Managers of the retail stores opening in a new mall in a mid-size Midwestern cit
ID: 405852 • Letter: M
Question
Managers of the retail stores opening in a new mall in a mid-size Midwestern city face many decisions. They must determine what inventory levels they are going to carry, how the merchandise is best displayed, how advertising campaigns can be used most effectively, what their pricing policies must be as well as an entire list of many other business matters that will have a direct effect on the stores’ bottom lines.
As if all that wasn't enough each establishment must concern itself with crime prevention. Here again they find themselves facing many critical decisions. Losses due to unlawful activities can originate from within the organization due to employee theft and embezzlement as well as illegal practices committed by customers and other outsiders.
As owner and director of security operations for Crime Prevention, Incorporated you have been retained by mall authorities to offer your services and advice in the effort to curtail losses due to unlawful activities. You must address each concern of all those store owners and managers, and apply your expertise in the crime prevention field. Each store has its own set of unique concerns regarding illegal activity.
Rick Blaine owns an upscale restaurant, Rick’s Café American, due to open in the new mall within the next two weeks. Sam, Rick’s long-time friend and confidant, has expressed concern regarding the mysterious loss of some of the more expensive liquors and other libations. Based on the financial records Sam has kept he can report to Rick the number of shipments that have inexplicably disappeared and the dollar loss in each case as reported in the table shown here.
Dollar Loss
Number of Shipments
$14,000
10
$22,000
7
$15,000
12
$18,000
14
$20,000
10
$10,000
17
Together Rick and Sam decide that if the average loss exceeds $5000 they will engage the security services offered by Louis Renault, another of Rick’s long-term acquaintances. Captain Renault charges $10,000 for each security detail, so the variation in Rick's losses is also quite important.
The French boutique owned by Ilsa Lund has experienced unusual levels of employee theft at other outlets that have been open for several months prior to the one located in the new mall. According to the reports Ilsa has studied, 85% of retail employees engage in some level of theft, no matter how small (see the Prologue). Ilsa intends to employ 20 sales personnel. If the number of dishonest employees exceeds seven, Ilsa feels it will be necessary to purchase expensive insurance to protect her against such losses. What can you tell her about the wisdom of doing so?
Victor, owner of Laszlo’s Men’s Haberdashery, purchases men’s suits and ties from 15 independent manufacturers, 12 of which have a record of late deliveries. Victor intends to order from eight of those 15 manufacturers to stock his initial inventory. He is concerned that the grand opening may be delayed if his orders include more than six chronically delinquent suppliers. How likely are his fears to be realized?
Several of the merchants consulted local police records and found that retail establishments report a monthly average of 17 burglaries that seem to follow a Poisson distribution. These stores plan to open in exactly two weeks. If the likelihood that five or more of the stores will experience a break-in exceeds 10%, they intend to hire additional security forces. Would you advise them to do so?
Delivery times for Mac Trucking, the firm that supplies Rick’s Café American, are normally distributed and average 2.5 hours with a standard deviation of 30 minutes. As costs increase, Sam MacGuiver, owner of the transport company, has become increasing concerned about dwindling profits levels. His first concern rests with delivery times and expenses associated with the deliveries. He has asked you, his able statistical wizard, to address a few of the issues.
Sam initially wants to know how quickly the fastest 20% of the deliveries are handled. Based on this information he can establish a pay scale for his employees.
In addition, if in a given week the company completes 75 deliveries, Sam must compute the total cost of the deliveries if he pays the workers
$150 for deliveries that take less than 1 hour
$100 for deliveries that take between 1 hour and 2 hours
$50 for deliveries that take between 2 and 2.5 hours
$25 for deliveries that take between 2.5 and 3.5 hours
nothing for deliveries that require more than 3.5 hours
The mean delivery time of 2.5 hours also displeases Sam. He is considering a new routing system that will reduce the standard deviation in times to 20 minutes. He wants to know what mean delivery times those new routes would have to produce to ensure that 30% of the deliveries could be made in less than 1.7 hours.
Loading the trucks prior to transport is a matter requiring some attention. Loading times appear to be uniformly distributed ranging from 10 hours to 18 hours for the more delicate merchandise. If loading costs average $50 per hour, Sam must know the average cost for loading each truck and the dispersion in those costs.
Finally, trucks arrive at the loading dock at a Poisson rate of 1.2 per hour. In order to determine the number of loaders he must hire Sam is interested in the probability that less than 2 hours pass between arrivals.
Prepare a Formal Statistical Report of Your Findings.
Dollar Loss
Number of Shipments
$14,000
10
$22,000
7
$15,000
12
$18,000
14
$20,000
10
$10,000
17
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