Networked Base‐Stock Inventory Control in Complex Distribution Systems

Abstract

This paper addresses the resource distribution problem in logistic networks with a complex, multi-echelon interconnection structure. The considered class of systems encompasses two types of nodes: controlled nodes subject to inventory management decisions and sources providing goods to the system to sustain the sales. The stock gathered at the controlled nodes is used to satisfy an exogenous, uncertain demand that may be placed at any controlled node. The stock is replenished from the sources and other controlled nodes, and the flow of goods proceeds with positive lead-time delay. The network topology does not assume any structural simplifications typically considered in inventory control problems, i.e., the nodes can form a link with any other node which leads to a mesh, multi-echelon structure. The contribution of this paper is twofold: First, the classical order-up-to policy is analyzed formally with respect to such nontrivial connectivity architectures, and conditions for full demand satisfaction under any bounded demand pattern are established. Next, a networked extension of the classical policy is proposed. The introduced networked policy is shown to generate smaller holding costs while maintaining the same service level as the classical policy. The formal study is supported by numerical tests involving genetic algorithms and simulation-based optimization.

Continuous Genetic Algorithms in the Optimization of Logistic Networks: Applicability Assessment and Tuning

“…The structural simplifications were found to be ill-suited for these kinds of systems [8], as they lead to undesirable side-effects, e.g., loss of economic gain and customer trust. The policy tuning in more elaborate cases of practical significance, especially in multi-echelon networks, is at an early stage though [38], and requires a detailed study [39]. In particular, in networked systems, unlike serial and arborescent simplifications, distributed vs. centralized policy tuning may lead to drastic cost differences, as evidenced in this work.…”

Intelligent Planning of Logistic Networks to Counteract Uncertainty Propagation

“…where x i ref is the reference level, e.g., that can be assigned to maximize sales [30], and OR i (k) is the open-order quantity, i.e., the goods in transit that have not yet reached the ordering node owing to lead-time delay.…”

Soft variable structure control in time-delay systems with saturating input

“…However, all those works assume that the control action can be exerted on the plant immediately, i. e., without any latency or time lag in the control channel. Motivated by their importance in many application areas, e. g., networked structures [8,12,15,27,30], biological [39], mechanical [42], and energy [43] systems, inventory and process control [10,11,31,35], remote regulation and sensing [6,29,44], in this paper, the possibility of using soft VSC in the systems with non-negligible delay is investigated. In order to overcome the potentially destabilizing effect of the delay in the feedback loop, a dead-time compensator is incorporated.…”

“…Since P is positive definite and q > 0, V (t) > 0 for t > 0 and V (t) = 0 at equilibrium (12). Therefore, in order for (15) to be a Lyapunov function for system (11), the derivativė…”

“…P r o o f . Consider Lyapunov function candidate (15). In uncertain system (28), V = 0 at equilibrium and V > 0 for t > 0.…”