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Manager Chris Channing of Fabric Mills, Inc., has developed the forecast shown in the table for bolts of cloth. The figures are in hundreds of bolts. The department has a normal capacity of 275(00) bolts per month, except for the seventh month, when capacity will be 250(00) bolts. Normal output has a cost of $40 per hundred bolts. Workers can be assigned to other jobs if production is less than normal. The beginning inventory is zero bolts.

Month 1 2 3 4 5 6 7 Total
Forecast 250 300 250 300 280 275 270 1,925

a.

Develop a chase plan that matches the forecast and compute the total cost of your plan. Overtime is $60 per hundred bolts.(Negative amounts should be indicated by a minus sign. Leave no cells blank – be certain to enter “0” wherever required. Omit the “$” sign in your response.)

Period 1 2 3 4 5 6 7 Total
Forecast 250 300 250 300 280 275 270 1,925
Output
Regular
Overtime
Subcontract
Output – Forecast
Inventory
Beginning
Ending
Average
Backlog
Costs:
Output
Regular $ $
Overtime
Subcontract
Inventory
Backorder
Total $ $

b.

Would the total cost be less with regular production with no overtime, but using a subcontractor to handle the excess above normal capacity at a cost of $50 per hundred bolts? Backlogs are not allowed. The inventory carrying cost is $2 per hundred bolts.(Round your Average values to 1 decimal place. Negative amounts should be indicated by a minus sign. Leave no cells blank – be certain to enter “0” wherever required. Omit the “$” sign in your response.)

Period 1 2 3 4 5 6 7 Total
Forecast 250 300 250 300 280 275 270 1,925
Output
Regular
Overtime
Subcontract
Output – Forecast
Inventory
Beginning
Ending
Average
Backlog
Costs:
Regular $ $
Overtime
Subcontract
Inventory
Backorder
Total
 
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The new Fore and Aft Marina is to be located on the Ohio River near Madison, Indiana. Assume that Fore and Aft decides to build a docking facility where one boat at a time can stop for gas and servicing. Assume that arrivals follow a Poisson probability distribution, with an arrival rate of 7 boats per hour, and that service times follow an exponential probability distribution, with a service rate of 12 boats per hour. The manager of the Fore and Aft Marina wants to investigate the possibility of enlarging the docking facility so that two boats can stop for gas and servicing simultaneously. Assume that the arrival rate is 7 boats per hour and that the service rate for each server is 12 boats per hour.

What is the probability that the boat dock will be idle? If required, round your answer to two decimal places. P0 =

What is the average number of boats that will be waiting for service? If required, round your answer to four decimal places. Lq =

What is the average time a boat will spend waiting for service? If required, round your answer to four decimal places. Wq = hours

What is the average time a boat will spend at the dock? If required, round your answer to four decimal places. W =

 
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.The Robotics Manufacturing Company operates an equipment repair business where emergency jobs arrive randomly at the rate of three jobs per 8-hour day. The company’s repair facility is a single-channel system operated by a repair technician. The service time varies, with a mean repair time of 2 hours and a standard deviation of 1.5 hours. The company’s cost of the repair operation is $28 per hour. In the economic analysis of the waiting line system, Robotics uses $35 per hour cost for customers waiting during the repair process.

a.What are the arrival rate and service rate in jobs per hour?

b.Show the operating characteristics including the total cost per hour.

c.The company is considering purchasing a computer-based equipment repair system

that would enable a constant repair time of 2 hours. For practical purposes, the standard

deviation is 0. Because of the computer-based system, the company’s cost of the

new operation would be $32 per hour. The firm’s director of operations said no to the

request for the new system because the hourly cost is $4 higher and the mean repair

time is the same. Do you agree? What effect will the new system have on the waiting

line characteristics of the repair service?

d. Does paying for the computer-based system to reduce the variation in service time

make economic sense? How much will the new system save the company during a

40-hour work week?

 
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Case Study: Cooper Vision Path to Growth

On a warm Sunday afternoon in June 1967, Davin Lynch first conceived of an idea that was later to emerge as a chain of shops retailing ophthalmic products. Reading a financial profile of an ophthalmic retailer in the UK, while relaxing in his back garden, Davin concluded that he could do a better job than the management of this company seemed to have done. He decided to investigate the possibility of entering the ophthalmic retailing business in America.

Cooper Vision’s first shop opened in South Anne Street in Dublin in Detroit in September 1998 October 1977 and the business grew quickly to a chain of 25 stores throughout the USA by 1981. However, having managed to break the mound in terms of the way ophthalmic products are retailed in USA, the company faced stiff competition from a number of foreign competitors concerns targeting the USA market. The key issue facing Cooper Vision in January 1981 seemed to be how they could build on past marketing successes to ensure continued growth in a period of increasingly tough competition.

The structure of the industry

The ophthalmic products industry can be defined as the manufacture and distribution of products designed to correct defects in vision (see Fig below). The first stage of spectacle manufacture was the production of glass blanks of suitable quality for grinding into lenses. These lenses were subsequently ground to standard specifications of size, strength and curvature. Lenses were then sent to glazing houses, sometimes known as manufacturing opticians, who performed two tasks.

First, they assembled spectacles to orders from optometrists and were involved in cutting, edging and fitting appropriate lenses to frames chosen by customers. Second, glazing houses provided special finishes such as tinting, anti-scratch surfaces, anti-reflective surfaces, etc. In order to fulfill this function, glazing houses needed to carry large stocks of lenses. The last link in the chain of supply of spectacles to the consumer was in the hands of three groups. Optometrists, previously known as ophthalmic opticians, were the most popular. They provided three services, namely the testing of eyesight, the issuing of prescriptions and the dispensing of corrective solutions. Ophthalmic medical practitioners or ophthalmologists tested eyesight and prescribed but did not dispense. Dispensing opticians could dispense only to prescriptions written by a member of the other two groups.

A regulated industry

Davin quickly realized that this would be an exceedingly difficult business to enter. First, there was the challenge posed by the existing competitors in the industry. There were about 75,075 optometrists operating throughout USA. These were generally small, family-owned, operations who were traditional and conservative in their approach to the business. They were not retailers in the general sense, as most required appointments and consultation tended to take place in private, in a manner similar to the general medical profession. Products were generally not displayed.

During consultation, spectacle frames were taken from drawers and consumers were invited to choose from a small selection, typically three or four. Industry regulations favoured optometrists as spectacles or contact lenses could be purchased only with a prescription, which they, in the main, provided. In addition, the Opticians Regulating Council placed further regulations on marketing activity in the industry. Only a limited number of spectacle frames could be put on display and optometrists could not include prices in their advertising. Thus, industry regulations effectively barred anyone who was not a qualified optometrist from the business.

In addition, employing an optometrist was likely to prove extremely difficult, due to their limited supply and the likelihood that anyone working for a new competitor would face censure from professional colleagues and the Association. However, there was one loophole in the Opticians Act 1956 which Davin was able to exploit. The Act allowed for a general medical practitioner to test eyesight and to prescribe corrective products. A further critical breakthrough came when a contact in the UK informed Davin of the availability of a product called an automatic refract meter, which could mechanically test eyesight. Thus, combining this new machine with the services of a medical practitioner would alleviate the need to hire an optometrist. This would be the means through which Cooper Vision would break into the industry.

Start up and growth

Committing personal savings of $500,000 and bank borrowing of $1 Million to the business, Davin bought the lease to an outlet in East Motor Street, in the centre of Detroit. This store opened for business in October 1977. Start-up costs were kept to a minimum with promotion efforts restricted to printed flyers distributed to bus commuters and publicity in local newspapers and television stations.

Davin felt that he would have difficulty sourcing supplies of frames and lenses in the USA as companies supplying optometrists may not be able to supply him. His search for suppliers took him to the Canada and eventually to the UK where he attended the industry’s premier trade fair, in 1977. Having to source supplies abroad proved to be a blessing in disguise as the company was able to offer a range of fashionable frames unlike anything previously available in the USA.

The company expanded rapidly over the next four years. Davin succeeded in hiring an optometrist who replaced the company doctor. In order to cover the cost of this new member of staff and to tap some potential that he felt existed in Detroit, Davin opened a second store in the city of Windsor, also in state of Michigan in February 19855, which is now the company headquarters. In addition, the company decided that they should do their own glazing and set up a laboratory in Detroit, at a cost of $10,000. Thus, Cooper Vision had now consolidated all their operations inhouse, giving them greater control. Two further shores were opened in 1987 and the expansion continued across the USA. This expansion in new stores allowed Cooper Vision to spread its cost base and reduced the company’s dependence on the Michigan market, which Davin felt would be the first market targeted by foreign competitors.

Marketing strategy

With this research and other information collected from visits to retailers in the Canada, the UK and France, Davin had developed a sense of how he wanted to position the business. He dismissed the idea of the discount retailer, popular in the UK. He felt that American consumers were not ready to make the big switch from the traditional mode of obtaining ophthalmic products through optometrists to literally buying them off the shelf in a retail store.

Furthermore, getting costs down to a level necessary to operate as a discounter required economies of scale which, given his limited resources, he would not be in a position to achieve for a substantial period of time. For similar reasons, he rejected what he saw in the United Kingdom as a trend towards super-optical outlets (that is, very large retailers, competing on the basis of offering the widest possible range of products).

Thus, he wanted to position Cooper Vision, as he describes it, as the Walmart of ophthalmic retailing, providing a range of quality products at affordable prices, backed by service that was second to none.

Three characteristics, which set Cooper Vision apart from the traditional optometrist, were price, product range and the speed with which the consumer could get a pair of spectacles. Cooper Vision were able to offer substantially lower prices than their competitors at the outset. In 1989, the company was offering ready-made reading glasses complete with case for $12.99. These were sold to people with a recent valid prescription, with the idea of being a cheap second pair of reading glasses. A new set of spectacles, made to order, was available for as little as $29.99, substantially cheaper than the prices charged by the traditional optometrist.

Publicity in 1990 described Cooper Vision as having few ‘safe frames’ in fashion terms. The company tried to convince the American consumers to be more adventurous when choosing spectacles. Colour was a distinctive feature of their frames with reds, blues, yellows and tortoise available. The company was so committed to its line of French designer frames that anyone who bought an avant-garde style and changed his or her mind, up to a year later, could get a new replacement frame free of charge.

Initially, the company aimed to supply a new pair of spectacles within 24 hours. With an in-house glazing laboratory, this timeframe was significantly reduced and the company’s promotion stressed that consumers could come to town in the morning or afternoon, have their eyes tested, choose from a variety of fashionable frames and within the hour wear their new glasses home. This was a significant advance on traditional practice, where the consumer often had to wait for up to two weeks for a new pair of spectacles.

Product range

The company carried a complete range of ophthalmic products. These included lenses, spectacle frames, sunglasses, ready readers, contact lenses, contact lens solutions and accessories like magnifying glasses, clip-on sunglasses, etc. The percentage of sales accounted for by each product category is shown in Table C29.1. At any one time the company had between 400 and 500 spectacle frames in stock. It catered for all market segments with ranges including children, college, family, economy and the exclusive/trendsetter range.

Discussion Question

1. From the above case study, write an executive summary.

 
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