Dynamic Programming – A Base for Understanding the Input-Output Model

Abstract

Dynamic Programming (DP) is a process of deriving an optimal solution to a mathematical problem that has an objective function and environmentally varying limitations. DP has some difficulties to set up structural equations as in other management science techniques. In this context, DP, generally at a basic level, deals with two types of problem-based models: (a) Route Determination Model (RDM) and (b) Varying Input-Output Model (VIOM). In this context, this paper has explained only the Varying Input-Output Model (VIOM) with the hypothetical exhibits. The solutions of such exhibits have been derived with two (2) methods: (a) Forward Pass and (b) Backward Pass towards optimisation of maximisation and minimisation issues. The applications of both methods have been illustrated with stage segmentations and their respective payoff tables to gradually improve the results towards optimality with a “Samsen Method of preliminary work” and two basic operational processes: (a) Initial Process and (b) Optimisation Process. Indicatively, the optimisation process consists of a ten-step approach that is applied to reaching the respective optimal solutions of the exhibits (problems).

Keywords: Dynamic Programming, varying input-output model, forward pass, Samsen Method, backward pass, optimal solution, optimality

JEL Classification: C00, C02, C6, C60, C61