Non-stationary Demand Research Articles

비정상적 수요를 갖는 품목들의 통합발주정책

This paper concerns a joint replenishment problem for a single buyer who sells multiple types of items to end-customers. The buyer periodically replenishes the inventory of each item to a preset order-up-to-level to satisfy the end customers' demands, which may be non-stationary. A joint replenishment policy characterized by variable order-up-to-levels is proposed for the buyer who wishes to minimize the expected cost of operating the retail system. The proposed policy starts each period by calculating the expected cost of ordering and not ordering action based on the information of the current inventory position and forecasted demand for the upcoming period. It then takes advantage of an integer programming model to get a cost effective joint replenishment plan. Computer experiment was performed to test efficiency of the proposed policy. When compared with the most efficient policy currently available, our policy showed a considerable cost savings especially for the problems having non-stationary demands.

Managing information and supplies inventory operations in a manufacturing environment. Part 2: An order-timing and sizing algorithm

We develop a new, flexible independent demand forecasting-optimisation algorithm, and apply it to nine difficult-to-manage maintenance and repair products at the AREVA nuclear fuel rod manufacturing facility. The algorithm results in a 27% reduction in inventory holding and ordering costs relative to AREVA's baseline ERP method. This is in addition to improving the line item fill rates from 96 to 98%. This new algorithm is more flexible than the baseline method in that (1) our forecast error distribution is not assumed to be normal—we automatically find the best-fitting distribution from a large family of distributions, (2) we jointly optimise the order quantity and reorder point by using an optimisation routine that is embedded in a simulation methodology. Our algorithm can therefore handle a non-stationary demand process during the planning horizon, and (3) we dynamically select the best time series forecaster for demand based on the most recent history. This flexibility drove the performance improvements. Our algorithm can be easily adapted to any independent demand situation across any industry's supply chain.

Solving the stochastic dynamic lot-sizing problem through nature-inspired heuristics

We investigate the dynamic lot-size problem under stochastic and non-stationary demand over the planning horizon. The problem is tackled by using three popular heuristic methods from the fields of evolutionary computation and swarm intelligence, namely particle swarm optimization, differential evolution and harmony search. To the best of the authors' knowledge, this is the first investigation of the specific problem with approaches of this type. The algorithms are properly manipulated to fit the requirements of the problem. Their performance, in terms of run-time and solution accuracy, is investigated on test cases previously used in relevant works. Specifically, the lot-size problem with normally distributed demand is considered for different planning horizons, varying from 12 up to 48 periods. The obtained results are analyzed, providing evidence on the efficiency of the employed approaches as promising alternatives to the established Wagner–Whitin algorithm, as well as hints on their proper configuration.

An Empirical Investigation of Dynamic Ordering Policies

Adaptive base stock policy is a well-known tool for managing inventories in nonstationary demand environments. This paper presents empirical tests of this policy using aggregate, firm-level data. First, we extend a single-item adaptive base stock policy in previous literature to a multi-item case. Second, we transform the policy derived for the multi-item case to a regression model that relates firm-level inventory purchases to firm-level sales and changes in sales forecasts. We focus on two research questions: Can the adaptive base stock policy explain cross-sectional ordering behaviors under sales growth? To the extent that the adaptive base stock policy fails to explain ordering behaviors under sales growth, are there frictions that explain such a finding? Our empirical results demonstrate disparities in ordering behaviors between firms experiencing high and moderate sales growth. Contrary to theoretical prediction, this implies that inventory purchases are a function of not only current sales and changes in sales forecast but also past sales growth. As potential explanations for this departure from theoretical prediction, we show that both future demand dynamics and inventory holding risks depend on past sales growth. In addition, we find that firms' inventory holding risks may also be affected by purchasing constraints imposed by supply chain contracts. Our results provide managerial implications for practitioners and inform future theoretical research. This paper was accepted by Martin Lariviere, operations management.

Value of Information Sharing and Lead Time Reduction in a Supply Chain with Autocorrelated Demand

We consider the two level supply chain of Lee et al. (Manage Sci 46(5):626–643, 2000) with nonstationary demand that follows an AR(1) process. Without information sharing in the supply chain, the retailer only conveys his order. With information sharing, the retailer at the end of the period, in addition to conveying his order also conveys his demand level for the period. The use of a model of autocorrelated demand becomes important, given empirical work that demand for a high percentage of SKUs at a supermarket can be autocorrelated. This is because of the repeat purchase behaviour of customers. We show some results which have been observed in the numerical experiments of Lee et al. (2000). In the two level supply chain of Lee et al. (2000), we show that the reduction in manufacturer costs with information sharing increases, as the demands become more correlated over time. In Lee, So and Tang’s model, we also consider the effects of a reduction in lead time from the manufacturer to the retailer, on retailer and manufacturer costs. We show that a reduction in lead time reduces the retailer’s costs more than the manufacturer’s costs.

Inventory Write-Downs, Sales Growth, and Ordering Policy: An Empirical Investigation

Adaptive base stock policy is a well-known tool for managing inventories in non-stationary demand environments. This paper presents empirical tests of this policy using aggregate, firm-level data. First, we extend a single-item adaptive base stock policy in previous literature to a multi-item case. Second, we transform the policy derived for the multi-item case to a regression model that relates firm-level inventory purchases to firm-level sales and changes in sales forecasts. We focus on two research questions: Can the adaptive base stock policy explain cross-sectional ordering behaviors under sales growth? To the extent that the adaptive base stock policy fails to explain ordering behaviors under sales growth, are there frictions that explain such a finding? Our empirical results demonstrate disparities in ordering behaviors between firms experiencing high and moderate sales growth. Contrary to theoretical prediction, this implies inventory purchases are a function of not only current sales and changes in sales forecasts, but also past sales growth. As potential explanations for this departure from theoretical prediction, we show that both future demand dynamics and inventory holding risks depend on past sales growth. In addition, we find that firms' inventory holding risks may also be affected by purchasing constraints imposed by supply chain contracts. Our results provide managerial implications for practitioners and inform future theoretical research.

Value of Information in a Serial Supply Chain Under a Nonstationary Demand Process

Value of Information in a Serial Supply Chain Under a Nonstationary Demand Process

Research on Inventory Control Policies for Nonstationary Demand based on TOC

An effective inventory replenishment method employed in the supply chain is one of the key factors to achieving low inventory while maintaining high customer delivery performance. The state of demand process is often not directly observed by the decision maker. Thus, in many literatures, the inventory control problem is a composite-state, partially observed Markov decision process (POMDP), which is an appropriate model for a number of dynamic demand problems. In practice, managers often use certainty equivalent control (CEC) policies to solve such a problem. However, in reality, Theory of Constraints (TOC) has brought a practical control policy that almost always provides much better solutions for this problem than the CEC policies commonly used in practice. In this paper, we proposed three different inventory control policies based on TOC buffer management framework, and use simulation approach to compare them with traditional adaptive (s,S,T) policy. The computational results indicate how specific probl...

Integration of channel decisions in a decentralized reverse production system with retailer collection under deterministic non-stationary demands

The inclusion of return flows of postconsumer materials into a forward supply chain system poses many challenging questions arising from the interaction between the forward and return flows of materials. This paper presents a model that integrates pricing, production, and inventory decisions in a reverse production system (RPS) with retailer collection. The returned products are assumed valuable to the manufacturer for creating as-new products, but the retailer must divide effort between selling the new product and collecting the returns. The manufacturer offers incentives to the retailer to participate in the overall system. The model employs a continuous time, differential game framework, based on a Stackelberg game with the manufacturer as leader and retailer as follower. Comparing two different optimal decisions in the RPS and the corresponding open-loop system, we show that the retailer retains the same form of decision by identifying an analogous closed-loop production efficiency. We identify key parameters which are important for determining the conditions under which the firms can obtain lower optimal prices to drive higher demands. We also show that our dynamic optimization approach is useful in determining a profitable apportionment of effort between the manufacturer and retailer for various types of product recovery processes.

An investigation of setup instability in non-stationary stochastic inventory systems

In stochastic inventory systems unfolding uncertainties in demand lead to the revision of earlier replenishment plans which in turn results in an instability or so-called system nervousness. In this paper, we provide the grounds for measuring system nervousness in non-stationary demand environments, and gauge the stability and the cost performances of ( R, S) and ( s, S) inventory policies. Our results reveal that, both the stability and the cost performance of inventory policies are affected by the demand pattern as well as the cost parameters, and the ( R, S) policy has the potential to replace the cost-optimal ( s, S) policy for systems with limited flexibility.

Case Study: Solving a Rental Fleet Sizing Model with a Large Time–Space Network

This article addresses a rental fleet sizing problem (RFS) in the context of the truck rental industry, subject to uncertain customer travel time and nonstationary customer demand that is dependent on geographical location, time, and the economic cycle of the industry. We integrate tactical (asset purchases and sales) and operational (empty truck movement and vehicle assignment) decisions, with the explicit incorporation of an asset age factor, to achieve lower cost solutions. Typically, the length of time horizon and number of locations under consideration are quite large, which makes the RFS model computationally challenging to solve. Aggregation procedures are employed for location clustering and end-of-horizon effects are examined through demand scenario-based analyses. For the reduced time–space networks, decision analyses are conducted for the RFS model to provide insights into the truck rental business regarding asset movement decisions and asset procurement/disposal decisions over time and locations.

Stability of Information-Sharing Alliances in a Three-Level Supply Chain

In their recent paper, Leng and Parlar (L&P) (2008) analyze information-sharing alliances in a three-level supply chain (consisting of a manufacturer, a distributor, and a retailer) which faces a nonstationary end demand. Supply chain members can share demand information, which reduces information distortion and thus decreases their inventory holding and shortage costs. We expand the results from L&P by considering dynamic (farsighted) stability concepts. We use two different allocation rules and show that under some reasonable assumptions there should always be some information sharing in this supply chain. We identify conditions under which the retailer in a stable outcome shares his demand information with the distributor, with the manufacturer, or with both remaining supply chain members.

On the interaction between forecasting and stock control: The case of non-stationary demand

The effect of using estimated (forecast) demand parameters on the performance of an inventory control system is an intriguing and important subject. Recent research has been undertaken on this phenomenon assuming stationary demand data. In this paper we extend the research to non-stationary demands, by means of simulation. The case of a periodic order-up-to-level inventory system is considered and the experimental structure allows us to evaluate in a progressive manner the accumulated effect of using the optimal forecasting method, optimal forecast parameters and correct variance expression procedures. The results allow insights to be gained into operational issues and demonstrate the scope for improving stock control systems.

On Replenishing Items with Seasonal Intermittent Demand

Problem statement: There are numerous difficulties associated with replenishing intermittent demand items and these are compounded when the demand distribution(s) vary seasonally. Excess inventories during an “off” season are typical, while shortages frequently occur during the “in” season, especially at the transition points between “seasons”. Approach: Evaluate the extent to which items characterized by non-stationary (seasonal) intermittent demand can be managed with commonly used forecasting and replenishment methods, including existing “intermittent demand” methods. Extensive simulation studies were conducted using combinations of two commonly used forecasting methods and two replenishment policies to evaluate the impact of non-stationary intermittent demand on key inventory performance measures, including average inventory and net profits, including the extent to which combinations of forecasting and replenishment models is adversely impacted by the non-stationary demand distributions. Results: No combination of forecasting and replenishment methods tested consistently outperformed the others and all methods demonstrated a propensity to replace demanded units an average of 10 weeks before the inventory was required to avert a shortage. Conclusion: The inventory performance of the policies tested was consistent with our expectations and offered evidence of the need for further development of forecasting and replenishment models addressing the special characteristics of items with non-stationary intermittent demand.

Research on Inventory Control Policies for Nonstationary Demand based on TOC

Research on Inventory Control Policies for Nonstationary Demand based on TOC

Managing Inventory in Supply Chains with Nonstationary Demand

Many companies experience nonstationary demand because of short product life cycles, seasonality, customer buying patterns, or other factors. We present a practical model for managing inventory in a supply chain facing stochastic, nonstationary demand. Our model is based on the guaranteed service modeling framework. We first describe how inventory levels should adapt to changes in demand at a single stage. We then show how nonstationary demand propagates in a supply chain, allowing us to link stages and apply a multiechelon optimization algorithm designed originally for stationary demand. We describe two successful applications of this model. The first is a tactical implementation to support monthly safety stock planning at Microsoft. The second is a strategic project to evaluate the benefits of using an inventory pool at Case New Holland.

A static-dynamic strategy for spare part inventory systems with nonstationary stochastic demand

Inventory control is especially difficult when demand is stochastic and nonstationary. We consider a spare part inventory control problem with multiple-period replenishment lead time, and describe a static-dynamic strategy for the problem. By solving a static-dynamic uncertainty model, the strategy first makes decisions on the replenishment periods and order-up-to-levels over the planning horizon, but implements only the decisions of the first period. It then uses the rolling horizon approach in the next period when the inventory status is revised, and the multi-period problem is updated as better forecasts become available. In light of structural property of the developed static-dynamic uncertainty model, the optimal solution to the model can be obtained without much computational effort and thus the strategy can be easily implemented. Computational experiments and result of a case study verify the efficacy of the proposed strategy.

Enhancing flexibility in supply chains: Modelling random demands and non-stationary supply information

The faster parts, information and decisions flow through supply chains, the faster they can respond to customer needs and to the demands of the market. In the last decade, interest has been focused on the volatile market conditions and thus, the issue of demand information sharing is paid much attention. The principal objective of this study is to understand the potential values of sharing timely supply information with random demands at retail outlets. This paper proposes a theoretically rigorous framework for the modelling, qualitative analysis and computation of solutions to supply chain network problems within an equilibrium context in the case of non-stationary demands and information associated with supply chains. More specifically, a mathematical model to understand the potential values of sharing timely supply information with random demands is presented in this research. In dynamic supply chain networks, an unforeseen change may occur at any material and gradually influence the material flow at downstream stages with time. Therefore, in this paper, the impact of the change from the time aspect and the expenditure aspect is quantified respectively. By implementing the proposed algorithm, a participant at the downstream stage can figure out how long and how much the change may impact on its own performance just when the change occurs on the upstream stage. The aim of this research is not only to demonstrate the existence of bullwhip effect, but also to quantify it, i.e. to quantify the increase in variability at each stage of the supply chain and derive the market equilibrium conditions. Efficacy of the proposed approach is demonstrated with an illustrative numerical example.

A multiple-item inventory model for a non-stationary demand

Inventory decisions in supply chain are crucial for its success. These decisions become more important for the high-margin products with spiky random fluctuations in demand. As on one side the shortage costs are significant, on the other side, to maintain appropriate service levels and avoid shortages necessitates excessive inventory, which in turn affects the liquidity by blocking working capital. The problem gets compounded when the executives are required to deal with variety, randomness with respect to a particular product/SKU and to maintain rhythm in production set-up in line with fluctuations in supply chain. The other factors like constrained production capacity and obsolescence amplify the problems further. This article proposes a model that can be used for the cyclic replenishment-based dispatch system following rhythm in the non-dedicated production lines and using forecasts for the planning. The model presents a new scheme to arrive at the inventory replenishment levels and tries to improve the pull in the system. For validation, the model is simulated and the results are compared. This article offers an approach for optimisation considering organisational constraints of maintaining low inventory, rhythm, statistics and empirical understanding, and thus has business significance.

Dynamic re-order point inventory control with lead-time uncertainty: analysis and empirical investigation

A new forecast-based dynamic inventory control approach is discussed in this paper. In this approach, forecasts and forecast uncertainties are assumed to be exogenous data known in advance at each period over a fixed horizon. The control parameters are derived by using a sequential procedure. The merits of this approach as compared to the classical one are presented. We focus on a single-stage and single-item inventory system with non-stationary demand and lead-time uncertainty. A dynamic re-order point control policy is analysed based on the new approach and its parameters are determined for a given target cycle service level (CSL). The performance of this policy is assessed by means of empirical experimentation on a large demand data set from the pharmaceutical industry. The empirical results demonstrate the benefits arising from using such a policy and allow insights to be gained into other pertinent managerial issues.