(Use this if you would like projects in rows) Project Number Success Parameter 1 2 3 4 5 6 7 8 9 10 6.07 2.90 3.97 2.97 3.95 2.63 1.42 6.42 3.24 3.09 Mean Revenue/Loss (Millions $'s) Failure Challenged Success -0.955 1.353 2.234 -0.581 1.342 1.972 -1.958 3.695 5.469 -0.469 1.533 2.960 -0.421 0.954 1.560 -0.606 2.251 4.254 -1.453 3.384 5.263 -0.359 0.538 1.182 -0.771 1.895 2.707 -0.361 1.203 2.468 (Use this if you would like projects in rows) Project Number Success Parameter 1 2 3 4 5 6 7 8 9 10 6.07 2.90 3.97 2.97 3.95 2.63 1.42 6.42 3.24 3.09 L -1.210 -0.685 -2.299 -0.579 -0.533 -0.728 -1.762 -0.406 -0.865 -0.447 Failure M -0.946 -0.591 -1.932 -0.452 -0.410 -0.592 -1.493 -0.363 -0.766 -0.363 Mean Revenue/Loss (Millions $'s) Challenged H L M H -0.709 1.005 1.340 1.715 -0.467 1.078 1.365 1.583 -1.642 3.099 3.646 4.339 -0.376 1.227 1.479 1.893 -0.320 0.725 0.929 1.208 -0.497 1.848 2.200 2.706 -1.105 2.573 3.477 4.103 -0.308 0.462 0.543 0.609 -0.682 1.675 1.882 2.127 -0.273 0.908 1.211 1.490 s (Millions $'s) L 1.659 1.584 4.587 2.370 1.185 3.492 4.001 1.015 2.393 1.863 Success M 2.212 2.005 5.397 2.855 1.519 4.157 5.407 1.194 2.689 2.485 H 2.831 2.326 6.422 3.655 1.975 5.113 6.380 1.337 3.039 3.056 (Use this if you would like projects in columns) Mean Revenue/Loss (Millions $'s) Project SP 1 6.07 2 2.9 3 3.97 4 2.97 5 3.95 -0.955 -0.581 -1.958 -0.469 -0.421 Challenged 1.353 1.342 3.695 1.533 0.954 Success 2.234 1.972 5.469 2.96 1.56 Failure 6 2.63 7 1.42 8 6.42 9 3.24 10 3.09 -0.606 -1.453 -0.359 -0.771 -0.361 2.251 3.384 0.538 1.895 1.203 4.254 5.263 1.182 2.707 2.468 (Use this if you would like projects in columns) Mean Revenue/Loss (Millions $'s) Project SP 1 6.07 2 2.9 3 3.97 4 2.97 5 3.95 L -1.210 -0.685 -2.299 -0.579 -0.533 M -0.946 -0.591 -1.932 -0.452 -0.410 H -0.709 -0.467 -1.642 -0.376 -0.320 L 1.005 1.078 3.099 1.227 0.725 Challenged M 1.340 1.365 3.646 1.479 0.929 H 1.715 1.583 4.339 1.893 1.208 L 1.659 1.584 4.587 2.370 1.185 M 2.212 2.005 5.397 2.855 1.519 H 2.831 2.326 6.422 3.655 1.975 Failure Success 6 2.63 7 1.42 8 6.42 9 3.24 10 3.09 -0.728 -1.762 -0.406 -0.865 -0.447 -0.592 -1.493 -0.363 -0.766 -0.363 -0.497 -1.105 -0.308 -0.682 -0.273 1.848 2.573 0.462 1.675 0.908 2.200 3.477 0.543 1.882 1.211 2.706 4.103 0.609 2.127 1.490 3.492 4.001 1.015 2.393 1.863 4.157 5.407 1.194 2.689 2.485 5.113 6.380 1.337 3.039 3.056 Christopher P. Wright, PhD Peacock Programming, Inc. 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 Lean software development 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), which can then be use to estimate the chance of a Successful or Challenged completion: Pr [ Success ]=0.85 N ( N +SP ) Pr [Challenged ]=0.15 ( N +NSP ) given the number of programmer assigned to that project (N). 2015-16. This case was prepared by Dr. Christopher P. Wright solely for the purpose of a class assignment. It is not intended to illustrate effective or ineffective management. This case is fictionalized and any resemblance to actual persons or organizations is coincidental. No portion of this case may be reproduced or transmitted in any form or by any means - electronic, mechanical, photocopying, recording or otherwise - without the express permission of Dr. Wright. Part 1 The company is currently considering which of ten (10) available projects to accept. Additionally, the 30 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 Parameters for each project, as well as the expected revenues from each, given an outcome of Success, Challenged or Failure (see Appendix 1). Assignment Questions for Part 1: a) Assuming that programmers are not dedicated exclusively to one project (i.e., they may be partially assigned, so you need not assign only whole programmers), 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 has to be assigned to a project for the whole duration (i.e., no partial programmers 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 five (5) programmer. How would this policy affect your answers in (b)? Bonus: If Peacock can hire additional programmers for $100,000, how many (if any) should they hire and how would their hiring affect your answers in (c)? Note: for credit, you cannot solve this by manually increasing the staffing requirement. Solver must tell you. Part 2 With the projects selected and committed to (your answers in Part 1 (c)), Peacock has had the chance to further analyze and discuss the potential revenues associated with each project's outcomes. Beyond just the expected revenues for each outcome (Failure, Challenged and Success) listed in Appendix 1, more is now known about the distribution of revenues for each. Looking at historical values, the actual revenue achieved by a project for a given outcome seems to (at least approximately) follow a triangle distribution (see Appendix 3), which is characterized by lowest (L), highest (H) and most likely (M) revenues. These values for each project and outcome are given in Appendix 2. Assignment Questions for Part 2: a) What are the estimated mean and standard deviation of revenue for each project that had programmers allocated to it in Part 1(c), using the triangle distribution parameters (L/M/H) in Appendix 2? For total revenues*? *Assume that projects' revenues are independent. Note: Do not calculate these values directly; use simulation instead. Randomly generate an outcome and the associated revenue for each project, then repeat (over and over again.) b) What does the distribution of revenue for each project look like? Provide the appropriate chart (e.g., histogram) for each. Note: there should only be one chart per project. Appendix 1 Appendix 2 Appendix 3 Triangle distribution of revenue, R, characterized by L, M and H: f(r) L M H L M H R F(r) 1 M-L H-L 0 R F(r) = Pr[R r] = Note: Both give F(M) = (M - L)/(H - L). Also, if F(r) is < F(M), then r < M