DYNAMICS IN FLEET MANAGEMENT WITH COMPETITION FOR PASSENGERS AT OPTIMAL LEVELS

Abstract

It is always necessary to develop an economic strategy for exploiting any resource. This study aims at evaluating profitability of the transport business as an economic activity in Kenya. Investment for optimal returns in the passenger transport sector is a concern for both fleet operators and travelers, particularly in relation to fare prices, time wasted and the profitability of the business with a risk of incurring loss in the activity. A mathematical model describing the number of fleet units in two zones competing for passengers is developed. This is achieved by formulating a system of ordinary differential equations governing the evolution of traveler’s number, fleet management effort and the fleet fare price. The original system of three equations is reduced to a system of two equations by aggregating the fare price variable, assuming it evolves at a faster rate. Long term behavior of the model is then obtained by determination of equilibrium points. Stability and bifurcation analysis is performed. Three equilibrium points are obtained, then analyzed using local stability and local bifurcation. Model simulations are performed using MATLAB. Local stability analysis gives four main cases, as; unstable origin, a stable equilibrium at the carrying capacity, unstable (T2,E2) and a stable free equilibrium (T∗,E∗) which has bi-stability depending on C. In the later case, a stable equilibrium correspond to high cost of running fleet units relative to the urgency of passengers to travel, giving negative effort. The unstable equilibrium corresponds to high demand for public transport than the cost of running fleet units, allowing positive effort hence a saddle. The value Emax represents the optimal fleet management effort at the critical threshold value C0 = qa r . The findings of this study can assist fleet operators in making informed decisions on strategies that maximize economic returns.