Target Inventory Level Research Articles

Destocking, the bullwhip effect, and the credit crisis: Empirical modeling of supply chain dynamics

In this paper we analyze the strong sales dip observed in the manufacturing industry at the end of 2008, following the bankruptcy of Lehman Brothers and the subsequent collapse of the financial world. We suggest that firms׳ desire to retain liquidity during these times prompted a reaction characterized by the reduction of working capital, which materialized as a synchronized reduction in target inventory levels across industries. We hypothesize that such a reaction effectively acted as an endogenous shock to supply chains, ultimately resulting in the bullwhip-effect kind of demand dynamics observed. To test this proposition we develop a system dynamics model that explicitly takes into account structural, operational, and behavioral parameters of supply chains aggregated at an echelon level. We calibrate the model for use in 4 different business units of a major chemical company in the Netherlands, all situated 4–5 levels upstream from consumer demands in their respective supply chains. We show that the model gives a very good historical fit of the sales developments during the period following the Lehman collapse. We test the model׳s robustness to behavioral parameter estimation errors through sensitivity analysis, and the de-stocking hypothesis against an alternative model. Finally, we observe that the empirical data is aligned with experimental observations regarding human behavioral mechanisms concerning target adjustment times.

Calculating target inventory levels for constrained production: A fast simulation-based approximation

An accurate model for the inventory shortfall distribution is necessary to calculate the target level required to give a desired service level in manufacturing systems under stochastic demand and production capacity constraint. Existing methods for modelling the inventory shortfall require that the demand distribution be expressible in functional form and that the coefficient of demand variation be small. When these conditions cannot be met, the only recourse to a practitioner is to set target levels using simulation-based optimisation, which is computationally intensive and time consuming. By contrast, this paper presents a model in which the inventory shortfall is approximated by sampling from a single simulation run of the inventory process. The target level required for a given service level can then be calculated efficiently, to a high degree of reliability, using an iterative search. This new model is thus an efficient alternative to conventional simulation-based optimisation. Because the shortfall distribution is generated by simulating demand directly, the model makes no assumptions about the form of the demand distribution. By requiring no user modelling of the functional form or parameters of the demand distribution, this new method is easily used by inventory managers in practice or implemented in software.

Probe of the Replenishment Strategy and Grouping Rule in the Semiconductor Industry

Abstract The theory of constraint suggests the application of a demand-pull replenishment strategy combined with buffer management (DPBM) in order to effectively manage inventory. A demand-pull strategy caters to the customers’ demand to drive inventory replenishment, while buffer management is designed to adjust target inventory levels (buffer size). However, there is very limited literature looking into the parameters of buffer management in depth, such as the timing and the amount of buffer adjusted. Therefore, the objective of this study was to explore the product demand characteristics that affect the parameters of choice in buffer management when applying the DPBM strategy. This study first used a DPBM strategy (implemented via simulation, based on historical demand data) under different buffer management parameters to simulate the inventory replenishment for multiple products. The products were then grouped according to the simulated results by statistical analysis. A decision tree was applied to find the critical demand pattern factors that determined the product groups. An appropriate DPBM strategy is suggested for each product group. This study uses real demand data for 21 products, provided by a wafer foundry company located in Taiwan, to demonstrate the feasibility and effectiveness of the proposed method. The results show that it is possible to determine whether a product is suitable for DPBM strategy application after analyzing only its historical demand data.

Optimal Production Management When Demand Depends on the Business Cycle

We assume that the cumulative consumer demand for an item follows a Brownian motion, with both the drift and the variance parameters modulated by a continuous-time Markov chain that represents the regime of the economy. The management of the company would like to maintain the inventory level as close as possible to a target inventory level and would also like to produce at a rate that is as close as possible to a target production rate. The company is penalized for deviations from the target levels, and the objective is to minimize the total discounted penalty costs. We consider two models. In the first model the management of the company knows the state of the economy, whereas in the second model the management does not know it. We solve both problems and obtain the optimal production policy and the minimal total expected discounted cost. Furthermore, we compare the total expected discounted costs of the two models and determine the value of knowing the regime of the economy. We also solve the above problems in the case when the consumer demand rate follows a geometric Brownian motion modulated by a continuous-time Markov chain that represents the regime of the economy.

Control of Dividends, Capital Subscriptions, and Physical Inventories

Manufacturers manage interrelated flows of material and cash. Material needs capital, and sales contribute cash. Therefore, it may be beneficial to coordinate operational and financial decisions. We study a dynamic model of coordination in an equity-financed firm in which inventory and financial decisions interact in the presence of demand uncertainty, financial constraints, and a risk of default. The criterion is to maximize the expected present value of dividends net of capital subscriptions. The optimal target inventory level and financial decision variables are nondecreasing functions of the levels of inventory and retained earnings. Some important attributes of an optimal policy remain the same regardless of whether default precipitates Chapter 7 or Chapter 11 bankruptcy. The optimal policy is myopic, and if pertinent cost functions are piecewise linear, it is characterized with simple formulas. We show that the methods of inventory theory are useful in analyzing models of operational and financial coordination. This paper was accepted by Yossi Aviv, operations management.

불확실한 수요와 리드타임을 갖는 공급사슬에서 (s,S) 재고정책에 관한 연구

【As customers' demands for diversified small-quantity products have been increased, there have been great efforts for a firm to respond to customers' demands flexibly and minimize the cost of inventory at the same time. To achieve that goal, in SCM perspective, many firms have tried to control the inventory efficiently. We present an mathematical model to determine the near optimal (s, S) policy of the supply chain, composed of multi suppliers, a warehouse and multi retailers. (s, S) policy is to order the quantity up to target inventory level when inventory level falls below the reorder point. But it is difficult to analyze inventory level because it is varied with stochastic demand of customers. To reflect stochastic demand of customers in our model, we do the analyses in the following order. First, the analysis of inventory in retailers is done at the mathematical model that we present. Then, the analysis of demand pattern in a warehouse is performed as the inventory of a warehouse is much effected by retailers' order. After that, the analysis of inventory in a warehouse is followed. Finally, the integrated mathematical model is presented. It is not easy to get the solution of the mathematical model, because it includes many stochastic factors. Thus, we get the solutions after the stochastic demand is approximated, then they are verified by the simulations.】

On the strategy of supply chain collaboration based on dynamic inventory target level management: A theory of constraint perspective

After the financial tsunami in 2008, how to adjust the target inventory level dynamically and instantly in order to reduce the risk that an enterprise encountered in a rapid demand changing market has become a crucial issue in the field of supply chain management. This paper explores the strategies of supply chain collaboration by utilizing theory of constraint to achieve the goal of adjusting the target inventory level dynamically. Three time-series-data-mining techniques – Sequential Probability Ratio Test (SPRT), CUSUM chart and Auto-regression Test (AR(1)) are used to detect the timing of market demand change. The results are used to adjust the target inventory level. Simulation techniques are used to explore the relative efficiency of the demand-change detection for the three methods. The techniques are also used to explore the effectiveness of various inventory management strategies on inventory performance based on the three demand change detection methods.

시스템 다이내믹스 기법을 활용한 TOC 재보충방식의 적정재고 관리를 위한 시뮬레이션 모델 개발

Ptak과 Smith는 2011년 올리키의 MRP 3판을 통하여 TOC 재보충방식을 기반으로 기존 MRP 방식에 의한 재고관리의 문제점을 오늘날 급변하는 수요중심의 시장 상황에 대응할 수 있도록 발전시킨 수요 대응형 MRP 방법론을 제시하였다. TOC 재보충방식은 목표재고수준을 기준으로 재고 가용성을 유지하여 급격한 변화에 따른 혼란을 흡수하면서 수요량에 연동하여 목표재고수준을 조정하는 수요대응형 MRP의 기본이 되는 재고관리 방식이다. 본 연구에서는 Vensim 시스템 다이내믹스 시뮬레이터를 활용하여 적정 목표재고 수준을 관리하고자 할 때 적정한 목표재고수준 결정을 위한 기준 공식 및 절차를 예시하고, 임의 수요를 발생시켜 TOC 재보충방식의 목표재고수준 모형별 운영 결과 비교 검증을 통하여 모델의 효용성을 비교 검토하였다. 향후에는 기존의 MRP에 의한 재고관리 방식과 수요 대응형 MRP에 의한 재고관리 방식 운영결과의 차이를 실제 기업의 데이터를 활용하여 시뮬레이션 할 수 있도록 모델을 확대 적용할 예정이다. Ptak & Smith published ORLICKY'S Material Requirement Planning Third Edition in 2011 to correspond the rapidly changed market demand by improving the original MRP based on Theory of Constraints(TOC) replenishment inventory management. This study is to develop the simulation model to decide the proper target inventory level for TOC replenishment inventory management using system dynamics Vensim software. This study shows that the proper target replenishment level is how much significant to manage the inventory by the random sample data simulation. This simulation model will be extended to compare the results of the TOC replenishment inventory management planning with the results of the old MRP planning by the enterprise actual inventory data.

Optimal base-stock policy of the assemble-to-order systems

In this work, an ordinal optimization-based evolution algorithm (OOEA) is proposed to solve a problem for a good enough target inventory level of the assemble-to-order (ATO) system. First, the ATO system is formulated as a combinatorial optimization problem with integer variables that possesses a huge solution space. Next, the genetic algorithm is used to select N excellent solutions from the solution space, where the fitness is evaluated with the radial basis function network. Finally, we proceed with the optimal computing budget allocation technique to search for a good enough solution. The proposed OOEA is applied to an ATO system comprising 10 items on 6 products. The solution quality is demonstrated by comparing with those obtained by two competing methods. The good enough target inventory level obtained by the OOEA is promising in the aspects of solution quality and computational efficiency.

A fuzzy random periodic review system with variable lead-time and negative exponential crashing cost

In the present model a fuzzy random periodic review system has been investigated with the annual demand assumed to be a discrete fuzzy random variable with associated imprecise probabilities. Keeping in mind the widespread application of the Just-In-Time manufacturing philosophy and lead-time management being one of its most effective methods of implementation, the lead-time has been assumed to be an added control parameter. Also as it may not be always possible to resolve the lead-time into all its components and estimate their individual crashing costs, the crashing cost has been introduced as a negative exponential function of the lead-time. A methodology has been developed in this regard such that the total inventory cost is minimized and the optimal period of review, the optimal target inventory level and the optimal lead-time are determined in the process. An algorithm has been provided to encapsulate the methodology and it has been illustrated by way of a numerical example.

A dynamic model for the optimization of decoupling point and production planning in a supply chain

In this paper, we propose a dynamic model to simultaneously determine the optimal position of the decoupling point and production–inventory plan in a supply chain such that the total cost of the deviation from the target production rate and the target inventory level is minimized. Using the optimal control theory, we derive the closed form of the optimal solution when the production smoothing policy and the zero-inventory policy are applied. The result indicates that under the production smoothing policy, the overestimation of demand rate during the pre-decoupling stage guarantees the existence of the optimal decoupling point; meanwhile the optimal decoupling point exists under zero-inventory policy when the demand rate is underestimated. Also we perform mathematical analysis on the behavior of the optimal production rate and the inventory level and the effect of problem parameters such as the length of the product life cycle and the forecast error on the performance.

A robust approximation for setting target inventory levels in a constrained production environment

A model is developed to calculate the inventory target level required to provide a specified service level in a single-item single-stage inventory when production is subject to a capacity constraint. The model provides a reliable alternative when the exact Markov chain method is intractable, and where known approximations become unreliable due to high demand variability. The model derives the inventory shortfall distribution by simulating the unconstrained inventory process, from which the parameters of a continuous approximation are estimated. The inventory target level required to provide a desired service level can then be calculated efficiently. This new model requires that only one simulation trial is conducted, from which the optimization is then performed. It is thus an efficient alternative to conventional simulation-based optimization. By simulating the shortfall directly, the model makes no assumptions about the form of the demand distribution. By requiring no user modeling this new method is easily used by inventory managers in practice. The model is robust, with accuracy diminishing only by small degree under increased demand variability or production constraint. The degree of reliability increases as the desired service level increases. Sample size has little effect on the accuracy of forecast service levels.

A finite-horizon, stochastic optimal control policy for a production–inventory system with backlog-dependent lost sales

This article considers a problem of optimal production control of a one-product-type production–inventory system. The demand is a discrete-time stochastic process, while production of a limited capacity is continious in time. The dynamics of the inventory over a finite time horizon are investigated and an optimal feedback strategy for production control under a backlog-dependent lost sales effect is developed. This strategy is called a target level strategy since, contrary to the existing production–inventory control strategies, it determines an optimal target inventory level as a function of time period and the initial stock at that period. Numerical examples illustrate the applicability of the developed solutions.

Fuzzy adaptive agent for supply chain management

Recent technological advances in electronic commerce have fuelled the need for designing effective strategies for supply chain management. These strategies are essential in guiding various activities within a supply chain such as component acquisition, inventory management, customer orders bidding, scheduling for production, and delivery. Among these activities, planning of raw material acquisition for inventory and bidding for customer orders can be extremely complex since such activities are required to deal with external entities such as suppliers and customers. Specifically, in the context of the manufacturing industry, acquiring raw materials for maintaining a flexible yet adequate inventory level is a complex issue due to the potential fluctuation in suppliers' production capacity and market demand. Designing an effective strategy for bidding customer orders is also an intricate problem due to the intense competition in fast changing market environments. In this paper, we describe the strategies of a supply chain management agent which adaptively adjusts its target inventory level and customer order bidding price based on fuzzy logic reasoning. The agent has competed in the 2006 Trading Agent Competition for Supply Chain Management and has achieved good results.

Achieving better coordination through revenue sharing and bargaining in a two-stage supply chain

Coordination is essential for improving supply chain wide performance. In this paper, we focus on a two-stage supply chain consisting of one supplier and one retailer, and in the chain, the retailer’s profit is sensitive to the supplier’s lead time, which is influenced by the supplier’s target inventory level. The coordination between the two parties is achieved through revenue sharing and bargaining in such a way that their respective profit is better than that resulted from a decentralized optimization. The key contract parameter, the revenue-sharing fraction, along with the maximum amount of monetary bargain space, is obtained under explicit and implicit information, respectively. Numerical illustrations of the contracts for various scenarios are also given.

Application of multi-dimensional procurement auction in single-period inventory models

Procurement is one of the major activities in the Manufacturing Resource Planning (MRP II), which is closely coupled with inventory management. Any improvement in this area will have a direct impact on the performance of the entire supply chain. Auction mechanism can be a successful procurement method when there are several potential suppliers available. In this paper, we consider a single-period inventory model when the selection of the supplier is done through a reverse auction with bids consisting of several attributes, namely price, shortage quantity, and lead time. The multi-dimensionality of the bid increases the complexity of the underlying problem creating a need for an approach to determine an approximate optimal target level. This is needed for the initiation of the auction and the procurement process. Monte-Carlo simulation method was used to investigate the performance of the approximation. Simulation results show that the analytical method provides an acceptable approximation for the optimal target inventory level.

Periodic forecast and feedback to maintain target inventory level

In cases when a target inventory level is given and the demand is uncertain, it is difficult to provide an appropriate forecast and control policy that ensures a convergence to the inventory target. In this paper two different forecast formulae combined with two different feedback policies are investigated for a periodic review inventory system. A comparison based on analytical and simulation results is presented showing that the form of feedback is critical in case of large demand uncertainty.

Integrated safety stock management for multi-stage supply chains under production capacity constraints

In the petrochemical, chemical and pharmaceutical industries, supply chains typically consist of multiple stages of production facilities, warehouse/distribution centers, logistical subnetworks and end customers. Supply chain performance in the face of various market and technical uncertainties is usually measured by service level, that is, the expected fraction of demand that the supply chain can satisfy within a predefined allowable delivery time window. Safety stock is introduced into supply chains as an important hedge against uncertainty in order to provide customers with the promised service level. Although a higher safety stock level guarantees a higher service level, it does increase the supply chain operating cost and thus these levels must be suitably optimized. The complexities in safety stock management for multi-stage supply chain with multiple products and production capacity constraints arise from: (1) the nonlinear performance functions that relate the service level, expected inventory with safety stock control variables at each site; (2) the interdependence of the performances of different sites; and (3) finally the margin by which production capacity exceeds the uncertain demand. Given the complexities, the integrated management of safety stocks across the supply chain imposes significant computational challenges. In this research, we propose an approach in which the evaluation of the performance functions and the decision on safety stock related variables are decomposed into two separate computational frameworks. For evaluating the performance functions, off-line computation using a discrete event simulation model is proposed. A linear programming based safety stock management model is developed, in which the safety stock control variables (the target inventory levels used in production planning and scheduling models, base-stock levels for the base-stock policy at the warehouses) and service levels at both plant stage and warehouse stages are used as important decision variables. In the linear programming model, the nonlinear performance functions, interdependence of the performances, and the safety production capacity limits in safety stock management are properly represented. To demonstrate the effectiveness of the proposed safety stock management model, a case study of a realistically scaled polymer supply chain problem is presented. In the case problem, the supply chain is composed of two geographically separated production sites and 3–8 warehouses supplying 10 final products to 30 sales regions.

Intraday behavior of market depth in a competitive dealer market: A note

AbstractThis study is the first to examine the intraday behavior of quoted depth in a competitive dealer market. In sharp contrast to previous research that focuses on specialist markets, quoted depth is lowest at the open of trading, plateaus around the middle of the day, and then dramatically increases in the final hours of trading, peaking at the close. This peak in quoted depth coincides with a narrowing in bid‐ask spreads, and is contrary to intraday patterns documented for specialist markets. The authors conclude that the increase in depth and narrowing of bid‐ask spreads at the close is driven by dealers rebalancing inventories to achieve target inventory levels in a competitive market. © 2008 Wiley Periodicals, Inc. Jrl Fut Mark 28:294–307, 2008

A dynamic joint replenishment policy with auto-correlated demand

We consider a joint replenishment problem where the product demands are auto-correlated but independent of each other. A dynamic periodic review policy is developed, and its parameters are determined by a heuristic which aims at minimizing the total inventory cost, which includes the holding cost, the set up cost and the shortage cost. The heuristic updates the review interval and the target inventory level of every product at each review point based on the current inventory status and the past demand data. A simulation model is developed to compare the performance of this proposed policy with an existing periodic review policy. The results show that the proposed policy has consistently achieved significant saving in all the different experimental scenarios.