We consider a production-inventory planning problem with time-varying demands, convex production costs and a warehouse capacity constraint. It is solved by use of the Lagrangian form of the maximum principle. The possible existence of strong decision and forecast horizons is demonstrated. When...

In this paper, we have solved a general inventory model with simultaneous price and production decisions. Both linear and non-linear (strictly convex) production cost cases are treated. Upper and lower bounds are imposed on state as well as control variables. The problem is solved by using the...

This paper describes a maximum principle for distributed parameter systems, i.e. systems characterized by partial differential equations. The maximum principle is applied to solve the problem of a cattle rancher who must decide the number of cattle in different age groups to be bought and sold...

A quadratic model for production-inventory planning was made famous by Holt, Modigliani, Muth, and Simon in 1960 in [3], especially for its application to a paint factory. A discrete control version of a related quadratic production-inventory model was studied by Kleindorfer, Kriebel, Thompson,...

First-order necessary and sufficient conditions are obtained for the following quasilinear distributed-parameter optimal control problem:max{J(u)=IntF(x,u,t)dw IntG(x,t)dsigma},subject to the partial differential equationA(t)x =f(x, u, t),where t, u, G are vectors and x, F are scalars. Use is...