# The Method of Production Scheduling with Uncertainties Using the Ants Colony Optimisation
## 1 Introduction  
The criteria of cost, quality and time availability are always contradictory.reprene's look for solutions that will not be reflected in the loss of quality or extension of deadlines for the implementation of tasks. Entrepreneurs are looking for organizational, technological and IT solutions that will allow for improvements in these areas. Consider the problem of scheduling production tasks and planning technical inspections of machines. Production and maintenance tasks apply for access to the same resources, machines. Production and maintenance managers have divergent goals. Machines immobilization for maintenance decrease productivity. [PERSON] [1] investigated the robustness of joint production and maintenance scheduling in the problem of flow permutation and proved that the loss of efficiency due to the insertion of maintenance tasks into the production schedule increases. But costs incurred due to unplanned machine failure often outweigh the costs associated with predictive maintenance. Costs incurred due to unplanned machine failure include corrective maintenance, reworks, delays in deliveries, breaks in the work of employees and machines. Therefore, scheduling of production and maintenance tasks should be considered jointly. The related literature distinguishes three approaches to production and maintenance planning in disturbance conditions: predictive, proactive and reactive. The goal of the predictive approach is to obtain a schedule that can absorb the disturbance without affecting planned external activities, while maintaining high system efficiency [2, 3]. The proactive approach examines the influence of the disturbance on a schedule, using the criteria of stability. The schedule obtained for the best sequence of tasks related to maintenance andproduction is assumed for implementation [4]. The objective of the reactive approach is to adapt the schedule to the current situation [5]. There are two proactive approaches: proactive without or with prediction (Figure 1). In the first approach, only the impact of a disturbance on the schedule using robustness measures is examined. Researchers search for the best sequence of idle times between production tasks or batches taking the advantage of the simulation process [6; 7]. Considering only the relationship between production and maintenance tasks as a conflict in management decisions may cause unmet demand or unexpected machine failures. A common objective is to maximize a system productivity and efficiency. Usually, the time interval for maintenance task and the number of maintenance tasks are fixed in advance. The mentioned deficiencies of proactive-reactive approaches are eliminated in predictive-reactive approaches. The predictive-reactive approach is regarded as a combination of predictive and proactive scheduling techniques. Researchers predict maintenance time and then evaluate the effect of a disturbance on the predictive schedule using robustness measures [8; 9]. Using the probability theory to describe machine conditions allows for more reliable maintenance planning. However, accepting the assumption that machine conditions are observable at the beginning of each period is not sufficient. Popular maintenance strategies are based on the periodic inspection of a machine and age dependent inspection and are also not sufficient. Attributes to describe the machine age and the influence of maintenance should be drawn from analysis of historical data on failure-free times and observation of dynamic machine conditions. The predictive-reactive method is considered in the presented paper. [PERSON] et al. [10] propose the joint production and preventive maintenance scheduling problem in permutation flowshops with the objective of minimizing the makespan. The insertion of the maintenance tasks is done according to several heuristics. [PERSON] and [PERSON] [11] propose a joint optimization on a hybrid flow shop system. A preventive maintenance strategy is based on reliability.