Peacock Programming, Inc.
Part 1- The company is currently considering which of nine available projects to accept. Additionally, the 40 programmers employed by the company (assume that they are salaried and, to start, that additional programmers will not be hired) must be allocated to accepted projects in order to maximize the expected return for Peacock Programming (assume they are risk neutral.)
After consulting with area experts within the organization, Peacock was able to generate a table of Success and Challenged Parameters for each project, as well as the expected revenues fromeach, given an outcome of Success, Challenged or Failure (see Appendix 1).
Assignment Questions for Part 1:
a) Assuming that programmers may be partially assigned to projects, what is the optimal set of projects to initiate and number of programmers to allocate to each? What is the expected profit of this allocation?
b) If, instead, each programmer have to be assigned to a project for the whole duration (i.e., no partial workers may be assigned), how would your answers in (a) change?
c) Due to poor feedback when projects are minimally staffed, Peacock wants to implement a policy whereby any project accepted must be allocated at least four workers. How would this policy affect your answers in (b)?
d) If Peacock can hire additional programmers for $75,000 (for the duration of the projects), how many (if any) should they hire and how would their hiring affect your answers in (c)?
Part 2 - With the projects selected and committed to (your answers in Part 1 (d)), Peacock has had the chance to further analyze and discuss the potential revenues associated with each project's outcomes. Two factors that he has learned about seem critical to determining the potential profits from these projects and he would like to be able to better describe the potential outcomes.
First, the revenues for each outcome (Failure, Challenged, Success) of the projects listed in Appendix 1 are not actuallythe expected revenues for those outcomes, but rather are their "most likely" revenues. Looking at historical values, the actual revenue achieved by projects for a given outcome seem to (at least approximately) follow a triangle distribution (see Exhibit 2), which is characterized by lowest (L), highest (H) and most likely (M) values.
The lowest and highest values for each project and outcome are determined by the multipliers given in Appendix 2. For example, if the "most likely" revenue for a project's successful outcome is $1.50M and the low and high multipliers are 0.9 and 1.2, respectively, then the actual revenues will follow a triangle distribution with L = 0.9(1.5) = $1.35M, H = 1.2(1.5) = $1.80M and M = $1.50M.
Note: for the failure case, reverse the multipliers, so that L is actually the biggest loss, while H is the smallest loss.
Assignment Questions for Part2:
1) What is the estimated mean revenue for each project with the programmers allocated to it in Part 1 and in total*? What is estimated standard deviation of revenue for each and in total*? Assume, for now, that programs cannot be terminated.
2) What does the distribution of revenue for each project look like? Provide appropriate charts (e.g., histogram) for each.
3) Repeat (1) and (2) with the ability to terminate projects, along with the associated effects on revenue (described above) and alternative use of staffing.
Attachment:- Assignment.rar