An application of the Stokes' theorem is illustrated by solving the two state problem, with inequality constraints, of Dobell and Ho concerning the optimal investment of resources. Whenever applicable, the Stokes' theorem approach seems to be elegant and parsimonious

This paper is concerned with long-run average cost minimization of a stochastic inventory problem with Markovian demand, fixed ordering cost, and convex surplus cost. The states of the Markov chain represent different possible states of the environment. Using a vanishing discount approach, a...

Most manufacturing systems are large and complex and operate in an uncertain environment. One approach to managing such systems is that of hierarchical decomposition. This paper reviews the research devoted to proving that a hierarchy based on the frequencies of occurrence of different types of...

We consider the problem of scheduling n jobs in a pallet-constrained two-machine flowshop so as to minimize the makespan. In such a flowshop environment, each job needs a pallet the entire time, from the start of its first operation until the completion of the last operation, and the number of...

We consider a production planning problem for a general jobshop subject to breakdown and repair of machines and subject to lower and upper bound constraints on work-in-process. The machine capacities and demand processes are assumed to be finite state Markov chains. The problem is to choose the...

This paper presents an asymptotic analysis of hierarchical production planning in a general manufacturing system consisting of a network of unreliable machines producing a variety of products. The concept of a dynamic job shop is introduced by interpreting the system as a directed graph, and the...

We study the recently identified class of generalized due date scheduling problems. These are machine scheduling problems for which due dates are specified according to the position in which a job is completed, rather than the identity of that job. Flexible manufacturing environments and public...

A single machine processing different types of parts is considered. Switching from one type to another involves a setup time. The part types may have different processing times. The resulting scheduling problem is treated as a dynamical system for which several feedback policies that are...

We consider the scheduling problem of cyclic production in a bufferless dual-gripper robot cell processing a family of identical parts. The objective is to find an optimal sequence of robot moves so as to maximize the long-run average throughput rate of the cell. While there has been a...

The introduction of a discounting term into the objective functional can be troublesome in terms of analysis by the standard maximum principle formulation. This is because it renders the Hamiltonian and the adjoint equations depend explicitly on time. In finite horizon problems it makes the...