*****PLEASE Only answer question 5, and 6 to your fullest ability. Thank you sincerely

Custom Vans, Inc., specializes in converting standard vans into campers. Depending on the amount of work and customizing to be done, the customizing can cost from less than $1,000 to more than $5,000. In less than 4 years, Tony Rizzo was able to expand his small operation in Gary, Indiana, to other major outlets in Chicago, Milwaukee, Minneapolis, and Detroit.

Innovation was the major factor in Tony's success in converting a small van shop into one of the largest and most profitable custom van operations in the Midwest. Tony seemed to have a special ability to design and develop unique features and devices that were always in high demand by van owners. An example was Shower-Rific, which was developed by Tony only 6 months after Custom Vans, Inc., was started. These small showers were completely self-contained, and they could be placed in almost any type of van and in a number of different locations within a van. Shower-Rific was made of fiberglass, and contained towel racks, built-in soap and shampoo holders, and a unique plastic door. Each Shower-Rific took 5 gallons of fiberglass and 3 hours of labor to manufacture.

Most of the Shower-Rifics were manufactured in Gary in the same warehouse where Custom Vans, Inc., was founded. The manufacturing plant in Gary could produce 300 Shower-Rifics in a month, but this capacity never seemed to be enough. Custom Van shops in all locations were complaining about not getting enough Shower-Rifics, and because Minneapolis was farther away from Gary than the other locations, Tony was always inclined to ship Shower-Rifics to the other locations before Minneapolis. This infuriated the manager of Custom Vans at Minneapolis, and after many heated discussions, Tony decided to start another manufacturing plant for Shower-Rifics at Fort Wayne, Indiana. The manufacturing plant at Fort Wayne could produce 150 Shower-Rifics per month.

The manufacturing plant at Fort Wayne was still not able to meet current demand for Shower-Rifics, and Tony knew that the demand for his unique camper shower would grow rapidly in the next year. After consulting with his lawyer and banker, Tony concluded that he should open two new manufacturing plants as soon as possible. Each plant would have the same capacity as the Fort Wayne manufacturing plant. An initial investigation into possible manufacturing locations was made, and Tony decided that the two new plants should be located in Detroit, Michigan; Rockford, Illinois; or Madison, Wisconsin. Tony knew that selecting the best location for the two new manufacturing plants would be difficult. Transportation costs and demands for the various locations would be important considerations. Production costs (materials and labour) at the new plants would also matter.

The Chicago shop was managed by Bill Burch. This shop was one of the first established by Tony, and it continued to out-perform the other locations. The manufacturing plant at Gary was supplying 200 Shower-Rifics each month, although Bill knew that the demand for the showers in Chicago was 300 units. The transportation cost per unit from Gary was $12, and although the transportation cost from Fort Wayne was double that amount, Bill was always pleading with Tony to get at least an additional 50 units from the Fort Wayne manufacturer. The two additional manufacturing plants would certainly be able to supply Bill with the additional 100 showers he needed. The transportation costs would, of course, vary, depending on which two locations Tony picked. The transportation cost per shower would be $26 from Detroit, $5 from Rockford, and $7 from Madison.

Wilma Jackson, manager of the Custom Van shop in Milwaukee, was the most upset about not getting an adequate supply of showers. She had a demand for 100 units, and at the present time, she was only getting half of this demand from the Fort Wayne manufacturing plant. She could not understand why Tony didn't ship her all 100 units from Gary. The transportation cost per unit from Gary was only $15, while the transportation cost from Fort Wayne was $25. Wilma was hoping that Tony would select Madison for one of the manufacturing locations. She would be able to get all the showers needed, and the transportation cost per unit would only be $7. If not in Madison, a new plant in Rockford would be able to supply her total needs, but the transportation cost per unit would be twice as much as it would be from Madison. Because the transportation cost per unit from Detroit would be $36, Wilma speculated that even if Detroit became one of the new plants, she would not be getting any units from Detroit.

Custom Vans, Inc., of Minneapolis was managed by Tom Polanski. He was getting 100 showers from the Gary plant. Demand was 180 units. Tom faced the highest transportation costs of all locations. The transportation cost from Gary was $35 per unit. It would cost $13 more if showers were sent from the Fort Wayne location. Tom was hoping that Detroit would not be one of the new plants, as the transportation cost would be $56 per unit. Rockford and Madison would have a cost of $28 and $23, respectively, to ship one shower to Minneapolis.

The Detroit shop's demand was 150 units. The 100 units that Detroit did receive came directly from the Fort Wayne plant. The transportation cost was $18 per unit from Fort Wayne, while it was $22 from Gary. Rick Lopez, manager of Custom Vans, Inc., of Detroit, placed the probability of having one of the new plants in Detroit fairly high. The factory would be located across town, and the transportation cost would be only $8 per unit. Even if Detroit was not selected, the other two locations were not intolerable. Rockford had a transportation cost per unit of $37, and Madison had a transportation cost of $42.

Tony pondered the dilemma of locating the two new plants for several weeks before deciding to call a meeting of all the managers of the van shops. The decision was complicated, but the objective was clear-to minimize total costs. The meeting was held in Gary, and everyone was present except Wilma.

Tony:Thank you for coming. As you know, I have decided to open two new plants at Rockford, Madison, or Detroit. The two locations, of course, will change our shipping practices, and I sincerely hope that they will supply you with the Shower-Rifics that you have been wanting. I know you could have sold more units, and I want you to know that I am sorry for this situation.

Rick:Tony, I have given this situation a lot of consideration, and I feel strongly that at least one of the new plants should be located in Detroit. As you know, I am now only getting half of the showers that I need. My brother, Leon, is very interested in running the plant, and I know he would doa good job.

Tom:Rick, I am sure that Leon could doa good job, and I know how difficult it has been since the recent layoffs by the auto industry. Nevertheless, we should be considering total costs and not personalities. I believe that the new plants should be located in Madison and Rockford. I am farther away from the other plants than any other shop, and these locations would significantly reduce transportation costs.

Rick:That may be true, but there are other factors. Detroit has one of the largest suppliers of fiberglass, and I have checked prices. A new plant in Detroit would be able to purchase fiberglass for $1 per gallon less than any of the other existing or proposed plants.

Tom:At Madison, we have an excellent labor force. This is due primarily to the large number of students attending the University of Wisconsin. These students are hard workers, and they will work for $1 less per hour than the other locations that we are considering.

Bill:Calm down, you two. It is obvious that we will not be able to satisfy everyone in locating the new plants. Therefore, I would like to suggest that we vote on the two best locations.

Tony:I don't think that voting would be a good idea. Wilma was not able to attend, and we should be looking at all of these factors together in some type of logical fashion.

Discussion Question

Q1. What is the total cost with the existing pattern involving only two plants in Gary and Ft. Wayne?

Q2. What would be the best solution (minimized cost) if Tony used the stepping stone algorithm to find the optimal solution for the current situation with these two plants only? How much money are they losing now?

Q3. Find the best pattern of shipments (optimal solution) for each pair of new plants added to Gary and Ft. Wayne:

a) Detroit and Madison

b) Madison and Rockford

c) Detroit and Rockford

Q4. Which of these three patterns of shipments is the lowest cost solution? Provide additional discussion/rationale in favour of (or perhaps against) your selected solution. Any managerial considerations, etc.?

Q5. For your optimal pattern of shipments found in Q4. above (FOCUS ONLY ON THIS ONE, NOT ON ALL THREE OF THEM), doalternative optimal solutions exist? Justify your answer.

Q6. If they exist, use the stepping stone algorithm and find manually the second optimal solution. Present your analysis in a graphically neat manner. Use any drawing technique you like - just make sure it looks fairly professional.

Q7. Finally, produce the third optimal solution by taking a combination of 40% of the first optimal solution and 60% of the second one.

Attach all relevant exhibits from Excel's Solver calculations. Use PrintScreen, edit/copy/paste, etc. - whatever you like. Fully explain your answers.