## 1 Introduction  
A risk is described as a \"hazard\", a chance of bad consequences, loss, or exposure to mischance (from the Concise Oxford English Dictionary, reported in [1]). Its assessment may be incorporated into the company's planning and decision-making processes, encompassing profits, reliability, and other performance objectives [2]. The minimization of financial risks is one of the keys to sustainable business development [3]. Risk identification and assessment provided specific indications of managerial attention to achieve the performance objectives [2]. Indeed, [PERSON] et al. [4] followed these indications using a timed Petri nets framework. Their main objective was to illustrate the challenges where coordination within supply chain networks brings to risk management. Furthermore, in his book, [PERSON] [5] introduced the application of the Monte Carlo simulation method for the analysis of system reliability and risk. Failure mode and effects analysis (FMEA) is a risk assessment tool that reduces potential failures in systems, process, designs, or services [6]. [PERSON] et al. [7] described a number of common scoring methods that are currently used to assess risk in a variety of different domains. In our study, we propose methods in order to quantify the risk of certain strategies or events that can disrupt the system. In the literature, many researchers are interested in risk issues, and they have tried to classify types and propose tools to cope with some risks that can lead to bad consequences. Our innovative contribution is to evaluate the impact of the use of optimization algorithms on certain events that may disrupt the calculated production and maintenance plan. In fact, the relevance of the tools and algorithms used is never discussed in terms of impact on an incident that may occur, and that disrupts the optimal production and maintenance plan decided. The paper proposes a new contribution to the literature, which proposes on the one hand analytical models to quantify the profit loss following an adopted strategy, and on the other hand the impact of the use of different optimization algorithms on the calculation of profit loss. In recent years, researchers have tried to investigate the problem of choice regarding a maintenance policy that is adequate to their stochastic problems from a robustness and effectiveness point of view. [PERSON] et al. [8] proposed mathematical cost models to assess jointly the economic performance and robustness of two maintenance policies. [PERSON] et al. [9] and [PERSON] et al. [10] also consider the same objectives. The purpose of their work was to help decision-makers choose the adequate maintenance policy that maximizes their profit as well as maintains a robust production system. The integration of production and maintenance planning problems is a significant challenge for industrial companies, and hence has received much research attention in the last few decades. According to [PERSON] [11], the increased importance of maintenance activities is due to their impact on system availability, performance efficiency, product quality, etc. One of the first authors to have dealt with integrated production-maintenance strategies is [PERSON] [12]. [PERSON] et al. [13] suggested a method for the joint optimization of preventive maintenance and inventory control in a production line that combined \(N\) machines, while [PERSON] et al. [14] developed joint production and preventive maintenance policies incorporating inventory levels. [PERSON] et al. [15] proposed a model to determine a joint optimal inventory control policy and an age-based preventive maintenance policy for a randomly failing production system. [PERSON] and [PERSON] [16] introduced another model for the same context. The work of [PERSON] et al. [17; 18] considered the impact of the production plan on equipment degradation. [PERSON] et al. [19] evolved a method to find the optimal production, replacement/repair, and preventive maintenance policies for a deteriorated manufacturing system.