PROFIT MAXIMIZATION AND STRATEGIC MANAGEMENT FOR CONSTRUCTION PROJECTS

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1 Slide 1 PROFIT MAXIMIZATION AND STRATEGIC MANAGEMENT FOR CONSTRUCTION PROJECTS Hakob Avetisyan Ph.D. Miroslaw Skibniewski Ph.D Project Management Symposium

2 Slide 2 Overview Resource Allocation Business as Usual Strategic and Business Attitude Modelling for Success Mathematical Formulation of the Tool Case Study and Results Questions?

3 Slide 3 Resource Allocation Business as Usual WHAT IS IT AND WHY IS IT NO LONGER ACCEPTABLE?

4 Slide 4 Resource Allocation Business as Usual Traditionally projects are scheduled with an assumption that resources are limitless and available The main reason was the complexity of analysis and the trouble associated with losing the critical path

5 Slide 5 Strategic and Business Attitude HOW TO MAKE IT BETTER?

6 Slide 6 Competition Competition acts as a driving force in the industry and companies try to become more cost effective and profitable Competition also makes the margin of potential profit smaller and smaller.

7 Slide 7 Managing and Competing for Projects When companies have more than one project resource allocation may become more challenging. When combined with the requirements from stakeholders and financial limitations the decisionmaking becomes more challenging.

8 Slide 8 Schematic Representation CPM and Resource Allocation for Site 1 Strategic and Business Management CPM and Resource Allocation for Site 2 Exchange of information among construction sites CPM and Resource Allocation for Site k

9 Slide 9 Modelling for Success WHAT IS IMPORTANT AND HOW TO DO IT?

10 Slide 10 Mathematical Formulation of the Tool With Management Science applications along with carefully designed constraints informed decision-making becomes easier The key of success is to identify the limitations that actually make a difference in decision-making and formulate those as constraints

11 Slide 11 Mathematical Model First lets discuss unlimited resource availability case Next the limited availability will be discussed

12 Slide 12 Notation I = set of origin where activity starts J = set of destination where activity finishes, J* is the last element in the set TD = total duration right hand sight value where necessary RR kk = construction resource types right hand sight value where necessary (e.g. material, labor, budget, time, stakeholder needs, sustainability, etc.) k K RR iiiiii = usage of resource type k for activity ij i I, j J, k K CCCC iiii = cost of crashing activity ij i I, j J LL iiii = right hand side value as limitation on crashing activity ij i I, j J LLLL iiii = estimate of the activity s crashing duration under the most favorable conditions LLbb iiii = estimate of the activity s crashing duration under the least favorable conditions LLmm iiii = most likely value for the activity s crashing duration tttt iiii = estimate of the activity s duration under the most favorable conditions ttbb iiii = estimate of the activity s duration under the least favorable conditions ttmm iiii = most likely value for the activity s duration

13 Slide 13 Notation Decision variables xx ii aaaaaa xx jj = start and finish times of activity ij, i I, j J CCCC iiii = crashing duration of activity ij, i I, j J where applied Z = objective function value

14 Slide 14 Mathematical Model Objective function: min ZZ = xx JJ xx 1 (1) Subject to: xx jj xx ii + tt iiii i I, j J (2) xx ii aaaaaa xx jj UUUUUU i I, j J (3)

15 Slide 15 Mathematical Model - limits Objective function: min ZZ = 0 JJ CCCC iiii CCCC iiii (4) Subject to: CCCC iiii LL iiii i I, j J (5) xx jj xx ii + tt iiii CCCC iiii i I, j J (6) xx JJ xx 1 TTTT i I, j J (7) CCCC iiii 0 i I, j J (8) xx ii aaaaaa xx jj UUUUUU i I, j J (9)

16 Slide 16 Mathematical Model - combined Objective function: min ZZ = xx JJ + 0 JJ CCCC iiii CCCC iiii xx 1 (10) Subject to: CCCC iiii (LLLL iiii+4llll iiii +LLLL iiii ) 6 xx jj xx ii + (tttt iiii+4tttt iiii +tttt iiii ) 6 i I, j J (11) CCCC iiii i I, j J (12) xx JJ xx 1 TTTT i I, j J (13) CCCC iiii 0 i I, j J (14) xx ii aaaaaa xx jj UUUUUU i I, j J (15)

17 Slide 17 Mathematical Model - SMCP Objective function of SMCP: min ZZ = xx JJ + JJ 0 CCCC iiii CCCC iiii + JJ 0 xx 1 (16) Subject to: CCCC iiii (LLLL iiii+4llll iiii +LLLL iiii ) 6 i I, j J (17) xx jj xx ii + (tttt iiii+4tttt iiii +tttt iiii ) CCCC iiii i I, j J (18) 6 xx JJ xx 1 TTTT i I, j J (19) RR iiiiii RR kk i I, j J (20 ) CCCC iiii 0 i I, j J (21) TPD = xx JJ xx 1 (22) TTTTTTTT = JJ 0 CCCC iiii CCCC iiii xx ii aaaaaa xx jj UUUUUU i I, j J (24) (23)

18 Slide 18 Case Study and Results Activity Predecessors Duration in Days A None 6 B None 9 C A and B 8 D A and B 7 E D 10 F C and E 12 Activity Crashing Cost Per Day ($) A 10 5 B 20 5 C 3 5 D 30 5 E 40 5 F 50 5 Limit on Crashing Duration (Days)

19 Slide 19 Case Study and Results Activity Predec Duration in Days essors ta tb tm A None B None C A and B D A and B E D F C and E LP OPTIMUM FOUND AT STEP 11 OBJECTIVE FUNCTION VALUE IS 415 VARIABLE VALUE REDUCED COST VARIABLE VALUE REDUCED COST X F 0 10 X1 0 0 X3 4 0 A 2 0 X2 4 0 B 5 0 X C 0 3 X4 6 0 D 5 0 TPD 25 0 E 3 0 TPCC 390 0

20 Slide 20 Case Study and Results Objective function value of SMCP as discussed above is not intuitive Values for Total Project Duration (TPD) and Total Project Crashing Cost (TPCC) (shaded cells) are reported as 25 days consistent with the constraint for duration limitation $390 as crashing cost

21 Slide 21 Case Study and Results SLACK OR DUAL SLACK OR DUAL ROW SURPLUS PRICES ROW SURPLUS PRICES 2) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )

22 Slide 22 Contact: QUESTIONS?

Profit Maximization and Strategic Management for Construction Projects

Profit Maximization and Strategic Management for Construction Projects Hakob Avetisyan, Ph.D. 1 and Miroslaw Skibniewski, Ph.D. 2 1 Department of Civil and Environmental Engineering, E-209, 800 N. State