This paper describes in detail an optimization model that provides a range of required number of autonomously operated vehicles (AUV and/or Drones) to monitor hazardous objects in offshore environment. In addition to the number of AUVs required it also calculates the number of docking stations required to service these AUVs. Finally, an attempt was made optimize the location of the docking stations. The paper will describe the general theory and an example application to monitor ice floes in offshore Arctic as described next. Arctic offshore exploration and development is inherently complicated due to harsh environment caused by extreme cold temperatures as well as the sea ice environment. The sea ice floes are dynamic in nature and have variable spatial size, thickness, speed and directions. The modern satellite imagery (particularly Synthetic Aperture Radar with its all weather capability) provides a powerful tool to get the size, speed and direction of the floes. However the ice floe thickness is not readily discernible from satellite images and attempts to calculate the thickness directly from satellite imagery have yielded mixed results. One method is to make use of Autonomous Underwater Vehicles (AUV) which can be equipped with upward looking sonar (either in single beam or a multi-beam mode) and then sent to hazardous sea ice floe on command. The idea is that AUV will then make all the required profiles of the ice floe underside providing concrete information about the thickness and then report back to the control center where a decision could be made whether we need to initiate an ice management response or not. If we are to use the AUV and ancillary docking stations to measure sea ice thickness then we need to know what is the suitable number of AUV and corresponding docking stations required for a near zero tolerance of failure (i.e. failed to detect a hazardous sea ice floe based on its thickness). We decided to solve this problem using a linear mixed-integer programming method.