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Case Study 1 (Adapted from MIT Sloan â€“ Professor Jim Hines)
Even with a gentle breeze coming through the window of her new office in the Dominican Republic, Rebecca Stanhope was irritated by her new partnerâ€™s email. She read it again:
I think we better talk before the board meeting next week. Your estimates are way off. I think the board might notice.
Rebecca was supposed to be the â€œnumbersâ€ part of the team; Felix was supposed to be the â€œpeopleâ€ person. And, here he was claiming that her numbers were wrong.
Rebecca and Felix had recently secured funding for their new venture, Stogy, Inc. Their idea was to take advantage of an eventual over-supply of cigar tobacco, which they believed was coming sooner rather than later. Stogy would use high-quality surplus cigar tobacco to produce vanilla-, rum- and cognac-flavored cigars for sale to the U.S. The founders believed that the market for flavored cigars, though small, was less competitive than the market for premium hand-rolls â€“ providing an opportunity to buy discounted tobacco leaf and sell full-priced cigars. Further, the flavorings would mask taste-differences between the various tobaccos available for purchase, permitting Stogy to sell a consistent product made from inconsistent (though premium-grade) raw material.
Rebecca and Felix had met in business school a number of years earlier, and had stayed in close touch after she joined a bank and he joined a marketing consulting firm. Through the years, Felixâ€™s quick business judgement and his people skills had impressed Rebecca. For her part, Rebecca believed she brought financial acumen and an ability to see patterns and relationships. One example of this ability had been her realization that cigar production would over-shoot demand.
The plan was for Felix to spend their first year in business traveling the country, arranging terms with retailers. Stogy would not actually ship product during this startup year, because tobacco and rolled cigars must age. However, Rebecca would start building an inventory at their site in the Dominican Republic. She would begin purchasing tobacco leaf and hiring cigar rollers. The idea was to build inventory to about 2.5 million rolled cigars when shipping began the following year. During the start-up year Rebecca would gradually grow workshop space and storage facilities to keep pace with the expanding workforce and inventory.
The first year of operation would involve significant cash outlays with no revenues. Finding start-up capital had not been easy, but Rebecca had eventually put together a package involving two venture capital firms as well as essentially every penny she and Felix had. The venture capitalists had put together a very strong board. The board meeting to which Felix had referred in his email was intended to provide a relatively serious preview or how inventory and workforce would grow in the Dominican Republic.
To help her visualize the process, Rebecca, had produced a model in Vensim (figure 1 and appendix).
Figure 4: Rebecca Stanhope's model
Rebecca believed that Stogy would be able to hire experienced cigar rollers whose output would be somewhere around 200 cigars a day, depending on the cigarâ€™s size and shape as well as on the rollerâ€™s skill. Her model indicated that if Stogy hired two rollers per week during the entire first year, inventory would stand at 2,697,000 cigars by yearâ€™s end. Now, Felix was saying she was way off.
Rebecca stopped stewing over the email and called Felix in New York. â€œHow do figure that Iâ€™m way off?â€ She asked. Did you run the model?â€
â€œNo,â€ came the response. â€œItâ€™s a back of the envelope calculation. At two hundred cigars per day, a roller can roll 1000 cigars in a week; and two rollers can roll 2000 cigars in a week. So, each week, production rises by 2000 cigars, representing the two new workers hired that week. 2000 cigars per week multiplied by 52 weeks per year yields only about 100,000 cigars. Sorry pal, but youâ€™re going to have to hire about 50 rollers every week. Iâ€™m flying into Santo Domingo tonight; so we can chat tomorrow.â€
Rebecca was stunned. Obviously, Felix did not realize what he was saying. There was no way the financials could support a workforce the size implied by Felixâ€™s statement. If Felix was right, their venture was finished, ruined. If Felix was right they had better invite their attorneys to the board meeting.
Rebecca turned back to her computer to see if she had made a mistake.
Recreate Rebeccaâ€™s model in Vensim. Run the model (using Euler integration). Check that you get Rebeccaâ€™s answer for the ending inventory level.
1) Transform the Vensim equations into equivalent differential equation and integral equation forms using the templates below.
2) ! Will the world behave exactly according to Rebeccaâ€™s equations? Explain briefly.
3) ! Pretend to be Rebecca and write an email to Felix explaining where he went wrong in his argument that inventory would only amount to some 100,000 cigars.
The next day in Dominican Republicâ€¦
The next day Felix walked into the office holding the email Rebecca had sent the day before. With a big smile he said, â€œWell, I guess I need to get a new envelope. I never could get the hang of that math stuff. Iâ€™m better with pictures. So, to make up for my gaffe yesterday, Iâ€™ve sketched what inventory and workforce will look like.â€ Felix handed Rebecca a drawing like that below.
â€œObviously our facilities should follow a similar pattern,â€ Felix continued. â€œI know that you were hoping to keep storage facilities very small through the first half of the year, but obviously by mid-year we will need half of our workshop space and half of our storage built. We just canâ€™t get by with having only a quarter of our storage built.â€
Rebecca took Felixâ€™ drawing and wearily opened Vensim on her computer.
4) a) !Calculate inventory and workforce for week 26.
b) !Will inventories and workforce behave roughly as Felix thinks? Why or why not? Please use graphs in your analysis.
For groups of 2:
5) a) !Draw the Causal Diagram for this Model
b) !How many causal loops?
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