Operations Management - Practice Quizzes - Final Exam Study
If I sell items for $100 each after purchasing them from my supplier at $50 each, what is the Net Marginal Benefit (also known as the cost of under-ordering) if I ignore all other effects of stocking out?
$100 - $50 This is simply the lost contribution since a sale was not made that could have been made.
If I sell items for $100 each after purchasing them from my supplier at $50 each, what is the Net Marginal Benefit (also known as the cost of under-ordering) if stocking out damages my reputation and I estimate this damage to be $100?
$100 - $50 + $100 Damage to customer relationships should be added into the calculation even if the value is hard to know exactly.
Since the Mean and Variance of an exponential distribution are the same, what is the Coefficient of Variation for an exponential distribution?
1 COV is the Mean divided by the Variance.
Consider the same process from Question 6 but assume that on average, an hour of waiting also takes place. What is the average flow time for this process?
1 hour longer than in question 6 Flow times do include waiting times as part of their definition.
If I buy 364 units per year at a cost of C = $4 each, H is 25% * C, S is $10, and the order size Q = 91. What is my total annual cost, TC?
364 * $4 + 91/2 * $1 + 364/91 * $10 If TC = (D/Q) * S + (Q/2) * h, where TC is total cost, D is annual demand, Q is the order quantity, S is the setup cost, and h is the holding cost in dollars/unit/year
If this process is exactly meeting demand, what is the takt time of this process?
4 minutes The takt time is the maximum time that a resource can spend without falling behind demand. If capacity matches demand now, the takt time must the 4 minutes.
Consider a 2-step process (Steps 1 and 2) involving 2 resources (Resources A and B). Resource A is involved for 2 minutes during Step 1 and 2 minutes in Step 2. What is the unit load of Resource A?
4 minutes The unit load is how much time from the Resource is occupied to process one unit, regardless of how many steps are involved.
If demand is written as 10 units per hour, what is the utilization of Resource A?
4/6 This can be done in two ways. Busy time to meet demand divided by available time. For example (10 units * 4 minutes per unit) / 60 minutes = 40/60 = 4/6. It can also be time to process a unit (4 minutes) divided by time between arrivals (6 minutes).
Consider a process with steps A B C D where each step takes 1 hour of processing time and the average waiting time within the process is an addition 4 hours. What is the flow-time efficiency?
4/8 Flow time efficiency is theoretical flow time / average flow time = 4/(4 + 4).
Consider a process involving 2 subcomponents that follow 2 different paths. One takes 4 hours and the other takes 5 hours. What is the theoretical flow time?
5 hours The longer path is also the critical path and defines flow time.
Consider the same process with one change. Assume that the two paths correspond to two components that must be combined (in a step that takes no time) to make the desired output. What is the critical path?
A - B - C - D The longest path and the critical path mean the same thing here because both paths must be completed to finish the job.
Consider a flowchart that shows two paths. One includes steps A B C D and the other path includes steps A C E F. Steps A, C, and E take 1 hour and steps B, D, and F take 2 hours. The longest path is:
A - B - C - D This path length is 1 + 2 + 1 + 2 = 6 hours. A - B - C - D - E - F would be longer but this path is not used for the process so it is not relevant
To implement a Pull system you need:
A means to signal when an action needs to take place This relates to the use of kanbans to signal when work needs to begin at each step.
Dedicating part of a work area to a single product and organizing material, people, and information flows around that product is known as what?
A plant within a plant This is related to the notion of focus because it allows a part of the operation to focus on one thing.
If the average time between arrivals is 10 minutes, what is the arrival rate?
All of the above Changing units of measurement does not change the rate. All of these are equivalent.
The ordering cost, S should include:
All of the above Delivery fees Administrative fees Cost if inspection at arrival Cost of labor that unloads the delivery truck Ordering cost should include all expenses associated with placing and receiving the order whether these are direct or indirect costs.
As the COV of arrival times (Ci) increases what happens to average queue length (L)?
As Ci rises L rises An increase in variability for either the arrival or service process increases L.
If I am willing to assume that demand is normally distributed with a mean of 1000 units and I want to guarantee that I never stock out I should order:
Cannot be done Technically speaking there is really no such thing as normally distributed demand because the range on a normal distribution is from negative to positive infinity.
The goal of Lean operations is:
Continuous flow One main idea is getting continuous flow without the loss of flexibility
To maximize expected profit taking the cost of under-ordering (Cu) and the cost of over-ordering (Co) into account I find what ratio?
Cu / (Cu + Co) Note that this is exactly the same as MB / (MB + MC) in the text.
If TC = Q/2 * H + D/Q * S then the second derivative of TC with respect to Q is:
DS/Q^3 This is just the derivative of the derivative
If the EOQ is 90 and I have only two options - order 80 or order 100 I know that:
Don't have enough information here to know for sure Holding cost is a linear function of Q but ordering cost is not. Therefore, it is not necessarily true that TC at 80 is greater than, equal to, or less than TC at 100.
If we add a unit of Resource 1, what happens to takt time?
Drops to 3 minutes The takt time will be the greater of the unit loads for the 2 resources. Max(4/2, 3) = 3 minutes as defined by Resource B
If we order 90 units in each order, demand is fixed, and it always takes exactly 2 weeks to get each order the average inventory level will be ...
Equal to 45 units The lead time does not matter as long as demand and lead times are both fixed.
Controlling inventory levels helps us to indirectly control what?
Flow time and flow rate This is a direct consequence of Little's Law
If my demand forecast for the next period is 1000 units and I can only place one order to serve that demand I should:
Get more information You would like to know how good your forecast is, what happens if you order too many, and what happens if you order too few.
After I find the resource with the greatest unit load, I can increase capacity by:
Getting more of that resource Since the capacity of a resource pool is increased when the pool is larger, getting more in the pool will increase capacity.
If Throughput is 10 units per hour and the theoretical flow time is 1 hour the inventory level will be:
Greater than or equal to 10 units 10 units is the Theoretical Inventory and can be achieved if actual capacity equals theoretical capacity.
If TC = Q/2 * H + D/Q * S then the derivative of TC with respect to Q is:
H/2 - DS/Q^2 Remember that 1/Q is the same as Q-1. This explains why the negative sign enters into the derivative. If TC = (D/Q) * S + (Q/2) * h,
If TC = Q/2 * H + D/Q * S + P * D where P is the purchase price, then the derivative of TC with respect to Q is:
H/2 - DS/Q^2 Since P * D is independent of Q it does not change the derivative with respect to Q.
Consider a grocery store. If H is the cost to hold a unit in inventory for one year in the store how does H compare for milk (HM) compared to apples (HA) if they have the same procurement cost per unit?
HM > HA Both items will spoil, but milk spoils quicker, costs more to keep cool, and takes up more space.
Consider a grocery store. If H is the cost to hold a unit in inventory for one year in the store, how does H for toilet paper (HTP) compare to H for apples (HA)? Assume that they both have the same procurement cost per unit.
HTP < HA Apples spoil while toilet paper does not, thus it costs more to store apples.
Under the assumptions of the basic EOQ approach, to find the best order size when per unit price is fixed I need to balance
Holding cost and ordering cost This assumes that the purchase price does not change if the order size changes.
A process with rigid, fixed routes and specialized resources that produces only a narrow set of tasks repeatedly to produce discrete units of output is probably a;
Line Flow Process Remember a continuous flow process as defined in the text refers to outputs that flow continuously, meaning that 1.1 units can be produced.
If the expected marginal benefit is the marginal benefit times the probability of receiving this benefit, the expected marginal benefit equals what?
MB * Prob(Demand >= Q) The benefit if realized for all scenarios in which demand is as least as great at Q.
If the expected marginal cost is the marginal cost times the probability of experiencing this cost, the expected marginal cost equals what?
MC * Prob(Demand < Q) The benefit if realized for all scenarios in which demand is as least as great at Q.
What is the theoretical flow time of this process?
The same as in question 6 Theoretical flow times do not include waiting times.
When considering TC we probably want to:
Minimize it
If TC = Q/2 * H + D/Q * S then the value of Q that makes the first derivative equal to 0 does what?
Minimizes TC (total cost) Since the 2nd derivative is positive we know that the extreme point minimizes the function.
If I only accommodate a finite number of customers waiting, what happens if I reduce the size of this buffer?
More customers will be blocked In this context blocked means customers cannot get into the system. Thus, fewer customers will be served and more will be blocked.
Given exactly 1 unit of each resource, what is the maximum sustainable throughput rate for this process?
One job every 4 minutes If capacity matches demand, takt time defines capacity.
If the EOQ is 90 but the most I can order is 80 I should:
Order 80 Since the TC function is convex, the further I am below the EOQ, the higher my total cost
If I am willing to assume that demand is uniformly distributed with a mean of 1000 units and a range from 0 to 2000 units, and I want to guarantee that I never stock out I should order:
Order more than 1000 units The only way to guarantee that I never stock out would be to order 2000 units. This may be economically silly, but it is possible.
If I place an order from my supplier once per week regardless of demand I have:
Periodic review system This is a system in which I review my inventory level once per period and I define a period to be 1 week.
To maximize expected profit taking the cost of under-ordering (Cu) and the cost of over-ordering (Co) into account place an order for an amount Q such that:
Prob(Demand <= Q) = Cu / (Cu + Co) Note that this is the probability of satisfying realized demand.
If demand is realized at rate D and we have received an order of Q units just as our inventory level hit 0 how long will we have a positive level of inventory if no additional order is placed?
Q/D Q units divided by D units per year gives a result in which units cancels out leaving us with an amount of time.
If we choose an ROP which equals demand during the lead time and demand is uniformly distributed, how often will I stock out before the order arrives?
Roughly ½ the time Means and variances nicely add when variables are normal.
If demand drops to 10 units per hour, what happens to capacity?
Stays the same Capacity is not a function of demand. It is unchanged by a drop or a rise in demand. To change capacity you have to do something to the process.
Gus wants to purchase the most popular book on the market right now and he wants it to look exactly like the copy that everyone else has. What type of production process makes sense for this product?
The flow shop is almost always more efficient when producing a standardized product at high volumes.
Assume I have a process in which I occasionally make mistakes. When this happens I have to spend twice as much time to produce the desired output. Assume that I also have to wait for supplies sometimes from another step. If these two things are true I will see:
Throughput < Capacity < Theoretical Capacity If there are any mistakes, Throughput will be less than Capacity. If the resources are not being used well, Capacity < Theoretical Capacity.
Select the action that adds value.
Wastes do not add value, including production of defects, excess production, or producing to put into inventory.
A process must have:
all of the above a single path from start to finish multiple paths of the same length a different path for each job the same number of jobs on each path Remember a process may not be well designed, so any of these are possible but none are guaranteed.
Managing capacity for service delivery is critical because:
all of the above services cannot be stored for later consumption customers often have to wait while the service is being delivered different customers have different expectations about how long a service should take some services are highly time sensitive
If throughput is stated in jobs per hour, the reciprocal of that defines:
all of the above takt time for the process the maximum amount of time a resource can be busy per unit without slowing down the process hours per job Remember that throughput is a rate, thus its reciprocal is stated in time per job.
Little's law applies to:
any flows that are stable for the process defined The key point here is that the process must be stable regarding the flow unit being considered.
In a stable process:
average inflow rate equals average outflow rate This must be true over the "long run" but it may not be true over a shorter span of time. average inflow rate will equal throughput Stable means average inflow rate = average outflow rate = throughput
Little's Law states that:
average inventory will equal average throughput times average flow time Little's law applies to averages but may not hold perfectly at any instant.
Representing a process graphically by indicating inputs, outputs, and activities connected in a way that shows the sequence of steps is creating a:
flow chart This is the working definition of a flowchart as it is commonly defined in this text. Note that other texts may give this a slightly different name.
The number of flow units that pass through the process per unit time is the:
flow rate
Job shops and flow shops will differ along several dimensions, including:
flow shops will have all items travel along the same path Flow shops are laid out based on the steps involved. Consequently, the work follows a common path.
The amount of time a typical flow unit spends within the process boundaries is the:
flow time
Consider a loan approval process at the JHU credit union. A sample of 50 applications was taken and the completion times and start times were recorded for each application. This can be used to estimate:
flow time Note that this may not accurately give the flow rate because we did not assume that all jobs were measured.
Scottish economist Adam Smith proposed that the division of labor and functional specialization would lead to:
improvements in cost and quality at the expense of flexibility Keep in mind here that he was not defining quality in terms of individual preferences here.
The number of flow units within the process boundaries at any point in time is the:
inventory Some works may call this the work-in-process inventory to differentiate it from raw material or finished good inventory.
Considering the same process from question 1, the manager decides to look over the process once per hour over a 3-day period and count how many jobs are within the system at each point in time. This can be used to estimate:
inventory This will estimate average inventory. However, this assumes that the time period in question is representative of the norm.
If average flow time is 1 week, what do we know about inventory turns?
inventory turns over once per week Inventory turns is the reciprocal of average flow time
Job shops and flow shops will differ along several dimensions, including:
job shops will have different items travel along different paths In a job shop the demands of the specific job can determine the path through the workspace
Process effectiveness and process efficiency must be:
none of the above Any of these answers can be true in specific settings but none "must" be true.
Gus Toomer buys books from the Hopkins bookstore. Gus defines quality as " how large the book is and how pretty the cover is." Gus is wrong because:
none of the above There is no universal definition of quality, so it can vary from one customer to the next.
Operations strategy configures and develops processes that best enable a firm to produce and deliver:
products specified by the business strategy This follows the hierarchical view that the operations strategy is created to serve the business strategy, which is created in line with the corporate strategy.
The flow units of a process are:
specific to the process being considered Different processes will handle different types of flow units depending on what they are designed to accomplish
If we say that "we take raw potatoes and do two things to them" we have not defined a process because:
we have not specified the outputs We have to specify the inputs and outputs to define a process.
If I sell items for $100 each after purchasing them from my supplier at $50 each, what is the Net Marginal Cost (also known as the cost of over-ordering) if stocking out damages my reputation and I estimate this damage to be $100?
$50 Damage to customer relationships associated with stocking out is not relevant if I have too many.
If one unit flows into the process each minute and one unit flows out after every 2 minutes, what is the inventory accumulation rate?
1/2 units per minute The buildup rate is 1 unit per minute minus ½ unit per minute = ½ unit per minute.
Consider a 1-step process using 1 resource that produces 2 different outputs. One output takes 4 minutes, the other takes 6, and customer orders alternate between these two outputs. What is the capacity of this process?
12 jobs per hour Two ways to look at this. The average unit load is 5 minutes so capacity is 60/5 = 12 jobs per hour. You can also think of a big job as being one 4-minute task and one 6-minute task, so we do 10 of these big jobs per hour and each big job delivers 2 units. 6 * 2 = 12 units per hour.
For a system with 2 servers, if the arrival rate is 12 jobs per hour and the average service rate for each server is 8 jobs per hour, what is utilization?
12/(8*2) Remember, cutting time in half and doubling the rate are the same thing.
If I am willing to assume that demand is uniformly distributed with a mean of 1000 units and a range from 0 to 2000 units, I order 1500 units, and demand is 1650 units what is the fill rate?
1500/1650 I satisfied 90% of realized demand. Note that this assumes that I can find out what demand is even after I stock out. This is not always possible.
If I am willing to assume that demand is uniformly distributed with a mean of 1000 units and a range from 0 to 2000 units, and I order 1500 units what is the cycle service level?
1500/2000 The probability that demand will be less than or equal to the order size is 1500/2000. This is also the probability that realized demand is satisfied.
Customers walk into a bank and take an average of 15 minutes to complete their business. On average there are 5 customers in the bank. What is the throughput rate?
20 customers per hour T = I/R so R = I/T or 5 customers / ¼ hour. This is 5 * 4 = 20 customers per hour.
If Resource B is busy for 3 minutes for Step 1 and is not used for Step 2, what is the unit load of Resource B?
3 minutes
If annual demand is 364 units and I order 91 units at a time how often will I need to receive an order?
3 times per year , once per quarter 364/91 = 4
What is the average flow time for this process if half of the jobs follow the first path, the other half follow the other path, no waiting is involved, and the two paths make 2 different products?
5.5 hours The two path lengths are 5 hours and 6 hours, so the average for the process is just the average for the paths.
For a system with a single server, if the arrival rate is 6 jobs per hour and the average service time is 5 minutes, what is utilization?
5/10 Remember to be consistent when the chosen scale. Here we have minutes/minutes. We could convert both times to seconds, hours, etc. It makes no difference.
Customers walk into a bank and are served at an average rate of 20 per hour. On average there are 5 people waiting in queue to be served. How long does the average customer wait in queue?
5/20 hours T = I/R = 5/20 = 0.25. This is in hours because the rate is specified in customers per hour.
If I sell items for $100 each after purchasing them from my supplier at $50 each, what is the Net Marginal Cost (also known as the cost of over-ordering) if I can sell the left over items for $25?
50 - 25 If I order one too many, I spent $50 but I get $25 of this back when I "dump" this merchandise.
For a system with 2 servers, if the arrival rate is 6 jobs per hour and the average service time for each server is 5 minutes, what is utilization?
6/(12*2) The arrival rate is given as 6 jobs per hour, the service rate of each server is 60/5 = 12, and there are 2 servers.
In service settings such as airports and restaurants, what happens to the inventory accumulation rate?
It can change over time During peak demand it is likely to rise and during slow periods it is likely to fall.
What is the relationship between arrival rate (Lambda) and queue length (L)?
It depends on utilization Arrival rate increases queue length only if it increases utilization. If we increase arrival rate but increase the service rate as well utilization may not rise
If I have a process that produces what is needed, when needed and places it where it is needed, have I achieved perfect synchronization?
It depends on whether the amount produced matches the amount needed If the production system is not synchronized with needs there is either wasted production of unmet need
If 15 minutes of activity time could be moved from the longer path to the shorter one what happens to theoretical flow time?
It drops by 15 minutes The theoretical flow time becomes max(4.25, 4.75) = 4.75 so there is a drop of 0.25 hours or 15 minutes.
My old policy was to place orders when the inventory level equals LTD. I now decide to place an order before I reach the inventory level that matches lead time demand. What happens to the probability that I stock out?
It goes down Holding safety stock increases safety. In other words it reduces the probability of running out.
What happens to the average length of the line (L) if we move from a system that can accommodate an infinite queue length to one with a finite queue length?
It goes down The mean of any distribution that is truncated from above must be lower than the mean from the distribution that is not truncated.
If one unit flows into the process each minute and one unit flows out after every 2 minutes, and this pattern holds for 1 hour, what happens to the inventory level in this process?
It rises by 30 The buildup rate is 1 unit per minute minus ½ unit per minute = ½ unit per minute. ½ units per minute * 60 minutes is 30
If an activity on the shorter path now takes 30 minutes longer what happens to the theoretical flow time?
It stays the same The theoretical flow time was max (4, 5) = 5. The new theoretical flow time will be max (4.5, 5) = 5 so nothing has changed
Little's Law teaches that Inventory = Throughput * Cycle time. If L is the length of the line, including the customer being served, and W is the time in the system, including the service time, and we have a throughput rate of Lambda, then what does Little's Law say about this system?
L = Lambda * W Remember that for a stable system Lambda will also equal the arrival rate.
A process can produce:
a combination of goods and services A process can be a single step or a combination of many steps and can have multiple inputs and outputs, thus it may be designed to produce a combination of goods and services.
If lead time is 1 week (7 days) and daily demand is normally distributed with a mean of 100 and a variance of 10, I know that lead time demand is normally distributed with:
a mean of 700 and a variance of 70 Means and variances nicely add when variables are normal.
If we wish to compete based on low production cost for a manufactured item, it makes sense to:
define quality based on conformance to specifications Reduced response time, variety, flexibility and customization all cost money and increase cost.
In terms of a business strategy, product attributes lie along at least 4 dimensions. Indicate the one that is NOT listed in the text:
demand Demand is not a product attribute; it is a function of the marketplace
For a process with multiple steps, Little's law applies to:
each step and the entire process You can define any part of a process as a "sub-process" and Little's law applies to all sub-processes.
