## 1 Introduction
The aim of the model was to decrease the overall weighted job slowness. [PERSON] and [PERSON] [19] investigated an integrated model for maintenance and production scheduling with the aim to minimize the overall anticipated weighted job completion time. [PERSON] and [PERSON] [20] introduced an inventory model combining preventive maintenance and production and taking into account an inspection error. [PERSON] et al. [21] developed a hybrid production planning and maintenance model for a deteriorating production system. To renew and restore the system, preventive maintenance was carried out on a regular basis, and minimal repair was carried out. Production and maintenance plans have been developed to reduce overall production and maintenance costs. [PERSON] and [PERSON] [22] extended the [21] work for a system consisting of more than one production line which operates in parallel. [PERSON] et al. [23] formulated a model for a manufacturing system that was subjected to random failure and assuming the demand was stochastic. The failure rate was assumed to be a function of machine working time and production rate. The output of the model was an optimal production plan combined with a preventive maintenance policy, which minimized the total cost subject to a target service level. [PERSON] et al. [24] focused on the problem of maintenance and production planning in a parallel machine case by developing a bi-objective integrated model which enabled the manager to decide the production assignment to machine and plan the maintenance for each machine at the same time. Thus, machines not in duty can be taken for maintenance as per a pre-identified plan. [PERSON] et al. [25] developed a model for optimizing a manufacturing system that faces random failures. Due to failure, a random shortage demand was substituted by subcontracting from a different production system. It was assumed that the manufacturing system failure rates are both functions of time and production rate. A preventive maintenance schedule was determined to minimize manufacturing system decay. [PERSON] and [PERSON] [26] formulated an integrated production and maintenance planning model for a single machine that was subjected to random failure. Preventive maintenance is applied periodically, and minimal repair was performed to renew the machine to its normal state. [PERSON] et al. [27] developed a model similar to [22] work for multi-machines. [PERSON] et al. [28] developed a simulation model that integrated production, setup, and maintenance activities simultaneously. [PERSON] et al. [29] developed a robust mathematical model for designing a power supply chain. The model considers planning the power generation and scheduling of preventive and corrective maintenance due to possible failures in the electricity transmission system. [PERSON] et al. [30] proposed a model for a machining system in which the production rate affects both the cutting tool age and the reliability of the machine. The developed model takes into consideration the addition to production scheduling, a preventive maintenance of the machine, and the tool replacement. [PERSON] et al. [31] explored the aspect of integrated production operations and maintenance planning activities at the tactical level of multi-line systems. The policy of maintenance provides preventive substitutions at the start of every cycle as well as minimal repairs in the event random failures occur. The aim of the model was to minimize the total costs and concurrently determine the maximum production plan alongside the replacement time. [PERSON] et al. [32] presented a joint optimization model for integrating master production schedule and maintenance strategy for a manufacturing system. The proposed policy allows minimizing the impacts of potential random failures. A heuristic algorithm was invented for solving the proposed model. [PERSON] and [PERSON] [33] discussed a maintenance optimization strategy for a multi-component system with the use of the degradation information of the system.