26th International Association for Management of Technology Conference - IAMOT 2017

In literature, several works develop methodologies in order to evaluate the innovation capability (IC) of small and medium enterprises (SMEs) according to a set of actions performed by the firm, called innovations actions (Adams et al., 2006; Chiesa et al., 1996; Guan et al., 2016). A good example is the methodology proposed by the ERPI research team of the University of Lorraine in France, which allows to characterize and diagnose the IC of the SMEs from the computation of its Potential Innovation Index (PII). This methodology has been validated both theoretical and empirical through the opinion of experts (Boly, 2008; Corona, 2005) with numerous cases of application (Boly et al., 2014; Galvez et al., 2013; Nemery et al., 2012; Sepúlveda et al., 2010) Recent work linked to IIP seeks to determine recommendations for improving a company's IC subject to some constraints such as a budget and/or resources (Galvez, 2015). However, these studies have not considered yet the optimal schedule of innovation actions to maximize the benefits or minimize the costs of the proposed improvements. In this paper, we state the innovation actions scheduling problem for the improvement IC in SMEs, propose a binary linear programming (BLP) model for its formulation,evaluate the proposed model by performing several computation experiments based on French SMEs cases and analyze the obtained results. Formally, we propose a BLP model based on the statement of problem, which is defined as follows: Given an initial IC levels for each innovation practice $\lbrace{\hat{\ell}}\rbrace_{p \in \mathcal{P}}$. We denote $\sigma(j):=(\ell,p)$ the IC level $\ell$ to obtain in the innovation practice $p$ with an associated cost $c_j$. In addition, there exists a cost $c_{i,j}$ by performing action $i$ after action $j$. Let $y_j$ and $x_{i,j}$ binary variables that takes value 1 if the action $j \in \mathcal{J}$ is performed and if the action $j \in \mathcal{J}$ is performed after to perform the action $i \in \mathcal{J}\setminus\lbrace j\rbrace$ , respectively; and 0 otherwise. We want to maximize $ \displaystyle \sum_{j \in \mathcal{J}} y_j w_{\sigma(j)} \qquad (1) $ $\mbox{subject to}$ $\displaystyle\sum_{i \in \mathcal{J}\setminus\lbrace j\rbrace} x_{i,j}+x_{j,i}= y_j \quad \forall i\in \mathcal{J} \qquad (2)$ $x_{i,j}+x_{j,k}+x_{k,i}\leq2 \quad \forall i,j,k\in \mathcal{J} \qquad (3)$ $\displaystyle\sum_{j \in \mathcal{J}} \left( y_j c_j + \sum_{i \in\mathcal{J}\setminus\lbrace j\rbrace} c_{i,j}x_{i,j}\right)\leq b \qquad (4)$ $y_{j}= 0 \qquad \forall p\in \mathcal{P}, j \in \mathcal{J}_p, \sigma(j):=(\ell,p), \forall \ell<\hat{\ell} \qquad (5)$ $x_{i,j}, y_{j} \in \lbrace0,1\rbrace \qquad \forall i,j\in \mathcal{J} \qquad (6)$ Objective (1) maximizes the PII of the firm. Constraint set (2) forces that if the action $j \in \mathcal{J}$ is performed, then it is performed before or after some an action $i \in \mathcal{J}\setminus\lbrace j\rbrace$ . Constraint set (3) imposes a specific order among three different possible actions $i,j,k \in \mathcal{J}$ and constraint (4) defines the budget constraint . Constraints sets (5) fixed the binary variables $y_j=0$ for all action $j \in \mathcal{J}_p$ which do not improve the initial IC level for each innovation practice $p\in\mathcal{P}$ and constraints sets (6) states the domain of the variables. BLP model is implemented in C++, using the BLP solver provided by IBM ILOG CPLEX library version 12.6 and the expected results correspond to the optimum schedules of innovation actions necessary for the construction of improvement recommendations adapted to the studied companies.