Questions and Answers of Practical Management Science

A steel manufacturer needs to cool 17 pieces of steel. The weight and due date for each piece are listed in the file P08_38.xlsx. Processing and cooling a batch in the furnace takes five minutes
Suppose you are the ad manager for Fox NFL foot-ball. Thirty bids for ads on today’s game between the Packers and the Colts have been submitted. Information on these ads is given in the file
Assume that a consumer’s purchase decision on an electric razor is based on four attributes, each of which can be set at one of three levels (1, 2, or 3). Using conjoint analysis (a type of
An important problem in manufacturing is the assembly line balancing problem. When setting up a manufacturing line, activities must be assigned to workstations. The maximum time spent at a
Based on Meneses et al. (2004). A string is a list of characters such as “1differ%”. The length of the string is the number of characters in the string. The distance between two strings is the
A company has nine jobs that must be assigned to three ordered workstations. The file P08_44.xlsxlists the times required for each job, which are independent of the workstations they are assigned to.
The discussion at the beginning of section 8.8 mentions Claritas. If you were in the direct-mail business, how would you use the information sold by Claritas to improve your profitability?
How would you use cluster analysis to help test market a consumer goods product?
Your company sells credit card services, and you are concerned with churn. Describe how you could use discriminant analysis to learn what distinguishes the customers who switch to another company
Your company provides credit to customers. Some of these customers default on their loans, with very negative implications for you. Describe how you could use discriminant analysis to learn what
Two construction companies are bidding against one another for the right to construct a new community center building in Bloomington, Indiana. The first construction company, Fine Line Homes,
When you use a RISKSIMTABLE function for a decision variable, such as the order quantity in the Walton model, explain how this provides a “fair” comparison across the different values tested.
In the quantity discount model in Example 12.2, the minimum total annual cost is region 3 is clearly the best. Evidently, the larger unit purchase costs in the other two regions make these two
Equation (12.4) shows the optimal order quantity for the no-shortage model. Calculus can also be used to find the optimal order quantity and optimal maximum backlog for the EOQ model with shortages
As stated in Example 12.5, the critical fractile analysis is useful for finding the optimal order quantity, but it doesn’t (at least by itself) show the probability distribution of net profit. Use
Consider each change to the monetary inputs (the unit cost, the unit price, and the unit refund) one at a time in Example 12.5. For each such change, either up or down, describe how the cost of
You saw in Example 12.5 that the optimal order quantities with the triangular and normal demand distributions are very similar (171 versus 174). Perhaps this is because these two distributions, with
Change the model in the file R,Q Policy 2.xlsx slightly to allow a random lead time with a given mean and standard deviation. If the mean lead time is two weeks, and the standard deviation of lead
In the first (R,Q) model in Example 12.6, the one with a shortage cost, we let both Q and the multiple k be changing cells. However, we stated that the optimal Q depends mainly on the fixed ordering
In both (R,Q) models, the one with a shortage cost and the one with a service level constraint, we set up Solver so that the multiple k is constrained to be nonnegative. The effect is that the
In Example 12.6, we discussed the equivalence between the model with shortage costs and the model with a service level constraint. We also showed how to illustrate this equivalence with SolverTable.
We claimed that the critical fractile formula, Equation (12.8), is appropriate because the optimal Q should satisfy cunder[1 – F(Q)] = cover F(Q), that is, the cost of understocking times the
Turn the previous problem around. Now assume that the store’s service level requirement obligates it to meet customer demand on 99% of all order cycles. In other words, use model 4. What (R,Q)
The problem in Example 12.8 assumes that the heaviest demand occurs in the second (post-April) phase of selling. It also assumes that capacity is higher in the second production opportunity than in
The multiechelon inventory model in Example 12.9 requires about 595 items of on-hand or pipeline inventory, on average, to satisfy the fill rate constraint, even though the mean total demand per week
A bakery that orders cartons of bread mix has used an EOQ model to determine that an order quantity of 90 cartons per order is economically optimal. The bakery needs 150 cartons per month to meet
Consider the basic EOQ model. We want to know the sensitivity of (1) the optimal order quantity, (2) the sum of the annual order cost and the annual holding cost (not including the annual purchase
The efficiency of an inventory system is often measured by the turnover ratio.(TR), defined by TR = Cost of goods sold per year / Average value of on hand inventorya. Does a high turnover ratio
A consulting firm is trying to determine how to minimize the annual costs associated with purchasing high-quality paper for its printers. Each time an order is placed, an ordering cost of $50 is
The Gilette Company buys a product using the price schedule given in the file P12_32.xlsx. The company estimates the unit holding cost at 10% of the purchase price and the ordering cost at $100 per
Each year, Shopalot Stores sells 10,000 cases of soda. The company is trying to determine how many cases to order each time it orders. It costs $150 to process each order, and the cost of carrying a
The manager of a hardware store decides to use the EOQ with shortages model to determine the ordering policy for tape measures. Using economic considerations, the manager determines that she should
A car dealer must pay $20,000 for each car purchased. The annual holding cost is estimated to be 25% of the dollar value of inventory. The dealer sells an average of 500 cars per year. He is willing
Chicago Mercy Hospital needs to order drugs that are used to treat heart attack victims. Annually, 500 units of drug 1 and 800 units of drug 2 are used. The unit purchasing cost for drug 1 is $150
Software EG, a retail company, orders two kinds of software from Tele-Hard Software. Annually, Software EG sells 800 units of product 1 and 400 units of product 2. The unit purchasing cost is $30 per
Customers at Joe’s Office Supply Store demand an average of 6000 desks per year. Each time an order is placed, an ordering cost of $300 is incurred. The annual holding cost for a single desk is 25%
In the previous problem, assume that it costs $300 to place an order. The holding cost per DVD player held in inventory per year is $15. The cost each time a customer orders a DVD player that is not
Suppose the annual demand for Soni DVD players at an appliance store is normally distributed with mean 150 and standard deviation 45. When the store orders these DVD players from its supplier, it
A hospital must order the drug Porapill from the manufacturer of the drug. It costs $500 to place an order. Annual demand for the drug is normally distributed with mean 10,000 and standard deviation
How do your answers to part a of the previous problem change if, instead of incurring a $40 penalty cost for each shortage, the store has a service level requirement of meeting 95% of all customer
Chicago’s Treadway Tires Dealer must order tires from its national warehouse. It costs $10,000 to place an order. Annual tire sales are normally distributed with mean 20,000 and standard deviation
A hospital orders its blood from a regional blood bank. Each year, the hospital uses an average of 1040 pints of type O blood. Each order placed with the regional blood bank incurs a cost of $250.
A firm experiences demand with a mean of 100 units per day. Lead time demand is normally distributed with mean 1000 units and standard deviation 200 units. It costs $6 to hold one unit for one year.
A department store is trying to decide how many JP Desksquirt II printers to order. Because JP is about to come out with a new model in a few months, the store will order only a limited number of
Work the previous problem when the demands are positively correlated, as they might be with products such as peanut butter and jelly. Now use r = 0.3, r = 0.5, and r = 0.7 in your simulations.
Based on Ignall and Kolesar (1972). Dominic’s Pizza Parlor receives 30 calls per hour for delivery of pizza. It costs Dominic’s $10 to send out a truck to deliver pizzas. Each minute a customer
Suppose that instead of ordering the amount Q specified by the EOQ formula, the order quantity 0.8Q is used. Show that the sum of the annual ordering cost and the annual holding cost increases by
A drugstore sells 30 bottles of antibiotics per week. Each time it orders antibiotics, there is a fixed ordering cost of $10 and a cost of $10 per bottle. Assume that the store’s cost of capital
In terms of K, D, and h, what is the average length of time that an item spends in inventory before being used to meet demand? Explain how this result can be used to characterize a fast-moving or
A hospital orders its thermometers from a hospital supply firm. The cost per thermometer depends on the order quantity Q, as shown in the file P12_58.xlsx. The annual holding cost is 25% of the
In the previous problem, suppose that the cost per order is $1, and the monthly demand is 50 thermometers. What is the optimal order quantity? What is the smallest discount the supplier could offer
Based on Kolesar et al. (1974). Metropolis PD Precinct 88 must determine the minimum number of police cars required to meet its needs for the next 24 hours. An average call for service requires
A computer manufacturer produces computers for 40 different stores. To monitor its inventory policies, the manufacturer needs to estimate the mean and standard deviation of its weekly demand. How
Based on Brout (1981). Planner’s Peanuts sells 100 products. The company has been disappointed with the high level of inventory it keeps of each product and its low service level (percentage of
Austin (1977) conducted an extensive inventory analysis for the United States Air Force. He found that for over 250,000 items the annual holding cost was assumed to equal 32% of the item’s purchase
An extremely important concept in queueing models is the difference between rates and times. If λ represents a rate (customers per hour, say), then argue why 1/λ is a time and vice versa.
Use the complete information in the file c13_01.xlsx to answer the following questions:1. Approximately what fraction of the time is Betty idle? Is Ben’s estimate correct?2. Approximately how many
Explain the basic relationship between the exponential distribution and a Poisson process. Also, explain how the exponential distribution and the Poisson distribution are fundamentally different.
Assume that parts arrive at a machining center at a rate of 60 parts per hour. The machining center is capable of processing 75 parts per hour—that is, the mean time to machine a part is 0.8
Little’s formula applies to an entire queueing system or to a subsystem of a larger system. For example, consider a single-server system composed of two sub-systems. The first subsystem is the
Consider a bank where potential customers arrive at rate of 60 customers per hour. However, because of limited space, one out of every four arriving customers finds the bank full and leaves
Consider a fast-food restaurant where customers enter at a rate of 75 per hour, and three servers are working. Customers wait in a single line and go, in FCFS fashion, to the first of the three
The Decision Sciences Department is trying to determine whether to rent a slow or a fast copier. The department believes that an employee’s time is worth $15 per hour. The slow copier rents for $4
The MM1 Template.xlsx file is now set up so that when you enter any time value in cell H11, the formula in cell I11 gives the probability that the wait in queue will be greater than this amount of
Expand the MM1 Template.xlsx file so that the steady-state probability distribution of the number in the system is shown in tabular form and graphically. That is, enter values 0, 1, and so on (up to
Suppose that you observe a sequence of inter-arrival times, such as 1.2, 3.7, 4.2, 0.5, 8.2, 3.1, 1.7, 4.2, 0.7, 0.3, and 2.0. For example, 4.2 is the time between the arrivals of customers 2 and 3.
In the M/M/s model, where µ is the service rate per server, explain why λ < µ is not the appropriate condition for steady state, but λ < sµ is.
Expand the MMs Template.xlsm file so that the steady-state probability distribution of the number in the system is shown in tabular form and graphically. That is, enter values 0, 1, and so on (up to
A supermarket is trying to decide how many cash registers to keep open. Suppose an average of 18 customers arrive each hour, and the average checkout time for a customer is four minutes.
A small bank is trying to determine how many tellers to employ. The total cost of employing a teller is $100 per day, and a teller can serve an average of 60 customers per day. On average, 50
In this problem, assume that all inter-arrival and service times are exponentially distributed.a. At present, the finance department and the marketing department each has its own typists. Each typist
MacBurger’s is attempting to determine how many servers to have available during the breakfast shift. On average, 100 customers arrive per hour at the restaurant. Each server can handle an average
On average, 100 customers arrive per hour at the Gotham City Bank. The average service time for each customer is one minute. Service times and inter-arrival times are exponentially distributed. The
The limited source model can often be used to approximate the behavior of a computer’s CPU (central processing unit). Suppose that 20 terminals (assumed to always be busy) feed the CPU. After the
Consider an airport where taxis and customers arrive (exponential inter-arrival times) with respective rates of one and two per minute. No matter how many other taxis are present, a taxi
A bank is trying to determine which of two machines to rent for check processing. Machine 1 rents for $10,000 per year and processes 1000 checks per hour. Machine 2 rents for $15,000 per year and
A worker at the State Unemployment Office is responsible for processing a company’s forms when it opens for business. The worker can process an average of four forms per week. Last year, an average
For the M/M/1 queueing model, why do the following results hold? (Remember that 1/µ is the mean service time. Then think how long a typical arrival must wait in the system or in the queue.)a. W = (L
The manager of a bank wants to use an M/M/s queueing model to weigh the costs of extra tellers against the cost of having customers wait in line. The arrival rate is 60 customers per hour, and the
On average, 100 customers arrive per hour at Gotham City Bank. It takes a teller an average of two minutes to serve a customer. Inter-arrival and service times are exponentially distributed. The bank
Two one-barber shops sit side by side in Dunkirk Square. Each shop can hold a maximum of four people, and any potential customer who finds a shop full will not wait for a haircut. Barber 1 charges
The small mail-order firm Sea’s Beginning has one phone line. An average of 60 people per hour call in orders, and it takes an average of one minute to handle a call. Time between calls and time to
How long does it take to reach steady state? Use simulation, with the Multi-server Simulation.xlsm file, to experiment with the effect of warm-up time and run time on the key outputs. For each of the
Simulate the system in Problem 10. Make any assumptions about the warm-up time and run time you believe are appropriate. Try solving the problem with exponentially distributed copying times. Then try
In Example 13.4 of section 13.5, we examined whether an M/M/1 system with a single fast server is better or worse than an M/M/s system with several slow servers. Keeping the same inputs as in the
US Airlines receives an average of 500 calls per hour from customers who want to make reservations, where the times between calls follow an exponential distribution. It takes an average of three
On average, 50 customers arrive per hour at a small post office. Inter-arrival times are exponentially distributed. Each window can serve an average of 25 customers per hour. Service times are
On average, 300 customers arrive per hour at a huge branch of Bank 2. It takes an average of two minutes to serve each customer. It costs $10 per hour to keep a teller window open, and the bank
Ships arrive at a port facility at an average rate of two ships every three days. On average, it takes a single crew one day to unload a ship. Assume that inter-arrival and service times are
On average, 40 jobs arrive per day at a factory. The time between arrivals of jobs is exponentially distributed. The factory can process an average of 42 jobs per day, and the time to process a job
On average, 90 patrons arrive per hour at a hotel lobby (inter-arrival times are exponential) waiting to check in. At present there are five clerks, and patrons wait in a single line for the first
The mail order firm of L. L. Pea receives an average of 200 calls per hour, where times between calls are exponentially distributed. It takes an L. L. Pea operator an average of three minutes to
Bloomington Hospital knows that insurance companies are going to reduce the average length of stay of many types of patients. How can queueing models be used to determine how changes in insurance
Zerox has 16 service centers throughout the United States. Zerox is trying to determine how many technicians it should assign to each service center. How would you approach this problem?
Based on Quinn et al. (1991). Winter Riggers handles approximately $400 million in telephone orders per year. Winter Riggers’ system works as follows. Callers are connected to an agent if one is
Suppose that annually an average of λ library patrons want to borrow a book. A patron borrows the book for an average of 1/µ years. Suppose we observe that the book is actually borrowed an average
Excessive delays have recently been noted on New York City’s 911 system. Discuss how you would use queueing models to improve the performance of the 911 system.
The Newcoat Painting Company has for some time been experiencing high demand for its automobile repainting service. Because it has had to turn away business, management is concerned that the limited
The manager of a large group of employees must decide whether she needs another photocopying machine. The cost of a machine is $40 per eight-hour day regardless of whether the machine is in use. On
At the Franklin Post Office, patrons wait in a single line for the first open window. On average, 100 patrons enter the post office per hour, and each window can serve an average of 45 patrons per

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