Optimization of Resource Allocation Using Queueing Theory
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- Institutt for marin teknikk 
As the ice in the Arctic region is melting, new areas will open for oil exploration and production. These areas are however remote, with long sailing times from shore. In addition, themain warehouses of the oil companies are located in the southwestern part of Norway, thusincreasing the transportation distances further. To operate, the offshore installations need alot of equipment, some of which is absolutely necessary for the operation, so called missioncritical equipment. This type of equipment have been the main focus in this thesis. Whenthis type of equipment breaks down, or it is no longer needed, it is sent to one of the mainwarehouses for maintenance and recalibration. By storing spares of this equipment closer tothe installation, response time when equipment breaks down is reduced.Three possible supply chain scenarios were created. The first scenario is the current scenario,where equipment is sent by trucks from one of the main warehouses and to the Hammerfest depot, from where it is shipped to the offshore installations by Platform Supply Vessels(PSVs). The two other scenarios utilize a offshore depot. The depot is assumed to be a converted bulk-carrier. In scenario 2 this depot vessel sails from Hammerfest, while in Scenario3 it sails from one of the main warehouses. For scenario 2, the equipment is transported bytruck to Hammerfest. For a continous operation, it was assumed that two vessels are needed.By setting an operability constraint the supply chain could be optimized with respect tocosts. Operability is the percentage of time inventory of the equipment is present at theinstallation. Then, by combining the Genetic Algorithm in MATLAB with queueing theory,this optimization problem was solved. It was created as a closed queueing network, meaningthat a finite population of customers travel inside the network. This was chosen due to thenature of the equipment studied. The steady state probabilities was calculated using Buzen salgorithm.Three demand cases were studied. The first case was low demand, where demand arisestwice a year. In the medium demand case, demand arises every month. The final case, highdemand, demand arises twice a month. In queueing theory, demand is modelled as arrivingcustomers. In a closed queueing network where there are no customers arriving from outsidethe system, this arrival rate is equal to the service rate at the offshore installation. By varyingthe transportation costs for the system, an offshore depot vessel seemed more viable for thehigh demand case, thus preferring to allocate the inventory closer to the installation.