In this paper we discuss the resource-constrained project scheduling problem with discounted cash flows (RCPSPDC). We introduce a new schedule construction technique which moves sets of activities to improve the project net present value (NPV) and consists of two steps. In particular the inclusion of individual activities into sets, which are then moved together, is crucial in both steps. The first step groups activities based on the predecessors and successors in the project network, and adds these activities to a set based on their finish time and cash flow. The second step on the contrary does so based on the neighbouring activities in the schedule, which may but need not include precedence related activities. The proposed scheduling method is implemented in a genetic algorithm (GA) metaheuristic and we employ a penalty function to improve the algorithm's feasibility with respect to a tight deadline. All steps of the proposed solution methodology are tested in detail and an extensive computational experiment shows that our results are competitive with existing work.
The 0-1 knapsack problem is an important optimization problem, because it arises as a special case of a wide variety of optimization problems and has been generalized in several ways. Decades of research have resulted in very powerful algorithms that can solve large knapsack problem instances involving thousands of decision variables in a short amount of time. Current problem instances in the literature no longer challenge these algorithms. However, hard problem instances are important to demonstrate the strengths and weaknesses of algorithms and this knowledge can in turn be used to create better performing algorithms. In this paper, we propose a new class of hard problem instances for the 0-1 knapsack problem and provide theoretical support that helps explain why these problem instances are hard to solve to optimality. A large dataset of 3240 hard problem instances was generated and subsequently solved on a supercomputer, using approximately 810 CPU-hours. The analysis of the obtained results shows to which extent different parameters influence the hardness of the problem instances. This analysis also demonstrates that the proposed problem instances are a lot harder than the previously known hardest instances, despite being much smaller.
In this paper, we study the capital-constrained project scheduling problem with discounted cash flows (CCPSPDC) and the capital-and resource-constrained project scheduling problem with discounted cash flows (CRCPSPDC). The objective of both problems is to maximize the project net present value (NPV), based on three cash flow models. Both problems include capital constraints, which force the project to always have a positive cash balance. Hence, it is crucial to schedule activities in such an order that sufficient capital is available.The contribution of this paper is threefold. First, we propose three distinct cash flow models, which affect the capital availability during the project. Second, we introduce two new schedulers to improve capital feasibility, one for the CCPSPDC and one for the CRCPSPDC. The schedulers focus on delaying sets of activities, which cause cash outflows to be received at later time instances, in order to reduce capital shortages. Both schedulers are implemented as part of three metaheuristics from literature, in order to compare the metaheuristics' performance. Two penalty functions have been included, one to improve capital feasibility and another to improve deadline feasibility. Third, the proposed procedure has been tested on a large dataset and the added value of the schedulers has been validated. Managerial insights are provided with respect to the impact of key parameters.
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