Optimal number of fishing fleet for a sustainable fishery industry

This paper develops a mathematical model of optimal fleet number of fishing vessels. We considering two aspects related to the vessels. The first aspect is the availability and reliability of the vessels. The fishing vessel is vital equipment in the fishery industry that used to extract commercial marine species from the ocean. For this reason, to maintain a high level of profitability, a vessel should readily available when needed. Here we will consider a situation when there is a maintenance contract available from the agent. The owner of the fleet (a firm or a country) will decide the number of vessels for the fleet that should be bought from the agent together with the available maintenance service contract offer by the agent. The second aspect is the sustainability of the commercial marine stock in the ocean. In this paper we combine the two aspect simultaneously. Specifically, we will look for the number of fishing vessels that should be bought by the firm which maximizing the net profit earn by the firm from the use of the vessels to exploit the commercial fish stock while warranting that the fish stock is in the sustainable condition. We will assume that the fish species follow the logistic growth equation with and all the vesells maximize the fish catch at the maximum sustainable yield (MSY).