Stock Policy Research Articles

Newsvendor characterizations for one-warehouse multi-retailer inventory systems with discrete demand under the balance assumption

This paper considers a one-warehouse multi-retailer inventory system that faces discrete stochastic demand of the customers. Under the so-called balance assumption (also known as the allocation assumption), base stock policies are optimal. Our main contribution is to show that the optimal base stock levels satisfy newsvendor characterizations, which are in terms of inequalities, and to extend the newsvendor equalities known for the continuous demand model. These characterizations are appealing because they (i) are easy to explain to nonmathematical oriented people like managers and MBA students, (ii) contribute to the understanding of optimal control, (iii) help intuition development by providing direct relation between cost and optimal policy parameters.

On the value of customer information for an independent supplier in a continuous review inventory system

We consider the inventory control problem of an independent supplier in a continuous review system. The supplier faces demand from a single customer who in turn faces Poisson demand and follows a continuous review (R, Q) policy. If no information about the inventory levels at the customer is available, reviews and ordering are usually carried out by the supplier only at points in time when a customer demand occurs. It is common to apply an installation stock reorder point policy. However, as the demand faced by the supplier is not Markovian, this policy can be improved by allowing placement of orders at any point in time. We develop a time delay policy for the supplier, wherein the supplier waits until time t after occurrence of the customer demand to place his next order. If the next customer demand occurs before this time delay, then the supplier places an order immediately. We develop an algorithm to determine the optimal time delay policy. We then evaluate the value of information about the customer’s inventory level. Our numerical study shows that if the supplier were to use the optimal time delay policy instead of the installation stock policy then the value of the customer’s inventory information is not very significant.

Inventory routing problems in a context of vendor-managed inventory system with consignment stock and transshipment

The inventory routing problem involves the integration and the coordination of two components of the logistics value chain: the inventory management and the vehicle routing decisions. In fact, the aim is to jointly decide on the distribution tour, from a distribution centre to a set of locations, and on the inventory policy for each location. Although many research investigations show great interest in policies such as transshipment or dynamic routings on the distribution system performances, these approaches are often criticised in practice as being too restrictive. In this article, we consider the inventory routing framework in a supplier integration context, i.e. a vendor-managed inventory with a consignment stock policy. Under such framework, we show that the transshipment brings more benefits than the classical context. In particular, we consider the case of static routings and we numerically show that transshipment permits to better optimise the distribution tours and to improve the global performance of the supply network.

An adaptive base stock policy for repairable item inventory control

Abstract This paper presents an adaptive base stock policy for a repairable item inventory control problem. Base stock level of a repairable item is updated based on the work-in-process (WIP) inventory level in repair facility with update frequency modeled as a separate tactical control parameter together with a standard base stock level. Stock-out situations are handled by emergency shipments, and priority shipments are used when updating the base stock level. A single-item single-location problem is considered, with repair facility having a limited capacity, and the problem is modeled by a two-dimensional continuous-time Markov chain, which is then solved explicitly by using matrix geometric methods. Numerical results are provided that show, for a given downtime target, the new policy achieves substantial reduction in inventory on-hand and significant saving in total cost.

Ranking efficiency for twenty-six emerging stock markets and financial crisis: Evidence from the shannon entropy approach

In this paper the evolution of a weak-form efficiency for twenty six emerging stock markets is tested. To do this, a modified Shannon entropy and a Symbolic Time Series Analysis are employed over the period September 1997 to November 2007. A regression is performed for time windows with 100 observations and a rolling sample approach. The empirical results show that stock market efficiency changes over time and differs from one market to another and across geographic areas. For example, the Argentinian market is a more efficient market whereas the Tunisian stock market is less efficient. The inefficiency in stock markets is dynamic. Furthermore, a negative relationship was found between the financial crisis and stock market efficiency. The findings of this evolving market efficiency may be attributed to microstructure variables. These results have several implications for stock portfolio hedgers and policy makers.

Modeling Chaotic Behavior of Chittagong Stock Indices

Stock market prediction is an important area of financial forecasting, which attracts great interest to stock buyers and sellers, stock investors, policy makers, applied researchers, and many others who are involved in the capital market. In this paper, a comparative study has been conducted to predict stock index values using soft computing models and time series model. Paying attention to the applied econometric noises because our considered series are time series, we predict Chittagong stock indices for the period from January 1, 2005 to May 5, 2011. We have used well-known models such as, the genetic algorithm (GA) model and the adaptive network fuzzy integrated system (ANFIS) model as soft computing forecasting models. Very widely used forecasting models in applied time series econometrics, namely, the generalized autoregressive conditional heteroscedastic (GARCH) model is considered as time series model. Our findings have revealed that the use of soft computing models is more successful than the considered time series model.

Computing globally optimal (s,S,T) inventory policies

We consider a single-echelon inventory installation under the (s,S,T) periodic review ordering policy. Demand is stationary random and, when unsatisfied, is backordered. Under a standard cost structure, we seek to minimize total average cost in all three policy variables; namely, the reorder level s, the order-up-to level S and the review interval T. Considering time to be continuous, we first model average total cost per unit time in terms of the decision variables. We then show that the problem can be decomposed into two simpler sub-problems; namely, the determination of locally optimal solutions in s and S (for any T) and the determination of the optimal T. We establish simple bounds and properties that allow solving both these sub-problems and propose a procedure that guarantees global optimum determination in all policy variables via finite search. Computational results reveal that the usual practice of not treating the review interval as a decision variable may carry severe cost penalties. Moreover, cost differences between (s,S,T) and other standard periodic review policies, including the simple base stock policy, are rather marginal (or even zero), when all policies are globally optimized. We provide a physical interpretation of this behavior and discuss its practical implications.

Analysis of an assemble-to-order system with different review periods

We consider a single item assembled from two components. One of the components has a long lead time, high holding cost and short review period as compared to the other one. We assume that net stocks are reviewed periodically, customer demand is stochastic and unsatisfied demand is backordered. We analyze the system under two different policies and show how to determine the policy parameters that minimize average holding and backorder costs. First, we consider a pure base stock policy, where orders for each component are placed such that the inventory position is raised up to a given base stock level. In contrast to this, only the orders for one component follow this logic while the other orders are synchronized in case of a balanced base stock policy. Through mathematical analysis, we come up with the exact long-run average cost function and we show the optimality conditions for both policies. In a numerical study the policies are compared.

Inventory write-down prediction for semiconductor manufacturing considering inventory age, accounting principle, and product structure with real settings

The International Financial Reporting Standards (IFRS) No. 2 has been the worldwide accounting principle for the reduction of inventory to market allowance since January 1, 2005. Using make-to-stock manufacturing strategies and inventory accounting for only approximately 14% of the total costs, integrated device manufacturers have found maintaining robust records for financial statements increasingly difficult. For example, one company in the case study conducted in this study must write-down losses of 2–100% of the total inventory costs for products with inventory ages of 18months–3years. However, the average cycle time for producing flash memory is approximately 3months. In other words, when the system variation and safety stock policy are considered, the company must write-down the reduction of inventory to market allowance for most of work-in-process inventory. However, little research has been done to addressing the practical management of operations according to inventory aging processes. This study develops a polynomial-time-based model to obtain significant features, including inventory ages, accounting principles, and product structures (bill of material), for the accurate prediction of inventory write-downs to reduce the impact of the carrying value fluctuation of inventory. An empirical study was conducted on a Taiwanese semiconductor manufacturer. The results show that predicting 3-month inventory write-downs of a complete flash memory production line comprising approximately 8500 product types can be conducted in less than 10s, with the mean absolute percentage error (MAPE) less than 3.5%. Discussions regarding the sensitivity analysis and cost tornado diagrams suggest the priority of affecting factors. The results show the viability of implementing the proposed model to predict inventory write-downs in the semiconductor manufacturing industry.

Optimizing reliability and service parts logistics for a time-varying installed base

Performance based contracting (PBC) emerges as a new after-sales service practice to support the operation and maintenance of capital equipment or systems. Under the PBC framework, the goal of the study is to increase the system operational availability while minimizing the logistics footprint through the design for reliability. We consider the situation where the number of installed systems randomly increases over the planning horizon, resulting in a non-stationary maintenance and repair demand. Renewal equation and Poisson process are used to estimate the aggregate fleet failures. We propose a dynamic stocking policy that adaptively replenishes the inventory to meet the time-varying parts demand. An optimization model is formulated and solved under a multi-phase adaptive inventory control policy. The study provides theoretical insights into the performance-driven service operation in the context of changing system fleet size due to new installations. Trade-offs between reliability design and inventory level are examined and compared in various shipment scenarios. Numerical examples drawn from semiconductor equipment industry are used to demonstrate the applicability and the performance of the proposed method.

Análisis y minimización del riesgo de rotura de stock aplicado a la gestión en farmacia hospitalaria

To determine how many dispensary drugs should be in the safety stock in a tertiary hospital in accordance with the risk level and the number of days that the hospital is able to withstand a stockout. We statistically analysed the infliximab order recorded over a period of 120 days. This drug is relevant for this study as it is costly and is immediately supplied to the clinic. Using the data records for purchasing and dispensing in our department, we created a table to compare the level of risk assumed with the number of units in stock and the number of days that the safety stock should last. In addition, we calculated how much stock there should be in accordance with different heuristic rules used by pharmacy departments. In the period being studied, the daily order was 11.4±14.8 units of infliximab. Using the methodology proposed, we discovered that there should be 79 units in the safety stock. Other hospital rules determine values of 47 and 119 units. The method proposed allows us to discover the risk level that is assumed when selecting the safety stock. Therefore, we are able to design a safety stock policy consistent with the risk level adopted. Under certain assumptions the safety stock quota provided by this method could be reduced. Lastly, there is a notable difference between the safety stock values suggested by different rules, as it has been shown in this article.

Static-dynamic uncertainty strategy for a single-item stochastic inventory control problem

We consider a single-stage inventory system facing non-stationary stochastic demand of the customers in a finite planning horizon. Motivated by the practice, the replenishment times need to be determined and frozen once and for all at the beginning of the horizon while decisions on the exact replenishment quantities can be deferred until the replenishment time. This operating scheme is refereed to as a “static-dynamic uncertainty” strategy in the literature [3]. We consider dynamic fixed-ordering and linear end-of-period holding costs, as well as dynamic penalty costs, or service levels. We prove that the optimal ordering policy is a base stock policy for both penalty cost and service level constrained models. Since an exponential exhaustive search based on dynamic programming yields the optimal ordering periods and the associated base stock levels, it is not possible to compute the optimal policy parameters for longer planning horizons. Thus, we develop two heuristics. Numerical experiments show that both heuristics perform well in terms of solution quality and scale-up efficiently; hence, any practically relevant large instance can be solved in reasonable time. Finally, we discuss how our results and heuristics can be extended to handle capacity limitations and minimum order quantity considerations.

(S-1,S) Policy for Two-Commodity Stochastic Inventory System

This paper deals with two commodity continuous review inventory system with base stock policy. The maximum inventory level for the i-th commodity is S(subscript i) (i = 1, 2) units. The demands occur for either one unit of first commodity or one unit of second commodity or one unit of each commodity and the demand time points form independent Poisson process. A one-for-one ordering policy is adopted. According to this policy, orders are placed for one unit of i-th commodity, as and when the inventory level of i-th commodity drops by one unit due to a demand (i = 1, 2). The lead times are assumed to be negative exponential. The joint inventory level for both commodities is obtained in the steady state. Various system performance measures in the steady state are derived. The results are illustrated numerically.

Approximation methods for the analysis of a multicomponent, multiproduct assemble-to-order system

In this article, we consider the performance evaluation of a multicomponent, multiproduct assemble-to-order (ATO) system. Each component is managed independently using a base-stock policy at a supply facility with limited production capacity and an infinite buffer. The arrivals of demands follow a multivariate Poisson process and unfilled demands are backlogged. Because exact analysis of the proposed system is not feasible, we propose two approximation methods which provide upper and lower bounds for various performance measures such as fill rate, average waiting time, and average number of backorders of the proposed system. Our computational experiments demonstrate the effectiveness of the two approximation methods under various system settings. In this article, we consider an assemble-to-order (ATO) system in which multiple components are produced to meet demands of multiple products. Each component supply facil- ity has limited production capacity with i.i.d. exponential processing time; its inventory is replenished using a base- stock policy; and the replenishment orders for the component are placed in a queue with an infinite buffer size. The arrivals of demands follow a multivariate Poisson process, in which an arriving order of a certain product will request a num- ber of components with a fixed probability. The demand orders are filled on first-come-first-serve basis and unfilled orders, due to shortage of one or more components, will be backlogged. Throughout this article, we will call the above- described system the infinite buffer ATO system, or IBS in short. We are interested in the analysis of three order-based per- formance measures of the IBS, namely, average waiting time of an order, the average number of backorders, and

Non-cooperative consignment stock strategies for management in supply chain

This paper analyzes the coordination and competition issue in a two-level supply chain, having one vendor (or manufacturer) and one buyer (or retailer). A continuous deterministic model is presented. To satisfy the buyer's demands, the product is delivered in discrete batches from the vendor's stock to the buyer's stock and all shipments are realized instantaneously. We describe inventory patterns and the cost structure of production–distribution cycles (PDC) under generalized consignment stock (CS) policies. For the joint optimization case, the average total cost of production, shipment and stockholding is minimized. Optimal solution techniques are presented and illustrated with numerical examples. In a competitive situation, the objective is to determine schedules, which minimize the individual average total costs in the PDC obtainable by individual decisions. This paper presents a non-cooperative two-person constrained game with agents (a vendor and a buyer) choosing the number and sizes of deliveries. Generalized CS-policies are considered as feasible individual strategies in the game. We consider the class of non-cooperative sub-games, indexed by two integer parameters connected with CS policies. It is proven that there exists a unique Nash equilibrium strategy in each of the considered sub-game. ►The coordination of deliveries between the vendor and the buyer in a two-level supply chain with centralized and decentralized decision process is investigated. ► Generalized consignment stock (gCS) policies are analyzed. ► Mathematical analysis of the inventory patterns derived the structure of an optimal (gCS) policy for integrated vendor-buyer inventory system (with respect to their possible competition via non-cooperative game). ► Nash equilibrium strategies are presented and illustrated with numerical examples.

Price markdown scheme in a multi-echelon supply chain in a high-tech industry

This paper studies the price markdown scheme in a supply chain that consists of a supplier, a contract manufacturer (CM), and a buyer (retailer). The buyer subcontracts the production of the final product to the CM. The CM buys the components from the supplier and charges the buyer a service fee for the final product produced. The price markdown is made possible by the supplier with the development of new manufacturing technologies that reduce the production cost for the sourced component. Consequently, the buyer adjusts the retail price in order to possibly stimulate stronger demand that may benefit both the supplier and the buyer. Under this scenario, we identify the optimal discount pricing strategies, capacity reservation, and the stocking policies for the supplier and the buyer. We also investigate the optimal inventory decision for the CM to cope with the price discount by considering both demand and delivery uncertainties. Our results suggest that higher production cost accelerates the effects of higher price sensitivity on lowering the optimal capacity and stocking policies in the supply chain. The effect of mean demand error on the optimal prices is relatively marginal compared with that from price sensitivity. We also found that increasing the standard deviation of the random demand does not necessarily increase the stocking level as one would predict. The results show that delivery uncertainty plays an important role in the inventory carried beyond the price break. We discuss potential extensions for future research.

A belief-rule-based inventory control method under nonstationary and uncertain demand

This paper is devoted to investigating inventory control problems under nonstationary and uncertain demand. A belief-rule-based inventory control (BRB-IC) method is developed, which can be applied in situations where demand and demand-forecast-error (DFE) do not follow certain stochastic distribution and forecasting demand is given in single-point or interval styles. The method can assist decision-making through a belief-rule structure that can be constructed, initialized and adjusted using both manager’s knowledge and operational data. An extended optimal base stock (EOBS) policy is proved for initializing the belief-rule-base (BRB), and a BRB-IC inference approach with interval inputs is proposed. A numerical example and a case study are examined to demonstrate potential applications of the BRB-IC method. These studies show that the belief-rule-based expert system is flexible and valid for inventory control. The case study also shows that the BRB-IC method can compensate DFE by training BRB using historical demand data for generating reliable ordering policy.

Joint Control of Component Production and Inventory Allocation in an Assemble-to-order System with Lost Sales

This paper considers a joint control problem of combined component production and inventory allocation in an assemble-to-order system which consists of two components and three demand classes with lost sales. Each demand class arrives according to a Poisson process, and the production time of each component follows an exponential distribution. By formulating the system as a Markov decision process under the expected total discounted cost criterion, we obtain the optimality equation following the Lippman transformation, from which we derive the structural properties of the optimal control policy. Specially, the optimal production policy for each component is shown to be a base stock policy with the base-stock level non-decreasing in the inventory level of the other component, and the optimal inventory allocation for each component is a state-dependent threshold policy, where the threshold point for the demand for one kind of components is non-decreasing in the inventory level of the other component, while the threshold point for the demand for both components is non-increasing in the inventory level of the other component. Finally, we give some numerical examples to show how the optimal control policy changes with the system parameters, and we also provide some managerial insights.

Computation of approximate optimal policies in a partially observed inventory model with rain checks

This paper proposes a new methodology to solve partially observed inventory problems. Generally, these problems have infinite-dimensional states that are conditional distributions of the inventory level. Our methodology involves linearizing the state transitions via unnormalized probabilities. It then uses an appropriate functional basis to represent the state. Considering the speed and stability of computations, we choose truncated Chebyshev polynomials as the basis. We use Fast Fourier Transforms along with an appropriate discretization of inventory levels to speed up the computations. These main ideas are blended to obtain an iterative algorithm to solve a partially observed inventory model with rain checks. In this model, the inventory manager (IM) does not know the inventory level when it is positive. Otherwise, the IM fully observes it. This model provides a context to illustrate our methodology, which applies to other such models. Although this model has been studied mathematically in the literature, the use of our algorithm provides a numerical approximation of the optimal order quantities. These are compared to the orders released under a base mean-stock policy, where the IM replaces the unobserved inventory level with its mean and applies the well-known base stock policy. We show numerically that the optimal order quantity is very close to the base mean-stock order quantity, when the variance of the inventory distribution is small. When the mean of the inventory distribution is large, the optimal order quantity is more than the base mean-stock quantity, and it is the other way around when the mean is small or negative. These insights are explained via uncertainty and information effects and their interplay. We expect this interplay to show up in other partially observed inventory models.

Estimating a retailer's base stock level: an optimal distribution center order forecast policy

Errors in order forecasts are a salient source of inefficiencies in retail supply chains. Many operational decisions made by suppliers hinge on order forecasts, which typically are based solely on either order or point-of-sale (POS) history. Using a discrete-time formulation, this research demonstrates that if a supplier knows that a retailer is using a base stock policy, it should use that knowledge to forecast the retailer's orders, even if the supplier does not know the base stock level and/or have access to POS data.