Sigma: Methods and Tools
Six Sigma is about reducing variation to improve quality
There are methods:
DMAIC, PDCA, CI, Kaizen, etc.
There are tools:
Flowcharts, Run charts, Pareto charts, Check-sheets, Cause and Effect Diagrams, Control charts, etc.
PDCA Cycle
Plan, Do, Check, Act
Define, Measure, Analyze, Improve, and Control (DMAIC)
The DMAIC Project Process Define
What are we trying to achieve, why, for who?
What is the business case and project return?
Is this Realistic, Understandable, Measurable, Believable and Actionable (RUMBA)?
What are the CTQs?
The DMAIC Project Process Measure
What are the current processes?
How are they measured?
How are we currently performing on CTQs
The DMAIC Project Process Analyze
Where are the problems with our current performance?
What are the root causes [Y=f(x)]?
The DMAIC Project Process Improve
What should change to make improvements?
Effect on CTQs?
The DMAIC Project Process Control
How are improvements sustained?
Are we measuring performance against expectations?
Did we capture the learnings from this project?
Pareto Analysis
A variant of Bar Diagram that ranks quality problems so that most important can be identified
Process Flowchart or Value Stream Map
Current State
Run Chart
Can be used to identify the presence of variation. A plot of measurements across time.
Check Sheet
Useful for gathering histogram data
Count of occurrences
Data Analysis Example
Hotel Guest Complaints by Category
Cause & Effect Diagram (or “Fishbone”)
Can be used to systematically track backwards to find a possible cause of a quality problem (or effect)
Y = f (x)
Failure Mode and Effect Analysis (FMEA)
TECHNIQUE. analytical procedure in which each potential failure mode in every component of a product is analyzed to determine its effect on the reliability of that component and, by itself or in combination with other possible failure modes, on the reliability of the product or system and on the required function of the component; or the examination of a product for all was that a failure may occur. for each potential failure, an estimate is made of its effect on the total system and ite impact.
ISO 9000
International consensus on
good quality management practices
What the organization does to fulfill:
the customer’s quality requirements, and
applicable regulatory requirements, while aiming to
enhance customer satisfaction, and
achieve continual improvement of its performance in pursuit of these objectives.
ISO 14000
What the organization does to meet environmental compliance:
Many of the same basics as ISO 9000
Emergency and disaster preparedness
Environmental policy
ISO 14001
ISO 14001 specifies the requirements
ID and control environmental impact of activities and outputs
Continuously improve environmental performance
Systematic approach to setting, achieving and tracking performance
ISO 14004 provides guidelines
Internal validation to management and employees that the organization is environmental responsible
External validation to stakeholders that organization complies to regulations
Concept of Variation
outputs that should be the same to be different from each other
Reduction in Variation
Variability in processes, inputs and outputs makes it difficult to predict what the next item processed will look like.
Causes of Variation
Two basic categories of variation in output include common causes and assignable causes.

Common, Natural or Random Causes:

Assignable or Special Causes:

AlwaysRain Irrigation, Inc., would like to determine capacity requirements for the next four years. Currently two production lines are in place for making bronze and plastic sprinklers. Three types of sprinklers are available in both bronze and plastic: 90-degree nozzle sprinklers, 180-degree nozzle sprinklers, and 360-degree nozzle sprinklers. Management has forecast demand for the next four years as follows:


1 (IN 000s) 2 (IN 000s) 3 (IN 000s) 4 (IN 000s)
Plastic 90 32 44 55 56
Plastic 180 15 16 17 18
Plastic 360 50 55 64 67
Bronze 90 7 8 9 10
Bronze 180 3 4 5 6
Bronze 360 11 12 15 18

Both production lines can produce all the different types of nozzles. The bronze machines needed for the bronze sprinklers require two operators and can produce up to 12,000 sprinklers. The plastic injection molding machine needed for the plastic sprinklers requires four operators and can produce up to 200,000 sprinklers. Three bronze machines and only one injection molding machine are available.

What are the capacity requirements for the next four years? (Assume that there is no learning.) (Round your answers to 2 decimal places. Omit the “%” sign in your response.)

In anticipation of the ad campaign, AlwaysRain bought an additional bronze machine. Will this be enough to ensure that enough capacity is available?

Plastic Year 1 Year 2 Year 3 Year 4
Demand-r plastic sprinklers 97 115 136 141
Percentage- Used capacity used 48.5% 57.5% 68.0% 70.5%
Machine requirements .485 .575 .680 .705
Labor requirements 1.94 2.30 2.72 2.82

Bronze Year 1 Year 2 Year 3 Year 4
Demand- bronze sprinklers 21 24 29 34
Percentage- Used capacity 58.3% 66.7% 80.6% 94.4%
Machine requirements 1.75 2.00 2.42 2.83
Labor requirements 3.50 4.00 4.84 5.66

It is obvious that not enough capacity is available after year two to meet the increased demand. AlwaysRain will have to consider purchasing additional machines for the bronze operations.

Buckeye Sandal needs your help to develop a capacity plan for its manufacturing operations. The operations run for two eight-hour shifts, five days per week and 50 weeks per year. Experience has shown that a capacity cushion of 5% will be adequate.
Product Processing Time Set-up Time Batch Size Demand per Year







a. Using the above Table of product information, how many machines will be needed?
b. Marketing asks for an increased cushion of 10% in order to allow for more rush shipments.
Does this have any effect of the machine requirements?

b. Redo the calculation in part a. by changing the Capacity Cushion to 0.1 instead of 0.05.
This changes the value of the denominator to 3,600 and results in a solution of 4.05
Machines, which would be rounded UP to 5. From a practical standpoint it would be likely
that Buckeye Sandal operates with four machines, which is equivalent to an approximate
Cushion of 8.8% using overtime or other means to make up any shortfall.

a. The number of hours of operation per year, N, is N = (2 shifts/day)(8hours/shifts)(250 days/machine-year) = 4,000 hours/machine-year

The number of machines required, M, is the sum of machine-hour requirements for all three products divided by the number of productive hours available for one machine:

[Dp + (D/Q)s]men + [Dp + (D/Q)s]women + [Dp + (Dp + (D/Q)s]children
M =
N [1 – (C/100)]

[80,000(0.05) + (80,000/240)0.5] + [60,000(0.10) + (60,000/180)2.2]
+ [120,000(0.02) + (120,000/360)3.8]
4,000[1 – (5/100)]

14,567 hours/year
= = 3.83 or 4 machines
3,800 hours/machine – year

b. Redo the calculation in part a. by changing the Capacity Cushion to 0.1 instead of 0.05.
This changes the value of the denominator to 3,600 and results in a solution of 4.05
Machines, which would be rounded UP to 5. From a practical standpoint it would be likely
that Buckeye Sandal operates with four machines, which is equivalent to an approximate
Cushion of 8.8% using overtime or other means to make up any shortfall.

or the data shown, reduce the project completion time by three weeks. Assume a linear cost per week shortened.














Ray’s Satellite Emporium wishes to determine the best order size for its best-selling satellite dish (model TS111). Ray has estimated the annual demand for this model at 1,000 units. His cost to carry one unit is $100 per year per unit, and he has estimated that each order costs $25 to place. Using the EOQ model, how many should Ray order each time? (Round your answer to the nearest whole number.)
Qopt= 2ds/h = 2(1000)25/100 = 22.36 = rounded down = 22
Charlie’s Pizza orders all of its pepperoni, olives, anchovies, and mozzarella cheese to be shipped directly from Italy. An American distributor stops by every four weeks to take orders. Because the orders are shipped directly from Italy, they take three weeks to arrive.
Charlie’s Pizza uses an average of 150 pounds of pepperoni each week, with a standard deviation of 30 pounds. Charlie’s prides itself on offering only the best-quality ingredients and a high level of service, so it wants to ensure a 98 percent probability of not stocking out on pepperoni. Assume that the sales representative just walked in the door and there are currently 500 pounds of pepperoni in the walk-in cooler. How many pounds of pepperoni would you order? (Round your answer to the nearest whole number.)
Service level P = .98, = 150, T = 4 weeks, L = 3 weeks, o = 30 per week, and I =500 lbs

From Standard normal distribution, z = 2.05

q= d (t+l) + z (square root of T+L)(o)^2 – I
150(4+3) + 2.05(79.4) – 500 = 712.77 713 pounds

Given the following information, formulate an inventory management system. The item is demanded 50 weeks a year.

Item cost $ 10.00 Average demand 515 per week
Order cost $ 250.00 Standard deviation of weekly demand 25 per week
Annual holding cost (%) 33% of item cost Lead time 1 week
Annual demand 25,750 Service probability 95%

Determine the order quantity and reorder point. (Round your answers to the nearest whole number.)

Order quantity
Reorder point

Determine the annual holding and order costs. (Round your answers to 2 decimal places. Omit the “$” sign in your response.)

Holding cost $
Ordering cost $

If a price break of $50 per order was offered for purchase quantities of over 2,000, how much would you save annually? (Round your answer to 2 decimal places. Omit the “$” sign in your response.)

Q= square root (2DS/H) = 2(25750)250/ .33(10) = 1975.23

From Standard normal distribution, z = 1.64
= 515(1) + (1.64)25 = 556
b. Holding cost = Q/2 (H) = 1975/2 (.33)10 = $3,258.75
Ordering cost =D/Q(S) = 25750/1975 = $3,259.49

Total annual cost with discount is $6,518.75 – 50(25750/2000) = $5,875.00, without discount it is $6,518.24. Therefore, the savings would be $643.24 for the year.

C-Spec, Inc., is attempting to determine whether an existing machine is capable of milling an engine part that has a key specification of 4 ± .003 inches. After a trial run on this machine, C-Spec has determined that the machine has a sample mean of 4.001 inches with a standard deviation of .002 inch.
4.003-4.001/ 3(.002) = .333 4.001-3.997/3(.002) = .667

No, the machine is not capable of producing the part at the desired quality level.

The McDonald’s fast-food restaurant on campus sells an average of 4,000 quarter-pound hamburgers each week. Hamburger patties are resupplied twice a week, and on average the store has 350 pounds of hamburger in stock. Assume that the hamburger costs $1.00 a pound.

What is the inventory turnover for the hamburger patties? (Round your answer to 2 decimal places.)

Inventory turnover per year

On average, how many days of supply are on hand? (Round your answer to 2 decimal places.)

Days of supply days

Inventory Turnover= (Cost of Goods Sold)/(Average Aggregate Inventory Value)
inventory Turnover= (1.00*1000* 52)/((350))


The problem tells us that we sell 4,000 QUARTER pound burgers a week, therefore we sell 1,000 pounds a week, and each pound of hamburger costs $1.00. The problem also tells us that on average, the store has 350 pounds of inventory on hand. By dividing the Cost of Goods Sold by Average aggregate Inventory Value, We can figure the Inventory Turns. This means that their inventory turns 148.6 times a year.

Weeks of supply= (Average aggregate inventory value)/(Cost of goods sold)*52

Weeks of supply= 350/$52,000 * 52 =.35

D = Annual demand or usage of product
Annual demand or usage of product (units/year§)
S =
The ordering or set-up cost ($/order)
H =
Holding cost one unit per year§ (or C*h)
C =
verage price or value ($ per unit)
h =
Annual holding rate§ (as a % of product cost or value)
Q =
Order quantity, batch or lot size (units)
a unique, temporary endeavor with a specific objective to be met within prescribed time, budget and resource limitations made up of an interrelated set of activities that have a definite starting and ending point.
Slack is the difference, if any, between the earliest start and latest start times (or the earliest finish and latest finish times).
(S = LS – ES or S = LF – EF)
Project Management Tools and Techniques
The discipline of project management has available a number of tools and procedures that enable the project team to organize its work to meet the constraints:
Statement of Work
Work Breakdown Structure
Gantt Chart
Network Diagram
Critical Path Method (CPM)
Cost and Time Tradeoff Analysis (Crashing)
Program Evaluation and Review Technique (PERT)
Resource Management
Pure Project Organizational Structure – Pros
The project manager has full authority over the project.
All members of the project are directly responsible to the Project Manager.
Lines of communication are shortened.
Strong and separate identity of its own -React rapidly.
Unity of command; each subordinate has only one boss.
Pure Project Organizational Structure – Cons
Need more staffing.
To ensure access to technological knowledge and skills the PM may stockpile equipment and technical assistance in order to be certain that it will be available.
Team members can fall behind in other areas of their technical expertise.
PROJECTITIS – a “we versus they” divisiveness grows. Friendly rivalry may become bitter competition.
Life after the project uncertain.
Benefits of Project Management
Achievement of business goals and objectives
Completion of the project by making the most effective use of time, resources, and dollars
Timely information for decision making
Continuous improvement from lessons learned
Support for the quality systems
Common process for everyone involved
Project Goals
Each project must meet the three goals of:
Cost of resources
Time schedule
Characteristics of a Project
Numerous sequential and interrelated activities
Finite with definite beginning and end dates
Unique set of events
Limited resources and budget
Many people are involved, often cross functional
Specific end product or service must result
Methods for handling problems during execution
The earliest you can complete an activity — determined by adding the activity time to the earliest start time (ES + t).
The latest an activity can end without delaying the project. It is the same as the Latest Start time of the next activity. If there are two or more subsequent activities, this time is the same as the earliest of those “Latest Start” times.
Determined by the earliest finish time of the precedent activity. If there are two or more precedent activities, this time is the same as precedent activity with the latest “Earliest Finish” time.
This is the latest an activity can start, without delaying the project. Latest Finish time minus the activity time (LF – t)
Activity Slack
Maximum length of time an activity can be delayed without impacting the entire project completion date.
Activities on the critical path have zero slack.
Long delays of non-critical path activities can cause the critical path to change.
process mean
? =
process standard deviation
Cost of Goods Sold
Finished Goods Inventory
Work in Process
SC Performance
avg. % of orders filled by requested delivery date

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