## 1 Introduction
For instance, [2] developed a Mixed Integer Linear Programming (MILP) model for scheduling the preventive maintenance of units of a refinery plant. The proposed model aims to maximize the utilization level of units while satisfying maintenance constraints. [PERSON] et al. [3] developed an MILP model for the optimization of the short term blending and scheduling problem in applications of an oil refinery. The model aims to optimize the profit and satisfy the quality requirements. The authors developed a novel method to solve the proposed model. [PERSON] et al. [4] proposed an MILP model for the production scheduling of the oil-refinery problem. In the proposed model, the production process consisted of two hydro-treatment units and one unit of distillation. The aim of the scheduling was to decide which model of operation to use in each processing unit at each point in time in order to satisfy the demand while minimizing the production cost and considering storage capacities. [PERSON] et al. [5] developed a data-driven model for determining the type of maintenance that should be performed to a refinery plant. [PERSON] et al. [6] addressed an approach based on risk inspection and maintenance for maintaining activities in an oil refinery to minimize the risk. A heuristic algorithm was utilized to solve the proposed model, considering the time, human resources, and budget constraints. [PERSON] et al. [7] presented a multi-agent approach for the scheduling of dynamic maintenance activities for the petroleum industry using a reinforcement approach. [PERSON] et al. [8] proposed an MILP model for planning the turnaround activities of interconnected plants in a chemical site. The aim of the proposed model was to maximize the net present value. [PERSON] and [PERSON] [9] developed a stochastic model to schedule preventive maintenance for an oil refinery plant taking into consideration the uncertainty in maintenance time. The model aimed to minimize the total adjusted tardiness times while satisfying the amount of multiple-skill-level maintenance crew and budget limits. [PERSON] et al. [10] developed a proactive scheduling model for maintaining refinery plants under the uncertainty of crude shipping delays. A mixed-integer nonlinear programming model was developed to optimize crude unloading, transferring, and processing at the refinery plant. Recently, [11] extended the [10] work by integrating proactive and reactive scheduling. Several studies have tackled the issue of coordinating production and maintenance activities, especially in the inventory control area. The first pioneering work in this field was performed by [PERSON] and [PERSON] [12], who formulated a model to optimize economic production quantity and at the same time, generate a maintenance plan for a production system. [PERSON] and [PERSON] [13] employed the production plans along with a history of machine failure to optimize maintenance activities. In his dissertation, [PERSON] [14] proposed an integrated model for production and maintenance planning simultaneously. The aim of the developed model was to find out the period between two consecutive preventive maintenance tasks. [PERSON] et al. [15] proposed an MILP model for scheduling production jobs and the preventive maintenance of a multi-line production system. The aim of the model is to examine the possibility of performing preventive maintenance before a new job or run the job without performing preventive maintenance until a breakdown happened then repair the production system. [PERSON] and [PERSON] [16] reviewed inventory models that integrated production planning, quality, and maintenance activities. [PERSON] and [PERSON] [17] developed a policy for a production inventory system operated by a single machine subjected to deterioration. The maintenance and production decisions were optimized by solving the model using the Markov decision process. [PERSON] and [PERSON] [18] developed an integrated preventive maintenance and production scheduling model.