LQ optimal sliding-mode supply policy for periodic-review perishable inventory systems

2012 ◽  
Vol 349 (4) ◽  
pp. 1561-1582 ◽  
Author(s):  
PrzemysŁaw Ignaciuk ◽  
Andrzej Bartoszewicz
Keyword(s):  
Sliding Mode ◽  
Inventory Systems ◽  
Periodic Review ◽  
Perishable Inventory ◽  
Supply Policy

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

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Piotr Leśniewski ◽  
Andrzej Bartoszewicz
Keyword(s):  
Control Strategy ◽  
Sliding Mode ◽  
Quality Criterion ◽  
Bullwhip Effect ◽  
Distribution Center ◽  
Inventory Systems ◽  
Theoretic Approach ◽  
Time Varying ◽  
Periodic Review ◽  
Distant Source

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.

Sliding mode control of periodic review perishable inventories with multiple suppliers and transportation losses

2013 ◽  
Vol 61 (4) ◽  
pp. 885-892 ◽  
Author(s):  
A. Bartoszewicz ◽  
M. Maciejewski
Keyword(s):  
Management Strategy ◽  
Closed Loop ◽  
Sliding Mode ◽  
Inventory Systems ◽  
Periodic Review ◽  
Computationally Efficient ◽  
Closed Loop System ◽  
Fast Reaction ◽  
Holding Costs ◽  
Inventory Holding

Abstract The purpose of this paper is to develop robust and computationally efficient supply chain management strategy ensuring fast reaction to the demand variations for periodic review perishable inventory systems. For that purpose, we apply a sliding mode approach and we propose a new discrete time warehouse management strategy. The strategy employs the sliding hyperplane appropriately designed to ensure a dead-beat performance of the closed loop system. Our strategy not only explicitly takes into account decay of goods stored in the warehouse (perishing inventories) but it also accounts for transportation losses which take place on the way from suppliers to the warehouse. The proposed strategy ensures full customers’ demand satisfaction, minimizes the on-hand inventory volume and prevents from exceeding the warehouse capacity. This reflects the need of simultaneous minimization of the lost sales costs and inventory holding costs. Furthermore, the strategy ensures that the ordered quantities of goods are always non-negative and upper bounded. These favourable properties of the proposed strategy are formally stated as a lemma and three theorems and proved in the paper.

Dead-beat and reaching-law-based sliding-mode control of perishable inventory systems

2011 ◽  
Vol 59 (1) ◽  
pp. 39-49 ◽  
Author(s):  
P. Ignaciuk ◽  
A. Bartoszewicz
Keyword(s):  
Sliding Mode Control ◽  
Sliding Mode ◽  
Service Level ◽  
Inventory Systems ◽  
Supply Source ◽  
Perishable Inventory ◽  
Reaching Law ◽  
Mode Control ◽  
Perishable Goods ◽  
Varying Demand

Dead-beat and reaching-law-based sliding-mode control of perishable inventory systemsIn this paper we consider the problem of efficient control of inventory systems with perishable goods. In the analyzed setting the deteriorating stock at a distribution center used to fulfill unknown, time-varying demand is replenished with delay from a supply source. The challenging issue is to achieve the high service level with minimum costs when the replenishment orders are procured with lead-time delay spanning multiple review periods. On the contrary to the typical heuristic approaches, we apply formal methodology based on discrete-time sliding-mode (SM) control. The proposed SM controller with the sliding plane selected for a dead-beat scheme ensures that the maximum service level is obtained in the system with arbitrary delay and any bounded demand pattern. In order to account for the supplier capacity limitations in the systems with input constraints, we also develop an alternative control strategy based on reaching law. Both controllers achieve a given service level with smaller holding costs and reduced order-to-demand variance ratio as compared to the classical order-up-to policy.

Sign in / Sign up

Export Citation Format

Share Document