Stability analysis of constrained inventory systems with transportation delay

Stability is a fundamental design property of inventory systems. However, the often exploited linearity assumptions in the current literature create a major gap between theory and practice. In this paper the stability of a constrained production and inventory system with a Forbidden Returns constraint (that is, a non-negative order rate) is studied via a piecewise linear model, an eigenvalue analysis and a simulation investigation. The APVIOBPCS (Automatic Pipeline, Variable Inventory and Order Based Production Control System) and EPVIOBPCS (Estimated Pipeline, Variable Inventory and Order Based Production Control System) replenishment policies are adopted. Surprisingly, all kinds of non-linear dynamical behaviours of systems can be observed in these simple models. Exact expressions of the asymptotic stability boundaries and Lyapunovian stability boundaries are derived when actual and perceived transportation lead-time is 1 and 2 periods long respectively. Asymptotically stable regions in the non-linear Forbidden Return systems are identical to the stable regions in its unconstrained counterpart. However, regions of bounded fluctuations that continue forever, including both periodicity and chaos, exist in the parametrical plane outside the asymptotically stable region. Simulation shows a complex and delicate structure in these regions. The results suggest that accurate lead-time information is essential to eliminate inventory drift and instability and that ordering policies have to be designed properly in accordance with the actual lead-time to avoid these fluctuations and divergence

Econometric Estimation of Parameters of Preservation of Perishable Goods in Cold Logistic Chains

Paper discusses the parameters of preservation of perishable goods in cold logistic chains. The key parameters are the intensity of deterioration of goods, the conservation effect of perishable goods and the delay of activation of the conservation effect. The values of these parameters tell us the quantity of the product being deteriorated in the logistic chain and the extent to which the deterioration can be alleviated. Econometric estimation thus presents us with the quantity effects of preservation procedures, whereas the financial effects can be derived using the proper price categories in the calculation of the net present value or the annuity stream. In this way one can determine whether the implementation of preservation procedures is more rational than the purchase of attainable insurance policy.cold chains, Cold Chains Management, econometric estimation, intensity of deterioration, conservation effect, Input – Output analysis, Laplace transforms, MRP

The extension and exploitation of the inventory and order based production control system archetype from 1982 to 2015

In 1994, through classic control theory, John, Naim and Towill developed the ‘Automatic Pipeline, Inventory and Order-based Production Control System’ (APIOBPCS) which extended the original IOBPCS archetype developed by Towill in 1982 ─ well-recognised as a base framework for a production planning and control system. Due to the prevalence of the two original models in the last three decades in the academic and industrial communities, this paper aims to systematically review how the IOBPCS archetypes have been adopted, exploited and adapted to study the dynamics of individual production planning and control systems and whole supply chains. Using various databases such as Scopus, Web of Science, Google Scholar (111 papers), we found that the IOBPCS archetypes have been studied regarding the a) modification of four inherent policies related to forecasting, inventory, lead-time and pipeline to create a ‘family’ of models, b) adoption of the IOBPCS ‘family’ to reduce supply chain dynamics, and in particular bullwhip, c) extension of the IOBPCS family to represent different supply chain scenarios such as order-book based production control and closed-loop processes. Simulation is the most popular method adopted by researchers and the number of works based on discrete time based methods is greater than those utilising continuous time approaches. Most studies are conceptual with limited practical applications described. Future research needs to focus on cost, flexibility and sustainability in the context of supply chain dynamics and, although there are a few existing studies, more analytical approaches are required to gain robust insights into the influence of nonlinear elements on supply chain behaviour. Also, empirical exploitation of the existing models is recommended

Impact of uncertainties of lead times and expiration dates on the stability of inventory levels in a distribution system

International audienceIn this paper, we discuss the impact of uncertainties of lead times and expiration dates on the stability of the inventory regulation problem in productions systems using feedback control law structure, in the conception phase. The inventory control system is considered as an input-delay system with uncertainties on customer demands, and positive constraints due to the specifications of the agricultural supply chain. Also, the system is characterized by the presence of delay due to the process time and the distribution time, and the perishable products are modeled by a fixed preemption rate. We have first found the necessary and sufficient conditions that prove the existence and the admissibility of the control law. Secondly, a comparative analysis of impact of production delay and expiration date uncertainties on a robust design is given. Copyright c 2019 IFA

Optimizing campaign sizing policies: an application to a real-life setting.

This paper presents an integrated production inventory model that enables to capture the tradeoffs between average inventory, production capacity and customer service level in a semiprocess industry setting. The model includes different features that are specific for such a setting, such as differences in reactor yield and quality requirements across products, the need for cleaning reactors when switching between product types, and the requirement to produce products in campaign sizes that are an integer multiple of the reactor’s batch size. The model can be used to support midterm planning procedures. In this paper, we illustrate the application of the model to real-life data of two product families at a large specialty chemicals company, which for reasons of confidentiality is further referred to as Company C.Queueing; Campaign sizing; (Semi)process industries;

The Power of Online Learning in Stochastic Network Optimization

In this paper, we investigate the power of online learning in stochastic network optimization with unknown system statistics {\it a priori}. We are interested in understanding how information and learning can be efficiently incorporated into system control techniques, and what are the fundamental benefits of doing so. We propose two \emph{Online Learning-Aided Control} techniques, $\mathtt{OLAC}$ and $\mathtt{OLAC2}$, that explicitly utilize the past system information in current system control via a learning procedure called \emph{dual learning}. We prove strong performance guarantees of the proposed algorithms: $\mathtt{OLAC}$ and $\mathtt{OLAC2}$ achieve the near-optimal $[O(\epsilon), O([\log(1/\epsilon)]^2)]$ utility-delay tradeoff and $\mathtt{OLAC2}$ possesses an $O(\epsilon^{-2/3})$ convergence time. $\mathtt{OLAC}$ and $\mathtt{OLAC2}$ are probably the first algorithms that simultaneously possess explicit near-optimal delay guarantee and sub-linear convergence time. Simulation results also confirm the superior performance of the proposed algorithms in practice. To the best of our knowledge, our attempt is the first to explicitly incorporate online learning into stochastic network optimization and to demonstrate its power in both theory and practice

The Power of Online Learning in Stochastic Network Optimization

In this paper, we investigate the power of online learning in stochastic network optimization with unknown system statistics {\it a priori}. We are interested in understanding how information and learning can be efficiently incorporated into system control techniques, and what are the fundamental benefits of doing so. We propose two \emph{Online Learning-Aided Control} techniques, $\mathtt{OLAC}$ and $\mathtt{OLAC2}$, that explicitly utilize the past system information in current system control via a learning procedure called \emph{dual learning}. We prove strong performance guarantees of the proposed algorithms: $\mathtt{OLAC}$ and $\mathtt{OLAC2}$ achieve the near-optimal $[O(\epsilon), O([\log(1/\epsilon)]^2)]$ utility-delay tradeoff and $\mathtt{OLAC2}$ possesses an $O(\epsilon^{-2/3})$ convergence time. $\mathtt{OLAC}$ and $\mathtt{OLAC2}$ are probably the first algorithms that simultaneously possess explicit near-optimal delay guarantee and sub-linear convergence time. Simulation results also confirm the superior performance of the proposed algorithms in practice. To the best of our knowledge, our attempt is the first to explicitly incorporate online learning into stochastic network optimization and to demonstrate its power in both theory and practice

Why do nonlinearities matter? The repercussions of linear assumptions on the dynamic behaviour of assemble-to-order systems

The hybrid assembly-to-order (ATO) supply chain, combining make-to-stock and make-to-order (MTS-MTO) production, separated by a customer order decoupling point (CODP), is well recognised in many sectors. Based on the well-established Inventory and Order Based Production Control Systems (the IOBPCS family), we develop a hybrid ATO system dynamics model and analytically study the impact of nonlinearities on its dynamic performance. Nonlinearities play an important, sometimes even a dominant, role in influencing the dynamic performance of supply chain systems. However, most IOBPCS based analytical studies assume supply chain systems are completely linear and thereby greatly limit the applicability of published results, making it difficult to fully explain and describe oscillations caused by internal factors. We address this gap by analytically exploring the non-negative order and capacity constraint nonlinearities present in an ATO system. By adopting nonlinear control engineering and simulation approaches, we reveal that, depending on the mean and amplitude of the demand, the non-negative order and capacity constraints in the ATO system may occur and their significant impact on system dynamics performance should be carefully considered. Failing to monitor non-negative order constraints may underestimate the mean level of inventory and overestimate the inventory recovery speed. Sub-assemblers may suffer increased inventory cost (i.e. the consequence of varying inventory levels and recovery speed) if capacity and non-negative order constraints are not considered at their production site. Future research should consider the optimal trade-off design between CODP inventory and capacity and the exploration of delivery lead-time dynamics

An optimal-control based integrated model of supply chain

Problems of supply chain scheduling are challenged by high complexity, combination of continuous and discrete processes, integrated production and transportation operations as well as dynamics and resulting requirements for adaptability and stability analysis. A possibility to address the above-named issues opens modern control theory and optimal program control in particular. Based on a combination of fundamental results of modern optimal program control theory and operations research, an original approach to supply chain scheduling is developed in order to answer the challenges of complexity, dynamics, uncertainty, and adaptivity. Supply chain schedule generation is represented as an optimal program control problem in combination with mathematical programming and interpreted as a dynamic process of operations control within an adaptive framework. The calculation procedure is based on applying Pontryagin’s maximum principle and the resulting essential reduction of problem dimensionality that is under solution at each instant of time. With the developed model, important categories of supply chain analysis such as stability and adaptability can be taken into consideration. Besides, the dimensionality of operations research-based problems can be relieved with the help of distributing model elements between an operations research (static aspects) and a control (dynamic aspects) model. In addition, operations control and flow control models are integrated and applicable for both discrete and continuous processes.supply chain, model of supply chain scheduling, optimal program control theory, Pontryagin’s maximum principle, operations research model,