Reynold Peacock, owners of Peacock Programming, Inc., knows that he faces a daunting task. With several potential customer projects waiting to be accepted and limited resources at his disposal, some difficult choices lie ahead. Though the leansoftwaredevelopment strategies that his company has adopted have greatly increased the success rate of software projects (see Exhibit 1), a large portion still fall short (either partially or completely) of their stated goals.
Exhibit 1 – Comparison of Software Development Methods
A key factor in determining the chance of success for each project is the number of programmers allocated to its development. Specifically, using the outcomes of similar projects in the past, each project can characterized by a Success Parameter (SP) and Challenged Parameter (CP), which can then be use to estimate the chance of a Successful or Challenged completion:
Pr[Success]=0.75N/(N+SP) Pr[Challenged]=0.25N/(N+CP)
for the number of programmer assigned to that project (N).
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:
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?
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?
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)?
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.
Exhibit 2 – Generating a Random Value, X, from a Triangle Distribution
Second, the final outcome and revenues are fairly predictable approximately 2/3 (not a precise number that needs to be used in your calculations) of the way through the development of each project. At that point, the company can choose to terminate the project and reassign the programmers to small projects. For failures, doing so does not affect the loss, but would allow each programmer to generate some revenue. For a challenged or successes, terminating the project would cut the forecasted revenue by 40%, but each programmer would be able to make back some additional revenue. In either case,each reassigned programmer would generate $40,000 in revenue from small projects during the remaining time.
Assignment Questions for Part2:
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.
What does the distribution of revenue for each project look like? Provide appropriate charts (e.g., histogram) for each.
Repeat (1) and (2) with the ability to terminate projects, along with the associated effects on revenue (described above) and alternative use of staffing.
Note: Do not calculate these values directly; use simulation instead. Randomly generate an outcome and then an associated revenue for each project, then repeat (over and over again.)
*Assume that the projects’ revenues are independent, so that the means and variances are additive.
Part 3: Can you develop a simple method (i.e., a heuristic, not actually re-solving Part 1) utilizing the machinery in part 2 to make improvements in the allocations to those projects with programmers assigned? Show your process even if it shows that no improvements may be made.
Appendix 1
Appendix 2
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