LQ Optimal Sliding Mode Control of Periodic Review Perishable Inventories with Transportation Losses

Abstract

In this work we apply the control-theoretic approach to design a new replenishment strategy for inventory systems with perishable stock. Such systems are supposed to effectively satisfy an unknown and permanently time-varying consumers’ demand. The main obstacle of achieving this goal is the need of obtaining supplies from a distant source. During the supply process goods are inevitably lost due to various causes. Furthermore, those goods which successfully arrive at the distribution center still deteriorate while stored in its warehouse. We explicitly take into account both of these factors in designing our control strategy. We propose a sliding mode strategy and choose its parameters to minimize a quadratic quality criterion. This approach allows us to ameliorate the bullwhip effect (the amplification of the demand variations when going up in the supply chain). The control strategy proposed in this work ensures bounded orders, guarantees full consumers’ demand satisfaction, and eliminates the risk of exceeding the warehouse capacity. These properties are stated in three theorems and proved in the paper.

Fields of Action for Designing Measures to Avoid Food Losses in Logistics Networks

“…A total of six articles fit into this category. The identified articles primarily focused on implementing reasonable warehouse strategies, such as the "first expired first out" principle [47]. Other authors concentrated on warehousing and the specific requirements of the early stages of the logistics network, more specifically, on the level of farmers.…”

Inventory Model with Fixed Shelf Life under Generalized Non-Increasing Demand

“…Avinadav et al [14] expanded this inventory system to derive the optimal order quantity, price, and replenishment cycles for a demand that is linearly dependent on price and time. We recall that Avinadav and Arponen [13] considered the polynomial type demand λ(t) and then Avinadav et al [14] extended to λ(t, p) where p is the selling price such that λ(t, p) is the multiplication of a polynomial type function in t and a linearly decreasing function in p. Leśniewski and Bartoszewicz [15] study inventory models with defect items, warehouse capacity, and deterioration during storage in a warehouse under the bullwhip effect and supply chain. Aiello et al [16] constructed a mathematical model to optimize the food supply chain consist of retailers and potential recipients that operate the food recovery to include the benefits of donors and the operational charges for the food recovery.…”

Nonlinear modeling and performance analysis of a closed-loop supply chain in the presence of stochastic noise

“…SMC is useful in reducing inventory oscillation. In Ignaciuk et al's [32]research, LQ optimal sliding mode supply policy was developed for periodic review inventory systems. Piotr Levniewski et al [33] applied the control-theoretic approach to design a new replenishment law for supply chain systems with perishable inventory.…”