Optimal number of fishing fleet for a sustainable fishery industry with a generalized logistic production function

The paper presents a mathematical model of optimal fleet number of fishing vessels. Here we consider two aspects related to the vessels and to the fish stock to which the vessels are used to exploit to. The first aspect is the availability/reliability of the vessels. The fishing vessels are 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, the vessels should be readily available when it is needed. Here we will consider a situation when there is a maintenance contract available from the agent or the owner equipment manufactuer (OEM) of the vessels. The owner of the fleet (a firm or a country) shall decide the numbers of the vessels in the fleet (it is ussualy called the fleet number) that should be bought from the OEM, bounded together with the available maintenance service contract offered by the OEM. The second aspect is the sustainability of the commercial fish stock in the ocean. In this paper we combine the two aspects simultaneously. Specifically, we will look for the fleet number which maximizes the net profit earn by the firm from the use of the fleet to exploit the commercial fish stock, while warranting that the fish stock is in a sustainable condition. We will assume that the growth of the fish species follows the generalized logistic production function and all the fleet maximizes the fish catch at the maximum sustainable yield (MSY).