Improving Project Management Decision Making by Modeling Quality, Time and Cost Continuously

1. Improving Project Management Decision Making by Modeling Quality, Time and Cost Continuously By Udayarajan SV PrathameshMorde submitted to Professor Shervin Shirmohammadi in partial fulfillment of the requirements for the course ELG 5100

2. Agenda • Abstract • Current Scenario • Work done by other Authors • Drawbacks and Proposed work • Quality Function • Data Fitting • Case Study Systems • Model Formulation • Results • Conclusion • Future Work • References

3. Abstract A project is valued based on the level of quality of the completed tasks or the project on the whole. Quality plays an important role in the project management but time and cost also have equal responsibilities. So far no models had been developed that relate these three components. In this paper we present quality function for individual tasks and we use the functional form of the bivariate normal to model the task level quality. In this paper, we also present case studies of a translation agency and a software development company. Using real data from the case studies, we model the quality function and incorporate it into mathematical programming model which allows quality to be explicitly considered in project planning and scheduling. The creation of different levels of quality curves through alternative models can be used to evaluate the non-linear tradeoffs between quality, time and cost for each example projects. The development of this project is done with two different conditions: holding time constant, holding cost constant and keeping quality as a change function depending on the other functions.

4. Current Scenario • While planning and scheduling a project, the emphasis is on time and cost, with an implicit assumption of a fixed level of quality • But it is important to explicitly consider the level of quality to be delivered during each phase of project management for better project deliverables • According to Project Management Body of Knowledge quality must addressed throughout the life cycle of the project.

5. Work done by Other Authors • Paquin et al. Project quality is assessed by splitting client satisfaction into a hierarchical structure of quality dimensions; these measured and aggregated using analytical hierarchy process or multi-attribute utility theory • Pollack-Johnson and Liberatore Developed a mathematical programming model for determining optimal discrete options defined in terms of time, cost and quality combinations for specific tasks • Babu and Suresh Project quality is measured as the arithmetic or geometric mean of the quality of the activities or as the minimum quality of the activities

6. Drawbacks and proposed work Multicriterion approach: Requires to identify and evaluate a unique set of quality dimensions for each task Proposed work: Quality is modeled at the task level as a continuous nonlinear function of both cost and time Model by Babu and Suresh: Assumes that quality depends only on time and is independent of cost

7. Quality Function Assumptions • A given task can be completed with different allocations of time and cost by different entities • There is a quality function that assigns quality value to each combination of time and cost • For a given values of time t and cost c: • Quality q ∝ c; with a constant value of t • Quality q ∝ t; with a constant value of c Quality Function Goal To find a method to model the relationship between quality, cost and time at the individual task level in a project and at the overall project level Approach To formulate a model of the quality at the task level as a function of the cost and time allocated to it

8. Quality Function - Development Our assumptions lead to the graph as shown below and make us to consider bivariate normal distribution in probability as the required function Q(t, c) = K * e^[{(t-μt)/σt}2 + {(c-μc)/σc}2]

9. Alternative In situations when there are n bids for completing an activity with different time, cost and quality values, the four parameters can be calculated using nonlinear lest squares estimation: Minimize • ∑{Q(tj,cj│μtj,μcj,σtj,σcj)-qj}2; • where, • μtj tj; μcj cj; (since μ variables are upper bounds on the values of t and c variables) • j = 1, 2, ...., n Estimation Bivariate normal values μt, μc: maximum practical time and cost values for a given task Standard Deviation (based on our assumptions) σt = (t0-μt)/√-ln(q0/K) σc = (c0-μc)/√-ln(q0/K)

10. Data Fitting - Case Study Systems Case study systems Translation Agency Software Development Firm Hybrid system to measure quality level (combination of a system from Interagency Language Roundtable and Rubric) Scale: 0 to 100; based on the number of rework cycles Scale: 0 to 44

11. Translation Agency Data as provided by the project manager for two different translators based on the Hybrid system’s quality level scaling for different time and cost values:

12. Translation Agency Results based on Bivariate Normal Quality function estimation: Plots based on the bivariate normal function with the data provided:

13. Software Development Firm Values calculated based on bivariate normal function:

14. Software Development Firm Plot based on the data provided earlier (upper envelope concept is used here as the tasks can be performed by more than one category of staff persons with different time, cost and quality characteristics):

15. Model Formulation Notations: ti: duration of activity i ci: cost of activity i qi: quality of activity i Si: set of activities that are immediate successors of activity i TUB: upper bound on the total project time CUB: upper bound on the total project cost si: scheduled start time for activity i tmini: lower bound on the duration of activity i cmini: lower bound on the cost of activity i for i = 1, . . ., N Qmin= min qi; i = 1, . . ., N (we consider this as from the systems perspective, when the quality of all activities are considered, the overall project quality is as high as its weakest link)

16. Maximizing Minimum Quality We maximize minimum quality by setting an upper bound on total project time and cost: Maximize Qmin subject to; Qmin ≤ qi qi = Qi(ti, ci) = K*exp{-[(ti-μti)/σti)]2 – [(ci-μci)/σci)]2} ∑ci ≤ CUB; for all i = 1, . . ., N s0 = 0 sk si + ti; for all i = 0, . . ., N and kϵSi sN+1 ≤ TUB si  0; for all i = 1, . . ., N+1 ti  tmin, ci  cmin, ti ≤ μti, ci ≤ μci qi, ti, ci  0; for all i = 1, . . ., N

17. Minimum Cost Formulation As an alternative, minimize total project cost with bounds on project completion time and quality: Minimize total cost ∑ci; i = 1, . . ., N and QLB ≤ qi, i = 1, 2, . . ., N By analyzing minimum cost model for different total project times TUB, minimum cost possible that finishes the project within a given time and maintains a minimum quality of at least the lower bound can be found.

18. Results – Translation Agency Maximizing Qmin Requirement: A decision is needed at 4 pm Monday concerning how much to offer to pay each translator, and what deadline to give each of them, to maximize the overall quality of the job and have the results in hand by noon Friday, at a cost of no more than $2400 Using bivariate normal quality function estimates the model is solved using Lingo’s Global Solver and the results are as displayed below:

19. Translation Agency - Isocurves Isocurves are constructed using the minimum cost formulation as displayed below:

20. Results – Software Development Firm Minimizing Cost Specifications: TUB = 19; QLB = 69 Minimum values for the time and cost of each task set at 30% of the mean value and the results are shown below:

21. Results – Network Diagram 5.299 Network diagram of the activities of Software Development firm is shown below with the data available in the previous slide: 5.299 0.0 0.0 1.299 17.617 12.0 1.1 0.0 1.3 1.0 4.0 ti 0.3 0.0 0.3 slacki 0.0 11.3 0.0 0.0 0.0 0.0 0.0 0.0 12.3 0 3 4 1 7 8 2 6 task i 5 ci 0 3055 27 208 1045 1000 0.0 114 142 N/A 70.8 69.0 100 69.0 100 69.0 0.0 qi 69.0 5.299 18.700 Key: si 19.000

22. Software Development Firm-Isocurves Isocurves of the Software Development firm case study are shown below:

23. Conclusion • Our approach can be applied to different areas such as construction industry, new product development etc (in addition to the areas presented as the case study systems) • As quality is an important part of project management, managers should evaluate multiple alternatives to complete project activities to achieve better quality • Quality function has been introduced to model the relationship between time, cost and quality at task level • Real data from two case study systems have been analyzed and the quality function has been specified for each task and incorporated into a nonlinear programming model which allows the quality to be explicitly considered during project planning and scheduling

24. Future Work • Indirect Project Cost • Considering indirect project cost during model formulation • Formulation of methods to monitor and control during the progress of the project

25. References • Matthew J. Liberatore and Bruce Pollack-Johnson, “Improving Project Management Decision Making by Modeling Quality, Time and Cost Continuously”, IEEE Transactions on Engineering Management, vol. 60, no. 3, August 2013 • A.J.G. Babu and N. Suresh, “Project Management with time, cost and quality considerations”, Eur. J. Operational Res., vol. 88, no. 2, pp. 320-327, 1996 • D.B. Khang and Y.M. Myint, “Time, cost and quality trade-off in project management: A case study”, Int. J. Project Manage., vol. 17, no. 4, pp. 249-256, 1999 • Bruce Pollack-Johnson and Matthew J. Liberatore, “Incorporating Quality Considerations into Project Time/Cost Tradeoff Analysis and Decision Making”, IEEE Transactions on Engineering Management, vol. 53, no. 4, November 2006 • Rong Xian, MU Lingling and Liu Ping, “Project Evaluation with Time, Cost, and Quality Considerations”, Sixth International Conference on Fuzzy Systems and knowledge Discovery, vol. 3, pp. 316-319, August 2009