## 1 Introduction
[PERSON] [19] suggests that the contractor can use information about the project and its costs to construct an appropriate client-contractor payment model where the delivery dates for these payments are assigned to the various milestones and the amounts are estimated based on the cost of performance of activities. All progress payments are arranged during the scheduling at milestones specified while planning or payment models are created that allow contractors to identify milestones and related cash flows. For the project settlement between the client and the contractor, the bonus-penalty system [8; 20; 21] can be used to encourage the contractor to execute project (stages) as soon as possible. Penalties are determined for exceeding the contractual completion time of the project (stage), bonuses are given for early completion of the project (stage), etc. Contractual deadlines are specified for the project (stage) or time windows are defined where project (stage) completion is not awarded or penalized. For the RCPSP also the capital constrained project scheduling (CCPSP) models are analyzed [22; 23], where capital is one of the limited, non-renewable resources that is considered in the scheduling. At any time during the project, cash inflows and outflows must balance. Activities can be executed only if funds are available, such as those obtained by completing previous activities or stages of the project. In this work we propose the RCPSP model with the criterion of maximizing the discounted cash flows associated with the project from the contractor's perspective, with stage settlements in which client agrees with the contractor the work stages (milestones) with deadlines and the amounts of payment for completion of stage work. In the event of late completion of the contractual stages, penalties reducing stage client payments are applied. The proposed optimization model can be useful in practice where milestones are an important part of work planning, for example, to be used to determine the progress of a project. In the RCPSP studies, the stage settlement of project work, apart from the author's work, was not considered in this form. Milestone payments are considered in studies but optimization models differ from those discussed in this work [16; 24]. Milestone events are often assigned to events such as completion of individual activity [4; 19]. In this work, payments are made after the completion of the activity group as a stage of the project [8; 21; 25; 26]. For the proposed financial model used to optimize a multi-stage project, it is recommended to schedule the work so that activities are started as late as possible at the earliest possible completion of contractual stages. The aim of this work is to check the efficiency of the simulated annealing algorithm using the techniques of generating solutions, taking into account the specific stage settlements, that is: backward scheduling with optimization of project completion times, justification and right-shifting of activities for schedule with fixed resource allocation. The remainder of this paper is organized as follows. Section 2 contains a formulation of the problem. Section 3 presents the definition of an exemplary project illustrating the analyzed problem. Section 4 provides a simulated annealing algorithm and techniques for generating solutions that are presented for the example project. Section 5 describes the experimental analysis performed for the Project Scheduling Library (PSPLIB) test instances [27] with defined additional project financial settlements. At the end of the work, a summary is presented and directions for further study are provided.