Sales team's initiatives and stock sensitive demand — A production control policy

The present article deals with an optimal production control policy for stock and sales team's initiatives sensitive demand. The capacity of the production quantity and stock of produced items are state variable and the effort of sales-team/agent is a control variable in this model. Finally, a net profit function by trading off procurement cost, cost for effort of sales-team, cost for capacity of production and sales price is maximized by Pontryagin's Maximal Principle. The local and global stability analysis of the dynamical systems is well performed. The proposed model is justified by proper numerical illustration.