MGT 302
What are the "Three Ts" relevant to poka-yokes in service systems?
Task to be done, Treatment of the customer, Tangible features of the service facility
Using the fixed-order quantity model, which of the following is the total ordering cost of inventory given an annual demand of 36,000 units, a cost per order of $80, and a holding cost per unit per year of $4?
$2,400 Q = 1,200 = Square root of (2 x 36,000 x 80 / 4). Number of orders per year = 36,000 / 1,200 = 30 x $80 = $2,400
Assume the service rate for a queue in a truck-loading operation is 2 trucks per hour. Using the infinite queuing notion for the models presented in the textbook, which of the following is the average service time?
0.5 hours Average service time = 1 / average service rate = 1 / 2 = 0.5 hours.
Quick Lube Inc. operates a fast lube and oil change garage. On a typical day, customers arrive at the rate of three per hour, and lube jobs are performed at an average rate of one every 15 minutes. The mechanics operate as a team on one car at a time. Assuming Poisson arrivals and exponential service, find: The utilization of the lube team. The average number of cars in line. The average time a car waits before it is lubed. The total time it takes to go through the system (that is, waiting in line plus lube time).
1. 3/4 2. (3 x 3) / 4(4-3) 3. 2.25/3 4. (3/(4-3)) / 3
What is the average utilization of the servers in a system that has three servers? On average, 15 customers arrive every 15 minutes. It takes a server exactly three minutes to wait on each customer.
100 percent
We are ordering T-shirts for the spring party and are selling them for twice what we paid for them. We expect to sell 100 shirts and the standard deviation associated with our forecast is 10 shirts. How many shirts should we order?
100 shirts
For the item described in question 8, if we expect to sell approximately 15,600 units next year, how many trips will we need to make to the supplier over the year?
13 trips
Bobby the Barber is thinking about advertising in the local newspaper since he is idle 45 percent of the time. Currently, customers arrive on average every 40 minutes. What does the arrival rate need to be for Bobby to be busy 85 percent of the time?
2.32 customers per hour
If it takes a supplier four days to deliver an order once it has been placed and the standard deviation of daily demand is 10, which of the following is the standard deviation of usage during lead time?
20 The standard deviation of usage during lead time is equal to the square root of the sums of the variances of the number of days of lead time. Since variance equals standard deviation squared, the standard deviation of usage during lead time is the square root of 4(10x10) = square root of 400 = 20.
If the average time between customer arrivals is 2.50 minutes, what is the hourly arrival rate?
24.0
A company has recorded the last six days of daily demand on a single product they sell. Those values are 37, 115, 93, 112, 73, and 110. The time from when an order is placed to when it arrives at the company from its vendor is 3 days. Assuming the basic fixed-order quantity inventory model fits this situation and no safety stock is needed, which of the following is the reorder point (R)?
270 Average demand is 37+115+93+112+73+110 / 6 = 90. Lead time = 3 days so the reorder point is 90 x 3 = 270
The Bijou Theater shows vintage movies. Customers arrive at the theater line at the rate of 100 per hour. The ticket seller averages 30 seconds per customer, which includes placing validation stamps on customers' parking lot receipts and punching their frequent watcher cards. (Because of these added services, many customers don't get in until after the feature has started.) What is the average customer time in the system? What would be the effect on customer time in the system of having a second ticket taker doing nothing but validations and card punching, thereby cutting the average service time to 20 seconds? What would be the customer time in the system if a second window was opened with each server doing all three tasks? Would system waiting time which is obtained in part (c) be less than you found in (b)?
3 minutes 0.750 minutes 0.634 minutes Yes
Burrito King (a new fast-food franchise opening up nationwide) has successfully automated burrito production for its drive-up fast-food establishments. The Burro-Master 9,000 requires a constant 45 seconds to produce a batch of burritos. It has been estimated that customers will arrive at the drive-up window according to a Poisson distribution at an average of one every 50 seconds. To help determine the amount of space needed for the line at the drive-up window, answer the following questions. What is the average waiting line length (in cars)? What is the average number of cars in the system (both in line and at the window)? What is the expected average time in the system, in minutes?
4.05 4.95 4.13
Consider an item for which we have 120 units currently in inventory. The average demand for the item is 60 units per week. The lead time for the item is exactly 2 weeks and we carry 16 units for safety stock. What is the probability of running out of the item if we order right now?
50 percent
Assuming no safety stock, what is the re-order point (R) given an average daily demand of 50 units, a lead time of 10 days and 625 units on hand?
500 Fifty (50) times ten (10) equals 500.
We have an item that we stock in our store that has fairly steady demand. Our supplier insists that we buy 1,200 units at a time. The lead time is very short on the item, since the supplier is only a few blocks away and we can pick up another 1,200 units when we run out. How many units do you expect to have in inventory, on average?
600 units
If we decide to carry 10 units of safety stock for the item described in questions 8 and 9, and we implemented this by going to our supplier when we had 10 units left, how much inventory would you expect to have, on average, now?
610 units
If the average time between customer arrivals is eight minutes, what is the hourly arrival rate?
7.5
Firms that desire high service levels where customers have short wait times should target server utilization levels at no more than this percent.
70-80 percent
The queuing models assume that customers are served in what order?
First come, first served
What is the most commonly used priority rule for setting queue discipline, likely because it is seen as most fair?
First-come, first-served
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?
713 pounds
Assuming no safety stock, what is the reorder point (R) given an average daily demand of 78 units and a lead time of 3 days?
78 times 3 = 234
If it takes a supplier two days to deliver an order once it has been placed and the daily demand for three days has been 120, 124, and 125, which of the following is the standard deviation of usage during lead time?
About 3.06 The standard deviation (Equation 11.7) of daily demand = Square root of (14/3) = 2.1602. This number squared is 4.6667. The square root of (2 (days) times 4.6667) = the square root of 9.3333 or 3.055.
Which of the following is the set of all cost components that make up the fixed-order quantity total annual cost (TC) function?
Annual holding cost, annual ordering cost, annual purchasing cost
Which of the following is not included as an inventory holding cost?
Annualized cost of materials Holding costs include the costs for storage facilities, handling, insurance, pilferage, breakage, obsolescence, depreciation, taxes, and the opportunity cost of capital.
L. Winston Martin (an allergist) has an excellent system for handling his regular patients who come in just for allergy injections. Patients arrive for an injection and fill out a name slip, which is then placed in an open slot that passes into another room staffed by one or two nurses. The specific injections for a patient are prepared, and the patient is called through a speaker system into the room to receive the injection. At certain times during the day, patient load drops and only one nurse is needed to administer the injections. Use Exhibit 7.12. Let's focus on the simpler case of the two—namely, when there is one nurse. Also, assume that patients arrive in a Poisson fashion and the service rate of the nurse is exponentially distributed. During this slower period, patients arrive with an interarrival time of approximately three minutes. It takes the nurse an average of two minutes to prepare the patients' serum and administer the injection. a. What is the average number of patients you would expect to see in Dr. Martin's facilities? b. How long would it take for a patient to arrive, get an injection, and leave? c. What is the probability that there will be three or more patients on the premises? d. What is the utilization of the nurse? e. Assume three nurses are available. Each takes an average of two minutes to prepare the patients' serum and administer the injection. What is the average total time of a patient in the system?
Average number of patients 2.00 Average total time 6.00 minutes Probability 29.6 % Utilization of the nurse 66.7 % Average total time 2.03 minutes
In making any decision that affects inventory size, which of the following costs do not need to be considered?
Fixed costs In making any decision that affects inventory size, the following costs must be considered. 1. Holding (or carrying) costs. 2. Setup (or production change) costs. 3. Ordering costs. 4. Shortage costs.
The model most appropriate when a fixed amount must be purchased each time an order is placed.
Fixed-order quantity model
American Vending Inc. (AVI) supplies vended food to a large university. Because students often kick the machines out of anger and frustration, management has a constant repair problem. The machines break down on an average of three per hour, and the breakdowns are distributed in a Poisson manner. Downtime costs the company $250/hour per machine, and each maintenance worker gets $40 per hour. One worker can service machines at an average rate of five per hour, distributed exponentially; two workers working together can service seven per hour, distributed exponentially; and a team of three workers can repair eight per hour, distributed exponentially. What is the optimal maintenance crew size for servicing the machines?
Case I—One worker: λ = 3/hour Poisson, μ = 5/hour exponential There is an average number of broken machines in the system of Downtime cost is $250.00 × 1.5 = $375.00 per hour; repair cost is $40.00 per hour; and total cost per hour for 1 worker is $375.00 + $40.00 = $415.00. Case II—Two workers: 3/(7-3) multiply value against costs Case III—Three workers: 3/(8-3) multiply value against costs Comparing the costs for one, two, or three workers, we see that Case II with two workers is the optimal decision.
Daily demand for a certain product is normally distributed with a mean of 100 and a standard deviation of 15. The supplier is reliable and maintains a constant lead time of 5 days. The cost of placing an order is $10 and the cost of holding inventory is $0.50 per unit per year. There are no stockout costs, and unfilled orders are filled as soon as the order arrives. Assume sales occur over 360 days of the year. Your goal here is to find the order quantity and reorder point to satisfy a 90 percent probability of not stocking out during the lead time. a. To manage inventory, the company is using b. Find the order quantity. c. Find the reorder point.
Continuous review system Order quantity 1,200 units Reorder point 543
This is an inventory auditing technique where inventory levels are checked more frequently than one time a year.
Cycle counting
Service systems can be generally categorized according to this characteristic that relates to the customer.
Degree of customer contact
Term used to describe demand that can be accurately calculated to meet the need of a production schedule, for example.
Dependent demand
Which of the following is not an assumption of the basic fixed-order quantity inventory model?
Diminishing returns to scale of holding inventory These assumptions are unrealistic, but they represent a starting point and allow us to use a simple example: 1. Demand for the product is constant and uniform throughout the period. 2. Lead time (time from ordering to receipt) is constant. 3. Price per unit of product is constant. 4. Inventory holding cost is based on average inventory. 5. Ordering or setup costs are constant. 6. All demands for the product will be satisfied. (No backorders are allowed.)
Which following queue discipline is discussed in the textbook?
Emergencies first
A ride at an amusement park is an example of a service operation where there is direct contact between the customer and server, but little variation in the service process—neither the customer nor server has much discretion in how the service will be provided. As shown on the Service System Design Matrix, which type of service is being delivered?
Face-to-face, tight specs
Almost certainly you have seen vending machines being serviced on your campus and elsewhere. On a predetermined schedule the vending company checks each machine and fills it with various products. This is an example of which category of inventory model?
Fixed-time period model
The model most appropriate when inventory is replenished only in fixed intervals of time, for example, on the first Monday of each month.
Fixed-time period model
We are being evaluated based on the percentage of total demand met in a year (not the probability of stocking out as used in the chapter). Consider an item that we are managing using a fixed-order quantity model with safety stock. We decide to double the order quantity but leave the reorder point the same. Would you expect the percent of total demand met next year to go up or down? Why?
Go up (we are taking fewer chances of running out)
In most cases, if a firm increases its service capacity by 10 percent, it would expect waiting times to be reduced by what percent? Assume customer arrivals and service times are random.
Greater than 10 percent
Term used to describe demand that is uncertain and needs to be forecast.
Independent demand
What is the expected waiting time for the system described in question 7?
Infinite
This is the key feature that distinguishes a service blueprint from a normal flowchart.
Line of visibility
Buying food at a large food store with multiple checkout counters features which type of queuing system line structure?
Multichannel, single phase
Dunstreet's Department Store would like to develop an inventory ordering policy of a 95 percent probability of not stocking out. To illustrate your recommended procedure, use as an example the ordering policy for white percale sheets. Demand for white percale sheets is 5,000 per year. The store is open 365 days per year. Every two weeks (14 days) inventory is counted and a new order is placed. It takes 10 days for the sheets to be delivered. Standard deviation of demand for the sheets is five per day. There are currently 150 sheets on hand. How many sheets should you order?
Number of sheets 219
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 1,750 units. His cost to carry one unit is $95 per year per unit, and he has estimated that each order costs $36 to place. Using the EOQ model, how many should Ray order each time?
Optimal order quantity36 units
It is your responsibility, as the new head of the automotive section of Nichols Department Store, to ensure that reorder quantities for the various items have been correctly established. You decide to test one item and choose Michelin tires, XW size 185 × 14 BSW. A perpetual inventory system has been used, so you examine this as well as other records and come up with the following data: Cost per tire $35 each Holding cost 20 percent of tire cost per year Demand 1,000 per year Ordering cost $20 per order Standard deviation of daily demand 3 tires Delivery lead time 4 days Because customers generally do not wait for tires but go elsewhere, you decide on a service probability of 98 percent. Assume the demand occurs 365 days per year. a. Determine the order quantity. b. Determine the reorder point
Order quantity 76 tires Reorder point 24 tires
Students arrive at the Administrative Services Office at an average of one every 15 minutes, and their requests take on average 10 minutes to be processed. The service counter is staffed by only one clerk, Judy Gumshoes, who works eight hours per day. Assume Poisson arrivals and exponential service times. a. What percentage of time is Judy idle? b. How much time, on average, does a student spend waiting in line? c. How long is the (waiting) line on average? d. What is the probability that an arriving student (just before entering the Administrative Services Office) will find at least one other student waiting in line?
Percentage of time 33.3 % Average time 20 minutes Average length of the waiting line 1.33 customers Probability 44.44 %
Which of the following is not a suggestion for managing queues presented in the textbook?
Periodically close the service channel to temporarily disperse the line
This is done to make a system mistake-proof.
Poka-yoke
A framework that relates to the customer service system encounter.
Service-system design matrix
Based on an EOQ-type ordering criterion, what cost must be taken to zero if the desire is to have an order quantity of a single unit?
Setup or ordering cost
In a college registration process, several department heads have to approve an individual student's semester course load. What is the queuing system line structure?
Single channel, multiphase
The model most appropriate for making a one-time purchase of an item.
Single-period model
When developing inventory cost models, which of the following are not included as costs to place an order?
Taxes There are costs to place an order: labor, phone calls, typing, postage, and so on. Therefore, the larger each order is, the fewer the orders that need to be written. Also, shipping costs favor larger orders—the larger the shipment, the lower the per-unit cost. Ordering costs refer to the managerial and clerical costs to prepare the purchase or production order. Ordering costs include all the details, such as counting items and calculating order quantities. The costs associated with maintaining the system needed to track orders are also included in ordering costs.
A product is priced to sell at $100 per unit, and its cost is constant at $70 per unit. Each unsold unit has a salvage value of $20. Demand is expected to range between 35 and 40 units for the period; 35 definitely can be sold and no units over 40 will be sold. The demand probabilities and the associated cumulative probability distribution (P) for this situation are shown below. How many units should be ordered?
The cost of underestimating demand is the loss of profit, or Cu = $100 − $70 = $30 per unit. The cost of overestimating demand is the loss incurred when the unit must be sold at salvage value, Co = $70 − $20 = $50. The optimal probability of not being sold is 30/(30+50) From the distribution data above, this corresponds to the 37th unit.
Sheet Metal Industries Inc. (SMI) is a Tier 1 supplier to various industries that use components made from sheet metal in their final products. Manufacturers of desktop computers and electronic devices are its primary customers. SMI orders a relatively small number of different raw sheet metal products in very large quantities. The purchasing department is trying to establish an ordering policy that will minimize total costs while meeting the needs of the firm. One of the highest volume items it purchases comes in precut sheets direct from the steel processor. Forecasts based on historical data indicate that SMI will need to purchase 200,000 sheets of this product on an annual basis. The steel producer has a minimum order quantity of 1,000 sheets, and offers a sliding price scale based on the quantity in each order, as follows: 1000-9999 = $2.35 per unit 10,000 - 19,999 = $2.20 30,000 + = $2.15 The purchasing department estimates that it costs $300 to process each order, and SMI has an inventory carrying cost equal to 15 percent of the value of inventory. Based on this information, use the price-break model to determine an optimal order quantity.
The first step is to take the information in the problem and assign it to the proper notation in the model. D =200,000 units (annual demand) S =$300 to place and process each order I =15 percent of the item cost C =cost per unit, based on the order quantity Q, as shown in the table above Next, solve the economic order size at each price point starting with the lowest unit price. Stop when you reach a feasible Q. Q2.15 = sprt((2 x 200,000 x 300) / (.15 x 2.15)) = 19290(infeasible) The EOQ at $2.15 is not feasible for that price point. The best quantity to order at that price point is therefore the minimum feasible quantity of 30,000. Q2.20 = sprt((2 x 200,000 x 300) / (.15 x 2.20)) = 19069(feasible) The EOQ at $2.20 is feasible, therefore the best quantity to order at that price point is the EOQ of 19,069. Since we found a feasible EOQ at this price point, we do not need to consider any higher price points. The two ordering policies to consider are: Order 30,000 sheets each time at $2.15 apiece, or order 19,069 sheets each time at $2.20 each. The question is whether the purchase price savings at the $2.15 price point will offset the higher holding costs that would result from the higher ordering quantity. To answer this question, compute the total cost of each option. TC (Q = 30,000)= 200,000 x 2.15 + (200,000/30,000)(300) + (30,000/2)(.15)($2.15) = 436,837 TC (Q = 19069)= 200,000 x 2.20 + (200,000/19069)(300) + (19069/2)(.15)($2.25) = 446,293 The lowest total annual cost comes when ordering 30,000 units at $2.15, so that would be the best ordering policy. Are you surprised that the 5-cent difference in unit price would make such a difference in total cost? When dealing in large volumes, even tiny price changes can have a significant impact on the big picture.
To take into consideration demand uncertainty in reorder point (R) calculations, what do we add to the product of the average daily demand and lead time in days when calculating the value of R?
The product of the standard deviation of demand variability and a "z" score relating to a specific service probability. For example, suppose we computed the standard deviation of demand to be 10 units per day. If our lead time to get an order is five days, the standard deviation for the five-day period, assuming each day can be considered independent,
SOLVED PROBLEM 2 Items purchased from a vendor cost $20 each, and the forecast for next year's demand is 1,000 units. If it costs $5 every time an order is placed for more units and the storage cost is $4 per unit per year, answer the following questions. What quantity should be ordered each time? What is the total ordering cost for a year? What is the total storage cost for a year?
The quantity to be ordered each time is sqrt((2(1,000)(5))/4) = 50 units The total ordering cost for a year is (1000/50)(5) = $100 The total ordering cost for a year is (50/2)(4) = $100
Which of the following are the three major components of a queuing system?
The source population and the way customers arrive at the system, the serving systems, and how customers exit the system.
Which of the following is not a reason to carry inventory?
To keep the stock out of the hands of competitors All firms keep a supply of inventory for the following reasons: 1. To maintain independence of operations 2. To meet variation in product demand. 3. To allow flexibility in production scheduling. 4. To provide a safeguard for variation in raw material delivery time. 5. To take advantage of economic purchase order size.
Consider two queuing systems identical except for the service time distribution. In the first system, the service time is random and distributed according to a Poisson distribution. The service time is constant in the second system. How would the waiting time differ in the two systems?
Waiting time in the first system is two times the second
If we take advantage of a quantity discount, would you expect your average inventory to go up or down? Assume that the probability of stocking out criterion stays the same.
Will probably go up if the probability of stocking out stays the same
SOLVED PROBLEM 3 Daily demand for a product is 120 units, with a standard deviation of 30 units. The review period is 14 days and the lead time is 7 days. At the time of review, 130 units are in stock. If only a 1 percent risk of stocking out is acceptable, how many units should be ordered?
sqrt((14 +7)(30^2)) = 137.5 120(14+7) + 2.33(137.5) = 2710
SOLVED PROBLEM 4 A company currently has 200 units of a product on-hand that it orders every two weeks when the salesperson visits the premises. Demand for the product averages 20 units per day with a standard deviation of 5 units. Lead time for the product to arrive is seven days. Management has a goal of a 95 percent probability of not stocking out for this product. The salesperson is due to come in late this afternoon when 180 units are left in stock (assuming that 20 are sold today). How many units should be ordered?
sqrt((21 x 5^2)) = 23 z = 1.64 20(14+7) + 1.64(23) - 180 278 units
