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AssigneeKing Fahd University of Petroleum and Minerals
InventorAshraf Elazouni
Estimating the term…
a method and apparatus is disclosed for scheduling construction projects based on the available finance using integer programming. This method renders CPM/PERT schedules of construction projects executable using bank overdrafts of specified credit limits. Conveniently, the method is organized in three stages; input preparation, schedule extension, and model formulation. Input preparation stage supports preparing CPM/PERT schedule and financial data of the project. Schedule extension stage supports developing a scheme for schedule extension. The scheme is a framework of the original schedule that allows a definite extension increment in the critical path of the CPM. Model formulation stage supports building an integer programming model for the scheme and involves the components of formulating an objective function, setting constraints, and searching for a model solution. The model solution determines the activities' shifts that fulfill the constraints of the specified credit limit while minimizing the schedule extension. A search for a solution of the model is performed. If no solution is found, a repetition of the last two stages of the method is performed after allowing longer extension increment.
1- A method for revising a CPMP/PERT schedule of a construction project that determines revised start times of activities and a revised duration for completing said project, such that said project can be adequately financed throughout said revised duration using a bank overdraft of a predetermined credit limit, using integer programming technique, whereby said schedule is rendered executable with respect to the available finance of said predetermined credit limit comprising the steps of:
2- The method of claim I wherein the step of devising said scheme involves adding an extension increment to the duration of said schedule to produce an extended duration for said schedule.
3- The method of claim 2 wherein said extension increment is a plurality of days that are added to the total float of each of said activities to produce an adjusted total float.
4- The method of claim 3 wherein said adjusted total float allows for a shift in each of said activities such that negative cash flows at the end of periods of said project undervalue said predetermined credit limit.
5- The method of claim 4 wherein if said shift in each of said activities is within said respective adjusted total float, this causes said revised duration to remain below said extended duration.
6- The method of claim I wherein the step of formulating said model for said scheme using said integer programming technique involves setting an objective function and a plurality of constraints.
7- The method of claim 6 wherein said objective function of said model sets a goal of minimizing said revised duration of said project.
8- The method of claim 6 wherein said plurality of constraints involves constraints of activity shifting, activity sequence, and said predetermined credit limit.
9- The method of claim 8 wherein said constraints of activity shifting involve modeling of said shift in each of said activities to take up an integer value within said adjusted total float.
10- The method of claim 8 wherein said constraints of activity sequence establish and maintain the dependency between said activities.
11- The method of claim 8 wherein said constraints of said credit limit insure that said negative cash flows at the end of said periods undervalue said predetermined credit limit.
12- The method of claim 11 wherein said predetermined credit limit could be constant of different for said periods of said project.
13- The method of claim 11 wherein said negative cash flows at the end of said periods include accumulated net cash flows at start of said periods plus disbursements during said periods.
14- The method of claim 12 wherein said disbursements involve direct costs of material, labor, equipment, and subcontractors;
15- The method of claim 1 wherein the step of providing said processor includes:
16- The method of claim 1 wherein the result of said optimum solution involves the value of said shift in each of said activities.
17- The method of claim 1, further comprising if no said optimum solution is found, another said scheme is produced considering larger said extension increment until said optimum solution is found.
18- An apparatus for revising a CPM/PERT schedule of a construction project that determines revised start times of activities and a revised duration for completing said project, such that said project can be adequately financed throughout said revised duration using a bank overdraft of a predetermined credit limit, using integer programming technique, whereby said schedule is rendered executable with respect to the available finance of said predetermined credit limit, said computer comprising:
19- A computer for revising a CPM/PERT schedule of a construction project that determines revised start times of activities and a revised duration for completing said project, such that said project can be adequately financed throughout said revised duration using a bank overdraft of a predetermined credit limit, whereby said schedule is rendered executable with respect to the available fund of said predetermined credit limit, said computer comprising: