Contents lists available at ScienceDirect Computers & Industrial Engineering journal homepage: www.elsevier.com/locate/caie A hybrid TLBO-TS algorithm for integrated selection and scheduling of projects Manish Kumar ⁎ , M.L. Mittal, Gunjan Soni, Dheeraj Joshi Department of Mechanical Engineering, Malaviya National Institute of Technology, Jaipur, India ARTICLE INFO Keywords: Project selection and scheduling Meta-heuristic methods TLBO algorithm Tabu search Hybrid algorithms ABSTRACT Organizations dealing with projects often face the challenge of choosing right mix of projects for implementation and scheduling. The two steps have, however, traditionally been performed in sequential manner often resulting into problems such as scope changes/dropping/replacement/delayed completion of the projects. This paper deals with the problem of simultaneous selection and scheduling of the projects with maximization of total expected benefit of the portfolio as an objective. Expected benefit of the project is considered to be time sen- sitive. Further, the projects have a variety of interdependencies between them. Two types of interdependencies: mutual exclusiveness and complementariness have been considered. A zero-one integer programming model is proposed for the problem. Three meta-heuristics: TLBO, TS and hybrid TLBO-TS have been developed and compared with the existing algorithms in the literature. The performance of the algorithms is evaluated on the four different types of data sets. Performance of the hybrid TLBO-TS algorithm has been found to be quite promising in terms of solution quality and convergence. 1. Introduction Organizations dealing with multiple projects often face the chal- lenge of selection and scheduling of optimal mix of projects. The tra- ditional project selection exercise seeks to first select the portfolio of projects from a set of candidate projects and then schedule the selected projects respecting the resource, budget and other constrains. This se- quential approach, however, may lead to difficulty in scheduling the selected portfolio during given time frame resulting in scope changes/ dropping/replacement/delayed completion of some of the projects. Alternatively, availability of the resources may need to be increased or time frame for the projects has to be extended. Thus, the selection and scheduling of projects in sequential manner result into sub-optimality (Coffin & Taylor, 1996a, 1996b). Hence the scheduling needs to be considered as an integral part of the project selection process. This joint problem is termed as the project portfolio selection and scheduling problem (PPSSP) in literature. The PPSSP can be stated as the si- multaneous problem of selection and scheduling of projects to optimize organization’s stated objectives in specified time horizon without vio- lating budget and resource constraints (Chen & Askin, 2009). The PPSSP has been studied for a variety of objectives with max- imizing the overall benefit being the most common objective (Coffin& Taylor, 1996a, 1996b; Amirian & Sahraeian, 2017; Bhattacharyya, Kumar, & Kar, 2011; Chen & Askin, 2009; Ghorbani & Rabbani, 2009; Huang & Zhao, 2014; Shou, Xiang, Li, & Yao, 2014; Tofighian & Naderi, 2015; Tseng & Liu, 2011). The overall benefit to an organization, however, is time dependent as the earlier completion of a project is generally more beneficial. Consider, for example, IT projects where new gadgets are introduced in the market almost every day. Delayed in- troduction of a gadget may lead to reduced market share and hence profitability. This aspect of time dependent returns in project selection and scheduling has been considered by Chen and Askin (2009), Ghorbani and Rabbani (2009), Tofighian and Naderi (2015) and Amirian and Sahraeian (2017). The candidate projects for selection often exhibit a variety of in- terdependencies. Interdependencies are present if inclusion/exclusion of a project in the portfolio is affected by the selection of other candi- date project(s). Consideration of interdependencies yields more profit as the total benefit/cost from interdependent projects is not same as the sum of the individual project’s benefit/cost. Aaker and Tyebjee (1978) and Fox, Baker, and Bryant (1984) were the pioneers who considered project interdependencies during project selection. Later on, project interdependencies in project selection have been considered e.g. by Li, Fang, Guo, Deng, and Qi (2016), Abbassi, Ashrafi, and Tashnizi (2014), Bhattacharyya et al. (2011), Liesiö, Mild, and Salo (2008), Lee and Kim (2000), Santhanam and Kyparisis (1996). Out of the various types of interdependencies between the projects mutual exclusiveness is con- sidered the most in the literature. Projects are said to be mutually https://doi.org/10.1016/j.cie.2018.03.029 Received 4 October 2017; Received in revised form 14 March 2018; Accepted 19 March 2018 ⁎ Corresponding author. E-mail addresses: m81manishkumar@gmail.com (M. Kumar), mlmittal.mnit@gmail.com (M.L. Mittal), gsoni.mech@mnit.ac.in (G. Soni), dheerajjoshi25@gmail.com (D. Joshi). Computers & Industrial Engineering 119 (2018) 121–130 Available online 20 March 2018 0360-8352/ © 2018 Elsevier Ltd. All rights reserved. T