A Goal Programming Model for Allocating Time and Cost in Project Management - Example

School: Topic: Goal Programming Project Lecturer: Introduction For most managers, the need to undertake profit-oriented projects is something they appreciate as useful without a doubt. The main problem that most of these managers are faced with however has to do with the handling of several projects at a go. The intensity of their dilemma increases when they have to select among the projects those that should be given higher implementation priority. It is for this reason that Kerzner (2003) opined that the ability of different managers to handle project management decision issues is an important determinant for differentiating great managers from ordinary ones. To make the task of managerial decision making easier, there are a number of models and modalities that may be applied by managers where they are faced with complexity of project options where they have to make decision based on specific expectations and outcomes. In this paper, the goal programming model is selected and analysed for a real world business and managerial decision making at Standard Fireworks Inc where a multi-criteria objective arising from the management of three projects became necessary. How the company went about the use of the goal programming project and the outcomes that were yielded are analysed along with objective opinion and recommendations about the outcome of the model’s application. The description of the scenario The scenario used is a case application taken from Standard Fireworks Inc. The company is into the making of safety matches and firecrackers. As part of the company’s growth agenda, it became necessary for it undertake three different projects based on its business expansion idea into several regions across India and into the international market, specifically the United Kingdom. These three projects were all focused on the expansion of processing plants. As part of its set goals, the company was to commerce all three projects at the same time. However, the three projects were different in size and magnitude. Because of this, the estimated monthly cost and the allocated completion dates were different for the three projects. Each project was however to be undertaken or implemented through three phases namely planning, scheduling, and control stages. In table 1 and 2 below, the monthly breakdown of cost, and total allocations and project durations are presented respectively. The identification of decision variables and data A project is multivariate, involving several variables which are worked together to accomplish a common goal (Dinsmore et al., 2005). The nature of the variables also affects the data that will be collected or used in executing the project. From table 1 and 2, the main variables for the projects that the company had to handle were labour and material cost, cost including miscellaneous, and duration. Under the labour and material cost, and cost including miscellaneous the main data used were monetary values of the project phases. The data used for the duration variable was also time allocated for the completion of each project. Table 1: Monthly breakdown of cost in (£) Project number Project phase Action plan Labour and material cost (£) Cost including miscellaneous expenses (£) 1 1 Planning 1,523,258 2,486,547 2 Scheduling 4,606,985 76,574,001 3 Control 958,838 1,691,031 2 1 Planning 1,697,936 2,896,937 2 Scheduling 6,160,332 89,569,689 3 Control 116,529 1,964,625 3 1 Planning 2,116,867 3,550,578 2 Scheduling 6,467,463 111,926,318 3 Control 1,444,578 2,400,385 Table 2: Total allocations and project durations Project number Total labour and material cost (£) Total cost including miscellaneous (£) Duration (months) 1 7,089,081 80,751,579 6 2 7,974,797 94,431,251 8 3 10,028,908 117,877,281 11 Having known the exact allocations and time, specific priorities were set for each project, which acted as project goals. These have been broken down below. Project 1 P1(1): complete project in 6 months P2(1): keep total budget expenditure within £80,751,579 Project 2 P1(2): complete project in 8 months P2(2): keep total budget expenditure within £94,431,251 Project 3 P1(3): complete project in 11 months P2(3): keep total budget expenditure within £117,877,281 Multi-criteria objective function From scenario given, it would be noted that the projects that the managers of Standard Fireworks Inc had to deal with were those that were multi-criteria objective in nature. This is because for each project, there were different expected outcomes or objectives that the managers needed to achieve or attain. As noted by Stellman and Greene (2005) one major characteristic of projects is for its to have several objectives to be accomplished. In most cases, the objectives are spread across time of completion, budget, labour, and material cost (Berrouiguet, 2012). For Standard Fireworks Inc, it major concern as far as multi-criteria objective was concerned had to do with time and total budget expenditure. Time was a major issue for the company given the fact that it needed to achieve turnover from its investments into the projects within the shortest possible time. For managers at the company therefore, even though each project was going to require a different quantum of resources and efforts, the earlier the projects were completed, the better it was going to be for the company. Total budget expenditure was also an issue due to the effect of the expenditure on profitability. As stressed by Kerzner (2003), most companies fail to record profits from major projects and investment because they fail to cut down on implementation expenditure. Indeed when the expenditure is high, it becomes difficult to balance it out with the revenues to make profits. Definition and formulation of business and managerial decision making problem Comparing table 1 and 2, it would be seen that whereas the data for labour and material cost, and cost including miscellaneous have been broken down into project phases in table 1, no such breakdown was done for the duration in table 2. This was the premise under which the business and managerial decision making problem arose. Standard Fireworks Inc was faced with the business and managerial decision making problem of allocating time to each of the three phases involved in each project. As depicted in table 1, each project is made up of three phases namely planning, scheduling, and control. The problem of allocation of time to the project phases arose due to the need of ensuring that the proposed time will be achieved as well as the total budget expenditure that had been prepared for the projects. As explained earlier, the company believed that completing the projects on time would ensure that they started recording their breakeven points earlier. But for the breakeven to be a profit, it was also important that the most minimal amounts of expenditure would be invested into the projects (Fabiane, Neida & Carlos, 2003). Applying goal-programming Model to the problem Berrouiguet (2012) posited that projects problems having multiple objectives are best solved by the use of multiple-objective programming. Meanwhile there are several types of multiple-objective programming techniques, each of which seeks to achieve a unique purpose. Each of the multiple-objective programming techniques also fit well into different project scenarios. For the project scenario given and the decision making problem identified, the goal programming technique which was originally developed by Charnes and Copper in 1961 will be applied. The suitability of the goal programming technique is in the explanation of Aouni and Kettani (2001) who explained that the technique allows managers to take into account simultaneously many objectives when the decision-maker is seeking the best solution from among a set of feasible solutions. Already, the objectives and problem that will be used have been outlined. Mubiru (2010) developed the goal programming model based on the technique by Charnes and Copper. In this paper, the Mubiru (2010) goal programming model will be applied to see how best Standard Fireworks Inc can allocate time and cost in its project management. Under the model, Mibiru (2010) formulated a goal programming problem for allocating time and cost in project management based on the equation below. Subject to: From the above, (i = 1, 2, …, n) = set of projects (j = 1, 2, 3) = phases of project (k = 1, 2, 3) = 3 goals for each project Z = Value of objective function Pk(i) = Pre-emptive priority of Kth goal Dk+ = Overachievement of Kth goal Dk- = Underachievement of Kth goal Xij = Time allocated for project i during phase j Ti = Total time of completion Cij = Monthly total cost (including miscellaneous cost) TCi = Total cost of entire project Aij = Monthly labour and material cost LMCi = Labour and material cost Based on the model, it is possible to allocate time and cost specific to Standard Fireworks Inc by filling in the equations with data from table 1 and 2. When this is done for each of the projects, the following results will be attained. Project 1 Minimise Z = P1(1) D1+ + P1(1) D1- + P2(1) D2+ + P2(1) D2- Subject to: X11 + X12 + X13 – D1+ + D1- = 6 2,486,547 X11 + 76,574,001 X12 + 1,691,031 X13 – D2+ + D2+ = 80,751,579 1,523,258 X11 + 4,606,985 X12 + 958,838 X13 – D3+ + D3+ = 7,089,081 Project 2 Minimise Z = P1(2) D1+ + P1(2) D1- + P2(2) D2+ + P2(2) D2- Subject to: X21 + X22 + X23 – D1+ + D1- = 8 2,896,937 X21 + 89,569,689 X22 + 1,964,625 X23 – D2+ + D2+ = 94,431,251 1,697,936 X21 + 6,160,332 X12 + 116,529 X13 – D3+ + D3+ = 7,974,797 Project 3 Minimise Z = P1(3) D1+ + P1(3) D1- + P2(3) D2+ + P2(3) D2- Subject to: X31 + X32 + X33 – D1+ + D1- = 11 3,550,578 X31 + 111,926,318 X32 + 2,400,385 X33 – D2+ + D2+ = 117,877,281 2,116,867 X31 + 6,467,463 X32 + 1,444,578 X33 – D3+ + D3+ = 10,028,908 Solution For each of the projects, its outcomes can be computed using the LINDO software for the model. Once this was done, the following results were yielded were yielded for each project. Project 1 solution X11 = Time allocated for planning = 0.3 months X12 = Time allocated for scheduling = 1.05 months X13 = Time allocated for control = 4.65 months From the above, P1(1) which is goal for completing project 1 on time is achieved as expected as the sum of X11, X12 and X13 = 0.3 + 1.05 + 4.65 = 6 months. Secondly, goal for spending within the total budget expenditure is not fully achieved as 2,486,547 X11 + 76,574,001 X12 + 1,691,031 X13 = 2,486,547 (0.3) + 76,574,001 (1.05) + 1,691,031 (4.65) = 745964.1 + 80402701.05 + 7863294.15 = 89,011,959.9 Meanwhile the total budgeted amount is 80,751,579, which is less than what was used Project 2 solution X21 = Time allocated for planning = 0 months X22 = Time allocated for scheduling = 0.95 months X23 = Time allocated for control = 7.05 months From the above, P1(2) which is goal for completing project 2 on time is achieved as expected as the sum of X21, X22 and X33 = 0 + 0.95 + 7.05 = 8 months. Meanwhile the planned time to complete project 2 is 8 months Secondly, goal for spending within the total budget expenditure is partially achieved based on the following outcomes: 2,896,937 X21 + 89,569,689 X22 + 1,964,625 X23 = 2,896,937 (0) + 89,569,689 (0.95) + 1,964,625 (7.05) = 0 + 85,091,204 + 13,850,606.25 = 98,941,810.25 Meanwhile the total budgeted amount is 94,431,251, which is less than what was used Project 3 solution X31 = Time allocated for planning = 0.2 months X32 = Time allocated for scheduling = 0.78 months X33 = Time allocated for control = 10.02 months From the above, P1(3) which is goal for completing project 3 on time is achieved as expected as the sum of X31, X32 and X33 = 0.2 + 0.78 + 10.02 = 8 months. Meanwhile the planned time to complete project 3 is 11 months Secondly, goal for spending within the total budget expenditure is achieved based on the following outcomes: 3,550,578 X31 + 111,926,318 X32 + 2,400,385 X33 = 3,550,578 (0.2) + 111,926,318 (0.78) + 2,400,385 (10.02) = 710,115.6 + 87,302,528.04 + 24,051,857.7 = 112,064,501.34 Meanwhile the total budgeted amount is 117,877,281, which is more than what was actually used Constraints and Sensitivity analysis with objective opinion From the solutions, it can be found that for all three projects, the allocated time will be achieved. There is however a major constraint with project 1 and 2 because the model proposes that the planning time will be 0 months. This means that there will not be a planning phase for those two projects if the right allocation must be adhered to. From an objective opinion, it would be said that this solution is illogical and impractical because it will not be possible to complete the project without a planning phase. Certainly, trying to do this will mean that the project will fail because the planning phase is a major anchor on which all other phases of the project hang (Dinsmore et al., 2005). Another trend that the model reveals is that even though the scheduling phase has been allocated the highest total budget expenditure for all three projects, it is not going to be the phase to take a lot of time allocation as the control phase has the most number of months allocated for all three projects. The implication here is that for the scheduling phase, a lot of money will be spent on hardware and other expensive materials and parts within the short periods allocated for it. Lastly, it is seen that with the exception of project 3 which will use less money than budgeted, all the projects will require additional money. This will be a major constraint if the company’s ability to raise funds is poor. If the company has a good fund raising ability however, this issue will not pose much challenge. Conclusion, managerial implication and recommendation On the whole, it can said that the model gives satisfactory levels of solving the decision making problem of allocating time and cost across the three phases of the project. Even though the time allocated in some instances have been noted to be illogical, it does not render the model useful. Rather, it helps to give the company indications of how best it can position itself to go through all stages of the project without any challenge. For project 1 and 2, it will be important to increase the overall time so that there can be some allocation for planning phase. For the scheduling phase, because a lot of spending will be done within a short time, proactive monitoring of the use of money is required else misappropriation and operational risk could easily arise (Stellman & Greene, 2005). For projects 1 and 2 which will require additional money, there are two ways out for the company. It could be extending time for the planning phase by cutting the time for either schedule or control phase so that the amounts to be spent on these last two phases can reduce to keep the budget in check. Other than this, the company could use other means of raising money that will not affect stakeholder confidence. One such means is to use internally generated funds. Still on the excessive budgets, the company could also adopt the lean production thinking to ensure that as many forms of wastes as possible that can be identified with the projects are eradicated so that the amount spent on the projects can be reduced. References Aouni.B and Kettani.O.(2001). Goal programming : A glorious history and a promising future. Europrean Journal of Operational Research 133, 225-231. Berrouiguet A. Y. (2012). Application of goal programming model for allocating time and cost in project management: A case study from the company of construction Seror. Yugoslav Jounral of Operations Research. 34(2), 132-142 Charnes.A and Cooper.W.W. (1961). Management models and industrial applications of linear programming. Wiley, New York. Dinsmore P. C. et al (2005) The right projects done right! New York: John Wiley and Sons Fabiane.D.O, Neida.M.P, Carlos.R.S. (2003). Goal programming in a planning problem. Applied Mathematics and Computation 140, 165-178. Kerzner H. (2003). Project Management: A Systems Approach to Planning, Scheduling, and Controlling (8th Ed. ed.). New York: Wiley. Mubiru.P.K.(2010). A goal programming model for allocating time and cost in project management . Proceedings of the 6th ORSEA Conference - 14-15 October, Kampala. http://orsea.net/2010.htm Stellman, A. & Greene, J. (2005). Applied Software Project Management. London: OReilly Media. Read More