Question

Northwoods Backpackers

Bob and Carol Packer operate a successful outdoor wear store in Vermont called Northwoods Backpackers. They stock mostly cold-weather outdoor items such as hiking and backpacking clothes, gear, and accessories. They established an excellent reputation throughout New England for quality products and service. Eventually, Bob and Carol noticed that more and more of their sales were from customers who did not live in the immediate vicinity but were calling in orders on the telephone. As a result, the Packers decided to distribute a catalog and establish a phone-order service. The order department consisted of five operators working eight hours per day from 10:00 A.M. to 6:00 P.M., Monday through Friday. For a few years the mail-order service was only moderately successful; the Packers just about broke even on their investment. However, during the holiday season of the third year of the catalog order service, they were overwhelmed with phone orders. Although they made a substantial profit, they were concerned about the large number of lost sales they estimated they incurred. Based on information provided by the telephone company regarding call volume and complaints from customers, the Packers estimated they lost sales of approximately $100,000. Also they felt they had lost a substantial number of old and potentially new customers because of the poor service of the catalog order department.

Prior to the next holiday season, the Packers explored several alternatives for improving the catalog order service. The current system includes the five original operators with computer terminals who work eight-hour days, five days per week. The Packers have hired a consultant to study this system, and she reported that the time for an operator to take a customer order is exponentially distributed with a mean of 3.6 minutes. Calls are expected to arrive at the telephone center during the six-week holiday season according to a Poisson distribution with a mean rate of 175 calls per hour. When all operators are busy, callers are put on hold, listening to music until an operator can answer. Waiting calls are answered on a first-in, first-out basis. Based on her experience with other catalog telephone order operations and data from Northwoods Backpackers, the consultant has determined that if Northwoods Backpackers can reduce customer call waiting time to approximately one-half minute or less, the company will save $135,000 in lost sales during the coming holiday season.

Therefore, the Packers have adopted this level of call service as their goal. However, in addition to simply avoiding lost sales, the Packers believe it is important to reduce waiting time to maintain their reputation for good customer service. Thus, they would like about 70 percent of their callers to receive immediate service.

The Packers can maintain the same number of workstations/computer terminals they currently have and increase their service to sixteen hours per day with two operator shifts running from 8:00 A.M. to midnight. The Packers believe when customers become aware of their extended hours the calls will spread out uniformly, resulting in a new call average arrival rate of 87.5 calls per hour (still Poisson distributed). This schedule change would cost Northwoods Backpackers approximately $11,500 for the six-week holiday season.

Another alternative for reducing customer waiting times is to offer weekend service. However, the Packers believe that if they do offer weekend service, it must coincide with whatever service they offer during the week. In other words, if they have phone order service eight hours per day during the week, they must have the same service during the weekend; the same is true with sixteen-hours-per-day service. They feel that if weekend hours differ from weekday hours it will confuse customers. If eight-hour service is offered seven days per week, the new call arrival rate will be reduced to 125 calls per hour at a cost of $3,600. If Northwoods offers sixteen-hour service, the mean call arrival rate will be reduced to 62.5 calls hour, at a cost of $7,300.

Still another possibility is to add more operator stations. Each station includes a desk, an operator, a phone, and a computer terminal. An additional station that is in operation five days per week, eight hours per day, will cost $2,900 for the holiday season. For a sixteen-hour day the cost per new station is $4,700. For seven-day service the cost of an additional station for eight-hour per-day service is $3,800; for sixteen-hour-per-day service the cost is $6,300.

The facility Northwoods Backpackers uses to house its operators can accommodate a maximum of ten stations. Additional operators in excess of ten would require the Packers to lease, remodel, and wire a new facility, which is a capital expenditure they do not want to undertake this holiday season. Alternatively, the Packers do not want to reduce their current number of operator stations.

Determine what order service configuration the Packers should use to achieve their goals, and explain your recommendation.
Use Excel/ Excel Qm to solve this question

Answer 1

		Formula	Units	Option 0 - Single Shift, Mon-Fri		Option 1 - Two Shifts, Mon-Fri		Option 2a - Seven Days, Single Shift		Option 2b - Seven Days, Two Shifts		Option 3a - Five Days, Single Shift, Increased Seats		Option 3b - Five Days, Two Shifts, Increased Seats		Option 3c - Seven Days, Single Shift, Increased Seats		Option 3c - Seven Days, Two Shift, Increased Seats
Existing / Minimum Seats				5		5		5		5		10		7		9		6
Rate of Arrival	Ra	Convert /hr to /min	per min	175 /hr	2.917	87.5 /hr	1.458	125 /hr	2.083	62.5 /hr	1.042	175 /hr	2.917	87.5 /hr	1.458	125 /hr	2.083	62.5 /hr	1.042
Arrival Coeff of Variation	CVa		Poisson Distribution	1		1		1		1		1		1		1		1
Number of Servers (seats)	m			5		5		5		5		10		7		9		6
Mean Effective Process Time	Tp		minutes	3.600		3.600		3.600		3.600		3.600		3.600		3.600		3.600
Rate of Processing	Rp	=m/Tp	per min	1.389		1.389		1.389		1.389		2.778		1.944		2.500		1.667
Processing Coeff of Variation	CVp		Poisson Distribution	1		1		1		1		1		1		1		1
Utilization Rate	u	=Ra/Rp		210%		105%		150%		75%		105%		75%		83%		63%
Waiting Time in queue	Tq	=((CVa^2+CVp^2)/2)*(u^(sqrt(2*m+1)-1))/(m*(1-u)))*Tp	minutes	-3.65		-16.12		-3.68		1.48		-8.58		0.90		1.30		0.47
Feasibility				not feasible as utilization rate is 2.1, should be <=1		not feasible as utilization rate is 1.05, should be <=1		not feasible as utilization rate is 1.5, should be <=1		Feasible as utilization rate is 75% and Waiting Time is < 1.5 mins		not feasible as utilization rate is 1.05, should be <=1		Feasible as utilization rate is 75% and Waiting Time is < 1.5 mins		Feasible as utilization rate is 83% and Waiting Time is < 1.5 mins		Feasible as utilization rate is 63% and Waiting Time is < 1.5 mins
Cost										=(11,500+7,300)=$18,800				=(11,500+2*4,700)= $20,900		=(3,600+4*3,800)= $18,800		=(11,500+7,300+6,300)=$25,100

Option 2b - Seven Days, Two Shifts, Option 3c - Seven Days, Single Shift, Increased Seats are cheapest cost feasible options