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HI Everyone, I would like to ask for assistance on the below problem, a question

ID: 2778929 • Letter: H

Question

HI Everyone,

I would like to ask for assistance on the below problem, a question from my Quantitalive Management class. I am hoping that you could include a detailed illustrations/ solutions so I can fully understand the proposed solution. Thanks in advance.

Short-Term Scheduling: Old Oregon Wood Store

In 2002, George Brown started the Old Oregon Wood Store to manufacture Old Oregon tables. Each table is carefully constructed by hand using the highest quality oak. Old Oregon tables can support more than 500 pounds, and since the start of the Old Oregon Wood Store, not one table has been returned because of faulty workmanship or structural problems. In addition to being rugged, each table is beautifully finished using a urethane varnish that George developed over 20 years of working with wood-finished materials.

The manufacturing process consists of four steps: preparation, assembly, finishing, and packaging. One person performs each step. In addition to overseeing the entire operation, George does all of the finishing. Tom Surowski performs the preparation step, which involves cutting and forming the basic components of the tables. Leon Davis is in charge of the assembly, and Cathy Stark performs the packaging.

Although each person is responsible for only one step in the manufacturing process, everyone can perform any one of the steps. It is George's policy that occasionally everyone should complete several tables on his or her own without any help or assistance. A small competition is used to see who can complete an entire table in the least amount of time. George maintains average total and intermediate completion times. The data are shown in Figure 1.

Figure 1.

Manufacturing Time in minutes

100

160

250

275

Preparation

Assembly

Finishing

Packaging

Tom

80

160

220

230

Preparation

Assembly

Finishing

Packaging

George

110

200

290

Preparation

Assembly

Finishing

Packaging

Leon

120

190

290

315

Preparation

Assembly

Finishing

Packaging

Cathy

Figure 2

Randy's Completion Time in minutes

110

190

290

300

Preparation

Assembly

Finishing

Packaging

Randy

It takes Cathy longer than the other employees to construct an Old Oregon table. In addition to being slower than the other employees, Cathy is also unhappy about her current responsibility of packaging, which leaves her idle most of the day. Her first preference is finishing, and her second preference is preparation.

In addition to quality, George is concerned with costs and efficiency. When one of the employees misses a day, it causes major scheduling problems. In some cases, George assigns another employee overtime to complete the necessary work. At other times, George simply waits until the employee returns to work to complete his or her step in the manufacturing process. Both solutions cause problems. Overtime is expensive, and waiting causes delays and sometimes stops the entire manufacturing process.

To overcome some of these problems, Randy Lane was hired. Randy's major duties are to perform miscellaneous jobs and to help out if one of the employees is absent. George has given Randy training in all phases of the manufacturing process, and he is pleased with the speed at which Randy has been able to learn how to completely assembly Old Oregon tables. Total and intermediate completion times are given in Figure 2.

DISCUSSION QUESTIONS

What is the fastest way to manufacture Old Oregon tables using the original crew? How many could be made per day?

Would production rates and quantities change significantly if George would allow Randy to perform one of the four functions and make one of the original crew the backup person?

What is the fastest time to manufacture a table with the original crew if Cathy is moved to either preparation or finishing?

Whoever performs the packaging function is severely underutilized. Can you find a better way of utilizing the four- or five-person crew than either giving each a single job or allowing each to manufacture an entire table? How many tables could be manufactured per day with this scheme?

Figure 1.

Manufacturing Time in minutes

100

160

250

275

Preparation

Assembly

Finishing

Packaging

Tom

80

160

220

230

Preparation

Assembly

Finishing

Packaging

George

110

200

290

Preparation

Assembly

Finishing

Packaging

Leon

120

190

290

315

Preparation

Assembly

Finishing

Packaging

Cathy

Figure 2

Randy's Completion Time in minutes

110

190

290

300

Preparation

Assembly

Finishing

Packaging

Randy

Explanation / Answer

1.

2

Hungarian method 1.matrix reduction :row reduction preparation Asswmbly Finshing packaging tom 100 160 250 275 George 80 160 220 230 leon 110 200 280 290 cathy 120 190 290 315 2.Row reduction preparation Asswmbly Finshing packaging tom 0 60 150 175 George 0 80 140 150 leon 0 90 170 180 cathy 0 70 170 195 Column reduction preparation Asswmbly Finshing packaging tom 0 60 150 175 George 0 80 140 150 leon 0 90 170 180 cathy 0 70 170 195 Column reduction preparation Asswmbly Finshing packaging tom 0 0 10 25 George 0 20 0 0 leon 0 30 30 30 cathy 0 10 30 45 Initial solution preparation Asswmbly Finshing packaging tom 0 0 10 25 George 0 20 0 0 leon 0 30 30 30 cathy 0 10 30 45 non optimal preparation Asswmbly Finshing packaging tom 0 0 0 15 George 0 10 0 0 leon 0 20 20 20 cathy 0 0 20 35 optimal preparation Asswmbly Finshing packaging tom 0 0 0 15 George 0 10 0 0 leon 0 20 20 20 cathy 0 0 20 35 assign optimal solution tom finising Georg packaging Leon preparation Cathy Assembly Total time =optimal cost =780 preparation assembly finishing packaging Tom 100 160 assign250 275 george 80 160 220 assign230 Leon assign110 200 280 290 Cathy 120 assign 190 290 315 job Assigned to cost tom finising 250 Georg packaging 230 Leon preparation 110 Cathy Assembly 190 total 780