Linear dynamic model of production-inventory with debt repayment: optimal management strategies

TL;DR

This paper develops a linear continuous-time model for production-inventory systems with debt repayment, deriving optimal control strategies through maximum principle, and offers practical approaches for small firms to achieve positive profits.

Contribution

It introduces a novel linear dynamic model with explicit optimal control solutions for managing production, inventory, and debt repayment in small firms.

Findings

Exact solutions for optimal control under various scenarios

Proposed short-term strategies ensuring positive final profit

Discussion on practical implementation of control strategies

Abstract

In this paper, we present a simple microeconomic model with linear continuous-time dynamics that describes a production-inventory system with debt repayment. This model is formulated in terms of optimal control and its exact solutions are derived by prudent application of the maximum principle under different sets of initial conditions (scenarios). For a potentially profitable small firm, we also propose some alternative short-term control strategies resulting in a positive final profit and prove their optimality. Practical implementation of such strategies is also discussed.