Robust multi-echelon multi-period inventory control

We consider the problem of minimizing the overall cost of a supply chain, over a possible long horizon, under demand uncertainly which is known only crudely. Under such circumstances, the method of choice is Robust Optimization, in particular the Affinely Adjustable Robust Counterpart (AARC) method which leads to tractable deterministic optimization problems. The latter is due to a recent re-parametrization technique for discrete time linear control systems. In this paper we model, analyze and test an extension of the AARC method known as the Globalized Robust Counterpart (GRC) in order to control inventories in serial supply chains. A simulation study demonstrates the merit of the methods employed here, in particular, it shows that a good control law that minimizes cost achieves simultaneously good control of the bullwhip effect.     

Decomposition in multi-item inventory control

This paper considers a Lagrangian decomposition approach to a stochastic demand multi-item inventory control problem with a single resource constraint. The work is a generalization of existing decomposition methods.Three decomposition methods are proposed, and bounds on the loss of optimality for each are given in terms of the Lagrange multiplier used. One method allows the calculation of the complete decision rule in advance of the realization of the states, but is expected to perform worse than the other two methods. The second and third method allow the determination of decisions as an optimization problem as the states are realized. Since, in any problem with many states, only a small proportion will actually be realized even in a large time-horizon problem, there may be some advantage in taking this approach.     

Numerical aspects in Bayesian inventory control

Summary We consider a discrete review single product dynamic inventory model with incompletely known distribution of demand from the Bayesian point of view. We derive bounds for the optimal order points and order quantities of so-called (z, Z)-order-policies and construct nearly optimal (z, Z)-order-policies easy to compute.

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Zusammenfassung Es wird ein diskretes dynamisches Ein-Produkt-Lagerhaltungsmodell mit unbekannter Nachfrageverteilung vom Bayesschen Standpunkt betrachtet. In der Menge der sog. (z, Z)-Bestellpolitiken werden Schranken für die optimalen Bestellpunkte und Bestellmengen hergeleitet. Außerdem werden gute (z, Z)-Bestellpolitiken konstruiert, die leicht zu berechnen sind.

     

On the Hungarian inventory control model

In this paper we recall and further develop an inventory model formulated by the author [Prékopa, A., 1965. Reliability equation for an inventory problem and its asymptotic solutions. In: Prékopa, A. (Ed.), Colloquia Applied Mathematics in Economics. Publ. House of the Hung. Acad. Sci., Budapest, pp. 317–327; Prékopa, A., 1973. Generalizations of the theorems of Smirnov with application to a reliability type inventory problem. Math. Operationsforschung und Stat. 4, 283–297] and Ziermann [Ziermann, M., 1964. Application of Smirnov’s theorems for an inventory control problem. Publications of the Mathematical Institute of the Hungarian Academy of Sciences Ser. B 8, 509–518] that has had wide application in Hungary and elsewhere. The basic assumption made in connection with this model is that the delivery of the ordered amount takes place in an interval, according to some random process, rather than at one time epoch. The problem is to determine that minimum level of safety stock, that ensures continuous production, without disruption, by a prescribed high probability. The model is further developed first by its combination with another inventory control model, the order up to S model and then, by the formulations of a static and a dynamic type stochastic programming models.     

Value at risk and inventory control

The purposes of this paper are two-fold. On the one hand, we shall provide a decision analysis justification for the Value at Risk (VaR) approach based on ex-post, disappointment decision making arguments. We shall show that the VaR approach is justified by a disappointment criterion. In other words, the asymmetric valuation between ex-ante expected returns above an appropriate target return and the expected returns below that same target level, provide an explanation for the VaR criterion when it is used as a tool for VaR efficiency design. Second, this paper provides applications to inventory management based on VaR risk exposure. Although the mathematical problems arising from an application of the VaR approach, tuned to current practice in financial risk management, are difficult to solve analytically, solutions can be found by application of standard computational and simulation techniques. A number of cases are solved and formulated to demonstrate the paper's applicability.     

Construction of asymptotically optimal inventory control policies

Translated fromProblemy Ustoichivosti Stokhasticheskikh Modelei, Trudy Seminara, 1989, pp. 10–19.     

Impact of RFID technology on inventory control policy

RFID application can improve operation performance in a supply chain by reducing or eliminating inventory misplacement and shrinkage. In this paper, we present a periodic review inventory model to investigate and characterize the multiperiod inventory control policies in both non-RFID and RFID cases when the firm encounters misplacement and shrinkage. The optimal inventory control policy is proved to be a two-control limit policy. The control limits in both the non-RFID case and the RFID case are analyzed and examined, while considering the impact of shrinkage and misplacement on inventory policies. A critical inventory level is determined to identify the relationship of higher inventory level control limits between the RFID case and the non-RFID case. An intensive numerical study with sensitivity analysis of selling price, misplacement rate, shrinkage rate, inventory recovery rate, and tag price is conducted. We find that when RFID technology is adopted, the inventory control policy in the RFID case is much more stable than that of the non-RFID case, as the misplaced inventory can be recovered perfectly and instantly for sale and the inventory shrinkage can be reduced by RFID technology. In addition, one of our intriguing findings is that when the shrinkage rate is below a threshold value which is independent of parameters, RFID application has no effect on inventory control policy if the misplaced inventory can be recovered in a timely manner by physical audit, which has not been revealed in previous studies.     

Optimal control of a divergent multi-echelon inventory system

Consider a divergent multi-echelon inventory system, such as a distribution system or a production system. At every facility in the system orders are placed (or production is initiated) periodically. The order arrives after a fixed lead time. At the end of each period linear costs are incurred penalty costs are incurred at the most downstream facilities for back-orders. The objective is to minimize the expected holding and penalty costs per period. We prove that under the balance assumption it is cost optimal to control every facility by an order-up-to-policy. The optimal replenishment policy, i.e. the order-up-to-level and the allocation functions at each facility, can be determined by system decomposition. This decomposition reduces complex multi-dimensional control problems to simple one-dimensional problems.     

Analysis of an exhibiting inventory system

This paper deals with a continuous review (s,S) inventory system having one exhibiting item subject to random failure. It is assumed that the demand epochs form a renewal process and the probability distribution of demand magnitudes depend only on the time elapsed since the previous demand. Replenishment of stock is instantaneous. For this model expression for the limiting distribution of position inventory is derived by applying the techniques of semi-regenerative process. Some special cases are discussed in detail     

Optimal integrated production and inventory control of an assemble-to-order system with multiple non-unitary demand classes

We study a pure assemble-to-order system subject to multiple demand classes where customer orders arrive according to a compound Poisson process. The finished product is assembled from m different components that are produced on m distinct production facilities in a make-to-stock fashion. We show that the optimal production policy of each component is a state-dependent base-stock policy and the optimal inventory allocation policy is a multi-level state-dependent rationing policy. Using numerical experimentation, we first study the system behavior as a function of order size variability and order size. We show that the optimal average cost rate is more sensitive to order size variability than to order size. We also compare the optimal policy to the first-come first-serve policy and show that there is great benefit to inventory rationing. We also propose two simple heuristics and show that these can effectively mimic the optimal policy which is generally much more difficult to determine and, especially, to implement.     

Economic model predictive inventory routing and control

Central European Journal of Operations Research - The paper proposes an economic model predictive control (EMPC) strategy for the inventory routing problem under demand uncertainty. The strategy is...     

A practical inventory control policy using operational statistics

Consider the newsvendor inventory control problem with an ambiguous demand. The traditional approach of separating the parameter estimation and the maximization of the expected profit leads to a suboptimal inventory policy. Operational statistics, introduced in this paper, provides a better solution by integrating the estimation and the optimization tasks.     

Periodic review inventory control with fluctuating purchasing costs

For an inventory control problem in which the purchasing cost changes (e.g. exchange rate fluctuations), we show that an order up to policy is optimal and determine conditions under which the optimal up to levels are monotonically ordered. We also propose a simple method for predicting the effectiveness of myopic heuristics.     

Optimal inventory control with shrinkage and observed sales

We study a discrete-time periodic-review inventory system where the unmet demand is lost, and the excess inventory is subject to shrinkage. We first derive the state evolution and then introduce unnormalized conditional probabilities to transform the nonlinear state evolution into a linear one. We then prove the existence and uniqueness of the solution for the Bellman equation in the case of unbounded costs and show that the solution yields the value function.     

On the optimal control of partially observed inventory systems

This Note introduces recent developments in the analysis of inventory systems with partial observations. The states of these systems are typically conditional distributions, which evolve in infinite dimensional spaces over time. Our analysis involves introducing unnormalized probabilities to transform nonlinear state transition equations to linear ones. With the linear equations, the existence of the optimal feedback policies are proved for two models where demand and inventory are partially observed. In a third model where the current inventory is not observed but a past inventory level is fully observed, a sufficient statistic is provided to serve as a state. The last model serves as an example where a partially observed model has a finite dimensional state. In that model, we also establish the optimality of the basestock policies, hence generalizing the corresponding classical models with full information. To cite this article: A. Bensoussan et al., C. R. Acad. Sci. Paris, Ser. I 341 (2005).     

Cost-effective inventory control in a value-added manufacturing system

This paper considers the cost-effective inventory control of work-in-process (WIP) and finished products in a two-stage distributed manufacturing system. The first stage produces a common WIP, and the second stage consists of several production sites that produce differentiated products with different capacity and service level requirements. The unit inventory holding cost is higher at the second stage. This paper first uses a network of inventory-queue model to evaluate the inventory cost and service level achievable for given inventory control policy, and then derives a very simple algorithm to find the optimal inventory control policy that minimizes the overall inventory holding cost and satisfies the given service level requirements. Some managerial insights are obtained through numerical examples.     

Analyzing the effect of the inventory policy on order and inventory variability with linear control theory

In this paper we apply linear control theory to study the effect of various inventory policies on order and inventory variability, which are key drivers of supply chain performance. In particular, we study a two-echelon supply chain with a stationary demand pattern under the influence of three inventory policies: an inventory-on-hand policy that bases orders on the visible inventory at an installation, an installation-stock policy that bases orders on the inventory position (on-hand plus on-order inventory) at an installation, and an echelon-stock policy that bases orders on the inventory position at that installation and all downstream installations. We prove analytically that the inventory-on-hand policy is unstable in practical settings, confirming analytically what has been observed in experimental settings and in practice. We also prove that the installation-stock and echelon-stock policies are stable and analyze their effect on order and inventory fluctuation. Specifically, we show the general superiority of the echelon-stock in our setting and demonstrate analytically the effect of forecasting parameters on order and inventory fluctuations, confirming the results in other research.     

Coordinating pricing and inventory control in a fluctuating environment

This paper addresses the simultaneous determination of pricing and inventory replenishment strate- gies under a fluctuating environment. Specifically, we analyze the single item, periodic review model. The demand consists of two parts： the deterministic component, which is influenced by the price, and the stochastic component （perturbation）. The distribution of the stochastic component is determined by the current state of an exogenous Markov chain. The price that is charged in any given period can be specified dynamically. A replenishment order may be placed at the beginning of some or all of the periods, and stockouts are fully backlogged. Ordering costs that are lower semicontinuous, and inventory/backlog （or surplus） costs that are continuous with polynomial growth. Finite-horizon and infinite-horizon problems are addressed. Existence of optimal policies is established. Furthermore, optimality of （s,S,p）-type policies is proved when the ordering cost consists of fixed and proportional cost components and the surplus cost （these costs are all state-dependent） is convex.