ScienceDirect IFAC-PapersOnLine 48-25 (2015) 006–010 Available online at www.sciencedirect.com 2405-8963 © 2015, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. Peer review under responsibility of International Federation of Automatic Control. 10.1016/j.ifacol.2015.11.050 © 2015, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. Keywords: Scheduling algorithms, project management, parallel computation 1. INTRODUCTION Top innovation high-technology companies (e.g. Emer- son, Intel and etc., see http://thomsonreuters.com/ press- releases/ 102013/thomson-reuters-2013-top-100-global- in- novators) usually have large portfolio of mutually indepen- dent R&D projects under implementation. There can be hundreds of such projects at the same time for one com- pany. Besides that constantly new projects are appearing and some old projects are terminated. Most projects consist of stages, each stage represents some certain activity. Time delays between stages are not so crucial as time delays that lead to interruption of stage. If there are two competing alternatives: to start a new project or to continue existing project, the second alternative is usually much more preferable [Neumann et al. (2003)]. Many projects have uncertain duration [De Reyck et al. (2008)] because there can be different types of time delays caused by lack of investment, technological problems, staff motivation problems and etc. Projects can be terminated due to exceeding deadlines or for other reasons (e.g. insufficient competitive advantages, obsolescence, product failures) [Pinedo (2001)]. Some projects are more important to the company than other. The management of the company usually set the level of importance of the project using net present value (NPV) and other parameters of the project (competitive advantages, risk estimates and so on) [Kolish (1995)] . The main resource for any project is the value of available investment, because almost all resources of the project should be paid. If economy is developed and flexible enough, purchasing of resources is not a great problem. That is why budget matters are vital for decision making on project selection and scheduling [Lazarev et al. (2014)]. Time delays and uncertain external economic factors lead to uncertainty of budget schedule for projects. If the schedule is violated on some stage of the project, it usually results in increase of costs for the stage because any time delay requires additional human, material, energetic and other resources. As the rule innovation high-technology companies have a special R&D department for managing project selection and scheduling, which holds its meetings every week. At these meetings various matters considering projects are discussed: • project data update (duration of stages, resource needs, level of importance); • set of new projects for current week; • set of projects to be implemented in current week; • set of projects to be delayed in current week; • set of projects to be terminated in current week. So a week is an appropriate sampling step for time. Thus economic problem described above belongs to RCPSP problem with discrete time periods (weeks), avail- able budget constraints, deadlines and dynamic change of initial data [Neumann et al. (2003)], which is known to be NP-hard [Garey et al. (1979)]. 2. MATHEMATICAL DESCRIPTION OF THE PROBLEM 2.1 Schedule examples One example of project schedule with four projects is presented on Fig. 1 . Project 1 started in week 1, but there was a time delay in week 3, which led to stop of stage 1 of project 1. Then project 1 continued to be implemented. There were another time delay in week 24, After all project 1 was successfully implemented in week 26. Project 2 started in week 3. We have time delays for weeks 6, 7, 21 and 27. Time delays for weeks 6 and 7 led to delay at the beginning of stage 2, but stage 2 wasn’t interrupted. Time delays in weeks 21 and 27 caused interruption of stages 6 and 7 correspondingly. * Southern Ural State University, Chelyabinsk, Russia (e-mail: latipovaaat@susu.ac.ru) Abstract: There is discussed the multi-period problem of project selection and scheduling for research and development (R&D) projects. The problem is a NP-hard RCPSP problem with discrete time periods (weeks), available budget constraints, deadlines, interruption of stages and dynamic change of initial data. Due to this peculiarities and the computational complexity, splitting the problem into series of subproblems for each period is proposed. These subproblems can be solved using GPU programming. On optimization of R&D Project Selection and Scheduling On optimization of R&D Project Selection and Scheduling Alina T. Latipova *