## 3 Results  
To investigate the utility of the proposed model, the Saudi Arabian oil and gas supply chain was employed. The entities of the HCSC with their associated units and relevant data are reported in Section 4. The planning horizon is four years with a one week planning period. In this study, maintenance tasks are carried out on a weekly basis, while demand is on a monthly basis.  
The maintenance schedule for all HCSC entities over the planning horizon is displayed in Figure 4. The Gantt chart shows a schedule displaying which each unit will be taken for maintenance and in which weeks. The width of the bar indicates the duration of maintenance in weeks.  
The following conclusions can be derived to describe the Gantt chart:  
* It was observed that the proposed model distributes maintenance activities uniformly and perfectly among the HCSC plants along the time horizon of four years.  
Figure 4: Maintenance schedule for all hydrocarbon supply chain (HCSC) plants (operations and maintenance model); Color code: Orange: oil processing plants; Purple: Refinery plants; Red: Gas plants; Light Blue: Fractionator plants.  
* In addition, it is shown that the model minimizes the amount of lost sales by forcing most of HCSC units to be maintained during the months of low demand. Almost all HCSC units are taken for maintenance during the quarters of low demand (quarters 1, 2, and 4). The third quarter is the summer period, which represents the months of high demand.
* The HCSC is a complex network that involves multi-connections where each plant belongs to the upstream is connected to more than one downstream plant and even to more than one demand node. Similarly, each plant has tanks with enough capacity to feed the associated downstream plants during the maintenance period. This situation provides flexibility for choosing maintenance timing. Therefore, the majority of HCSC plants were taken for maintenance randomly at different times.
* Few connected plants have been taken for maintenance at the same time. For instance, Abqaiq oil processing plant and RasTunura refinery plant are maintained simultaneously. Similarly, both the Tanajib oil processing plants and PetroRabigh refinery plant are maintained at the same time.
* For natural gas plants, maintenance tasks are decoupled; almost all connected upstream and downstream plants are maintained randomly because each downstream plant has connections with more than one upstream unit, and the storage capacity is enough during the maintenance time. In the sensitivity analysis section, the impact of upstream storage capacities on maintenance schedule and arrangement will be investigated.  
For the deep investigation, a sample of output for some selected plants will be displayed. For instance, the maintenance schedule, utilization, and production for gas plants during the first year are shown in Figure 5. The third quarter represents the months of the highest demand. Therefore, almost all gas plants have been taken for maintenance during the months of the demand (Quarters 1, 2 and 4).  
Figure 5: Gas plants maintenance scheduling, production plans, and utilization (year 1).  
Similarly, Figure 6 shows the oil processing plants' maintenance schedule, production, and utilization for the first year.  
Figure 7 indicates the fractionation plant storage capacities and inventory levels fluctuations across the planning horizon. Production and maintenance are carried out on a weekly basis, while demand is on a monthly basis. As a result, the inventory level accumulated over the first four weeks of a month, then decreased as demand occurred at the end of the last week of a month.  
Figure 6: Oil processing plants maintenance scheduling, production, and utilization (year 1).