Optimization of order policies in supply networks

Abstract

The purpose of this paper is to develop a model which allows for the study and optimization of arbitrarily complex supply networks, including order policies and money flows. We propose a mathematical description that captures the dynamic behavior of the system by a coupled system of ordinary differential delay equations. The underlying optimization problem is solved using discretization techniques yielding a mixed-integer programming problem.

Data-Fitted Second-Order Macroscopic Production Models

“…From a modeling point of view it may be desirable to rewrite the derived model in semi-discretized form. For scalar models this interpretation has been given in [21]. Due to the non-negative eigenvalues of the flux we apply an Upwind semi-discretization by the method of lines of equation 5…”

Kinetic part-feeding models for assembly lines in automotive industries

“…Flows on structured media have been studied widely in the literature in the past years and appear in an almost infinite variety. 8,9,16,26,29,31 Here, we will use a similar description of the underlying process as in Refs. 34 Kinetic part-feeding models for assembly lines 3 general graph structure has been studied and a kinetic partial differential equation for high-volume part flows is derived.…”

Production systems with limited repair capacity

“…Additionally, we can also optimize the flow distribution at branching nodes in order to increase the throughput inside the network and thus the outflow, cf. routing problems in [8,10,11,14]. This leads to a so-called maximum flow problem, a well known problem in graph theory, see [5,12,20] for an overview.…”

“…the min-function) into a dynamic mixed-integer framework. This alternative has been originally introduced in [8] and has been successfully applied to a wide variety of production problems in the meanwhile, see [11,14]. First of all, we choose a uniform discrete time grid T = {t : t = 0, .…”

“…During the last years several dynamic production models have been developed either describing the trajectory of each good through the network, which is called discrete event simulation [2], or by using so-called fluid models models, where averaged quantities are used to track goods, see [1-4, 7, 9, 13] for an overview. Based on these continuous production models, optimization problems have been introduced [8,10,11,14]. These models typically deal with economic issues such as minimization of costs or maximization of output and allow for the interpretation of optimal routing of goods through a manufacturing system, best possible production mix or optimal order policies.…”