Problems

1. In the course of manufacturing sunglasses, workstation K must attach the lenses to the frame; lenses come from workstation J. These are the nonprescription type of sunglasses which may be bought off of the rack at the drugstore and this problem is concerned only with the lenses, not the frames. Management has scheduled the production of 160 sunglasses per 8-hour shift. Workstation J requires 3.0 minutes to produce a pair of lenses (left and right); once in a while a pair of lenses is defective, and management allows .20 for inefficiencies. The finished lenses are placed in containers of a dozen pairs each. When workstation K opens a container of lenses, it sends the kanban back to station J which takes 15 minutes, it takes 15 minutes for a container to be transported from station J to station K.

1. What is the value of D?
2. What is the value of T?
3. What is the value of X?
4. What is the value of C?
5. How many kanban cards (or containers) should be used in this system?

2. (One step beyond) One step in the manufacture of tennis rackets consists of weaving the cross strings into the head of the racket. This task requires a high level of skill and experience, and is slow. In workstation G, six skilled weavers work on tennis rackets; on the average, it takes 45 minutes for one weaver to weave a tennis racket. The head of the racket is produced by a supplier who has been certified; the supplier is located in Portland. OR, while the manufacturer is located in Los Angeles, CA, a distance of about 1,000 miles. Tennis racket heads are shipped by truck from Portland to Los Angeles; each truckload contains six dozen heads and the trip takes two days, i.e., the truck leaves Portland on the morning of the first day (say Monday) and arrives in Los Angeles on the evening of the second day (Tuesday); the racket heads are available for weaving on the morning of the third day (Wednesday). When any weaver opens the shipment, the kanban is sent to the computer room, where an operator faxes the order instantaneously to the supplier's computer; the order will be on the road the next business day. The six weavers work an eight-hour shift with two 15-minute coffee breaks. Production is continuous; with the current popularity of tennis, the firm can sell all of the rackets it can produce, and is in the happy position of having back orders. The weaving jobs are well done, and management allows .05 for inefficiencies and errors.

1. What Is the value of D?
2. What is the value of T?
3. What is the value of X?
4. What is the value of C?
5. How many kanbans should be in use?
6. Suppose that highway construction forces the trucks to take a detour which delays the arrival in Los Angeles one day. What effect will this have on the number of kanban cards?
7. After consultation with the supplier, It is decided to experiment with larger shipments of tennis racket heads. A larger truck is rented which can carry eight dozen heads. What effect will this have on the number of kanban cards?
8. Suppose one of the weavers retires. An apprentice must be hired and trained. During the training period, the average time required to weave a head is estimated at 60 minutes. What effect will this have on the number of kanban cards?
9. During the trial period, management anticipates that the rate of defective weaving jobs will increase, and the allowance is raised to .20. What effect will this have on the number of kanban cards?

3. The TruTime Corporation produces four styles of wrist watches, described below, with the daily requirements for each style for the month of September.

The setups for models MD and WD are similar. The setups for models MA and WA are similar but are more complicated and lengthy than the other setups.

1. What sequence of models should be used in a production cycle?
2. How many cycles should there be per day?
3. How many of each style should be produced in each cycle?
4. How can the answer to #1-c be improved?

4. Here are the production requirements for the TruTime Corporation (see #3) for the month of October.

1. How many cycles are required per day?
2. How many of each style should be produced in each cycle?

Solutions

1. a. D = 160/8 = 20 sunglasses per hour.
b. T = 12(3.0) + 15 + 15 = 66 min. = 1.1 hrs.
c. X = .20.
d. C = 12 pairs.
e. N = DT(1 + X)/C = 20(1.1)(1.2)/12 = 2.2 ® 3 kanban cards.

2. a. D = 6(7.5 hrs.)/(.75 hrs) = 60 woven heads per day.
b. T = 1 + 3 = 4 days.
c. X = .05.
d. C = 72 heads.
e. N = DT(1 + X)/C = 60(4)(1.05)/72 = 3.50 ® 4 kanban cards.
f. N = 4.375 --> 5.
g. N = 2.625 à 3.
h. N = 2.625 à 3.
i. Using the information in 2-h, N = 3.

3. a. Combine similar setups. MD-WD-MA-WA would be feasible. (So would MA-WA-MD-WD.)

d. Setting up three times for WD may be inefficient; you might schedule all of WD for one cycle.

Cycles

4. a. 5 cycles, since two requirements are divisible by 5.
   b. Try to smooth out production and reduce the number of setups. Here is one way to do it.

Cycles

See if you can devise a smoother schedule. You might also try for fewer setups.