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Techniques of generating schedules for the problem of financial optimization of multi-stage project

Klimek Marcin

Applied Computer Science

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2019

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Vol. 15, no 1

18--35

EN

The article presents the problem of scheduling a resource-constrained project with discounted cash flow maximization from the perspective of a contractor. The contractor's expenses (cash outflows for the contractor) are associated with the execution of activities. The client's payments (cash inflows for the contractor) are performed after fulfilling the agreed project stages. The following techniques are suggested for solving the problem: the activity right-shift procedure, the backward scheduling with the optimization of completion dates for the agreed project stages and the modified triple justification technique. The effect of these techniques of generating schedules is illustrated for an exemplary project. Finally, an experimental analysis of the proposed procedures is presented.

2

Financial optimisation of the scheduling for the multi-stage project

Klimek M., Łebkowski P.

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2017

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Vol. 65, nr 6

899--908

EN

The paper analyses the problem of discounted cash flow maximising for the resource-constrained project scheduling from the project contractor’s perspective. Financial optimisation for the multi-stage project is considered. Cash outflows are the contactor’s expenses related to activity execution. Cash inflows are the client’s payments for the completed milestones. To solve the problem, the procedure of backward scheduling taking into account contractual milestones is proposed. The effectiveness of this procedure, as used to generate solutions for the simulated annealing algorithm, is verified with use of standard test instances with additionally defined cash flows and contractual milestones.

3

Priority algorithms for the problem of financial optimisation of a multi-stage project

Klimek M.

Applied Computer Science

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2017

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Vol. 13, no 4

20--34

EN

The article presents the problem of the financial optimisation of a multi-stage project from the contractor's perspective, where customer's payments are analysed as a cash inflow (contractor's revenues) after completing contractual stages and contractor's expenses incurred for the activities executed. In order to solve the problem, priority algorithms are proposed: single-pass and multi-pass ones, using different priority rules and tech-niques for generating solutions dedicated to the investigated optimisation model. The article presents a comparison of the effectiveness of individual algorithms in the case of adequately prepared test problems.

4

Improvement algorithm for a scheduling problem with maximising criterion for discounted cash flows in a project settled by milestones

Klimek M., Łebkowski P.

Logistyka

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2015

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nr 2

352--358, CD1

EN

The paper presents the project scheduling problem with DCF maximising criteri on . The authors analyse their independently developed model in which a project is settled by milestones, while cash flows are linked to the execution of individual activities and milestones. Rules are discussed governing the development of a schedule appropriate for the NPV optimising problem. A procedure is proposed for improving solutions obtained with the use of schedule generation schemes; the procedure provides for right - hand side shifts of activities. The both model and improvement algorithm developed are applied to a specific project. The paper concludes with the presentation of results of computational experiments and analysis thereof.

PL

W artykule przedstawiony jest problem harmonogramowania projektu z kryterium maksymalizacji zdyskontowanych przepływów pieniężnych . Analizowany jest autorski model, w którym projekt rozliczany jest etapowo a przepływy pieniężne związane są z realizacją zadań i umownych etapów projektu (kamieni milowych). Omówione są zasady tworzenia harmonogramu odpowiedniego dla problemu optymalizacji NPV. Zaproponowana jest procedura poprawy rozwiązań uzyskiwanych przy użyciu schematów generowania harmonogramu przez przesunięcia prawostronne czynności. Model i opracowany algorytm poprawy zilustrowane są dla przykładowego projektu. Na koniec zademonstrowane są wyniki eksperymentów obliczeniowych i analiza tych wyników.

5

Heuristics for project scheduling with discounted cash flows optimisation

Klimek M., Łebkowski P.

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2015

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Vol. 63, nr 3

613--622

EN

The article presents the resource-constrained project scheduling problem with the maximisation of discounted cash flows from the contractor’s perspective: with cash outflows related to starting individual activities and with cash inflows for completing project stages (milestones). The authors propose algorithms for improving a forward active schedule by iterative one-unit right shifts of activities, taking into account different resource flow networks. To illustrate the algorithms and problem, a numerical example is presented. Finally, the algorithms are tested using standard test problems with additionally defined cash flows and contractual milestones.

6

A Two-Phase Algorithm for a Resource Constrained Project Scheduling Problem with Discounted Cash Flows

Klimek M., Łebkowski P.

Decision Making in Manufacturing and Services

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2013

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Vol. 7, no. 1-2

51--68

EN

This paper presents a Resource-Constrained Project Scheduling Problem (RCPSP) settled by contractual milestones. The criterion analysed here is the maximisation of aggregate discounted cash flows from the contractor´s perspective, known as an RCPSP problem with Discounted Cash Flows (RCPSPDCF). The cash flows analysed here cover the contractor´s cash outflows (negative cash flows), related to the commencement of individual activities, and cash inflows (positive cash flows) after the fulfilment of individual milestones. The authors propose a two-phase algorithm for solving the problem defined. In the first phase, the simulated annealing metaheuristics is used, designed to identify a forward schedule with as high total DCF as possible. In the second phase, the best first-phase schedule is improved by right shifts of activities. To this end, the procedure which iteratively shifts tasks by one unit is applied, with a view to maximising the objective function. Activity shifts take into consideration precedence and resource constraints, and they are performed for a specified resource allocation to activities. This paper also includes an analysis of the problem for a sample project. The results of computational experiments are then analysed. The experiments were run with the use of standard test problems from the Project Scheduling Problem LIBrary (PSPLIB), with additionally defined cash flows and contractual milestones.