Comparison of a new bootstrapping method with parametric approaches for safety stock determination in service parts inventory systems

In this paper, we address the problem of forecasting and managing the inventory of service parts where the demand patterns are highly intermittent. Currently, there are two classes of methods for determining the safety stock for the intermittent item: the parametric and bootstrapping approaches. Viswanathan and Zhou (2008) developed an improved bootstrapping based method and showed through computational experiments that this is superior to the method by Willemain et al. (2004). In this paper, we compare this new bootstrapping method with the parametric methods of Babai and Syntetos (2007). Our computational results show that the bootstrapping method performs better with randomly generated data sets, where there is a large amount of (simulated) historical data to generate the distribution. On the other hand, with real industry data sets, the parametric method seems to perform better than the bootstrapping method.     

Effects of correlation on intermittent demand forecasting and stock control

This study investigates the effects of three different types of correlation on forecasting and stock control of intermittent demand items. Applying appropriate forecasting and stock control methods to theoretically generated compound Poisson demand data we show that correlation in intermittent demand does play a role in forecast quality and stock control performance. Negative autocorrelation levels lead to higher service levels than positive values, while cost does not significantly change. Our results also show that high intermittency levels intensify these changes in service level. We also show that cross-correlation produces results in the opposite direction of autocorrelation in size or intervals; that is, positive (negative) cross-correlation leads to higher (lower) service levels.     

Inventory of differential items selling from two shops under a single management with periodically increasing demand over a finite time-horizon

Inventories of differential items including the defective ones purchased/produced in a lot and sold from two shops (primary and secondary shops) under a single management are considered here over a finite time-horizon. A primary shop receives the differential units in a lot but sells only the non-defective ones whose demand periodically increases with time and decreases during the shortage period in such a way that it comes back to the initial value at the beginning of the next cycle. Hence in this shop, shortages are allowed and fully backlogged. Moreover, at the beginning of the next cycle, the retailer purchases purely non-defective units at a higher price to meet up the shortage amount along with the usual lot of differential units for regular sale. The defective units identified at the time of selling at the primary shop are continuously transferred to the adjacent secondary shop from which the defective ones are sold at a reduced price after some rework. Normally, the price of a defective item is fixed depending upon the quantum of its defect and people go for these items if they are cheap. Hence, demand for these units is dependent on the selling price, which is again inversely proportional to the rate of defectiveness. There may be five scenarios for dealing with defective units depending upon the coincidence of the time periods at two shops. For all scenarios, problems have been mathematically formulated and solved by the use of both parametric study and a gradient-based non-linear optimisation method. The models are illustrated with the help of numerical examples.     

Inventory control in a two-echelon dual-channel supply chain with setup of production and delivery

This paper considers a two-echelon dual-channel supply chain model with setup of production and delivery and develops a new inventory control policy for the supply chain. Previously, a two-echelon supply chain model without setup of production and delivery is considered and a one-for-one inventory control policy is applied to the supply chain. In the inventory control policy, production is stopped when the warehouse inventory reaches the upper limit and is started again immediately after the inventory drops below the limit. Moreover, delivery to the retailer is stopped when the store inventory reaches the upper limit and is started again immediately after the inventory drops below the limit. The total cost that consists of inventory holding costs and lost sales cost is considered, and setup costs are not considered in the total cost. Once setup costs are introduced, the one-for-one inventory control policy is no longer appropriate. Then, this paper develops a new control policy for the two-echelon dual-channel supply chain with setup of production and delivery. As performance measure, the total cost that consists of inventory holding costs, lost sales cost, and production and delivery setup costs is considered, and the total cost calculated on the basis of Markov analysis demonstrates the effectiveness of the proposed control policy.     

Inventory control in a two-level supply chain with risk pooling effect

We consider an inventory control problem in a supply chain consisting of a single supplier, with a central distribution center (CDC) and multiple regional warehouses, and multiple retailers. We focus on the problem of selecting warehouses to be used among a set of candidate warehouses, assigning each retailer to one of the selected warehouses and determining replenishment plans for the warehouses and the retailers. For the problem with the objective of minimizing the sum of warehouse operation costs, inventory holding costs at the warehouses and the retailers, and transportation costs from the CDC to warehouses as well as from warehouses to retailers, we present a non-linear mixed integer programming model and develop a heuristic algorithm based on Lagrangian relaxation and subgradient optimization methods. A series of computational experiments on randomly generated test problems shows that the heuristic algorithm gives relatively good solutions in a reasonable computation time.     

Inventory model for an inventory system with time-varying demand rate

The standard inventory problems of the multi-period have been modeled under different situations. Specifically we have considered the demand subjects of a continuous distribution and a discrete distribution, and whether the demand of each period is unchanged or not. A method to get an economic order quantity in inventory systems with discrete and unchanged demand was presented in a previous paper, and this method has been generalized to an inventory model with varying continuous demand. However, it was not achieved due to there being many classified cases in the general situations. In this article the above method is discussed in the case discrete demand to determine whether it increases or decreases from period to period. A theoretical method is presented by using previous results and some examples are given which suggest how the concept can handle on inventory system. In order to make the decision, an algorithm is also presented under some conditions, and examples are shown by using the computer software program, Mathematica, which helps to explain the findings. In general cases, we view the optimal policy in the inventory problems in only a few periods.     

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.     

Product selection for newsboy-type products with normal demands and unequal costs

In this paper, we consider two newsboy-type products with unequal prices and costs. Both demands are independent and follow normal distributions with unknown parameters μ and σ. We study the product selection problem which deals with comparing two products and selecting the one that has a significantly higher profitability, in which the profitability is defined to the probability of achieving a target profit under the optimal ordering policy. The statistical hypothesis testing methodology is performed to tackle this selection problem. Critical value of the test is calculated to determine the selection decision. Sample size required for a designated power and confidence level is also investigated. An application example on comparing English-teaching magazines is presented to illustrate the practicality of our approach.     

Inventory investment and sectoral characteristics in some OECD countries

This paper discusses the effects of sectoral structure on the long run macroeconomic inventory behaviour of national economies. Data on 15 OECD countries are included in the analysis, which is based on correlation and cluster analysis methodologies. The study is part of a long-term research project exploring factors influencing the inventory behaviour of national economies.First, we introduce some basic characteristics of macroeconomic inventory formation in the 15 OECD countries. We argue that our previous results on the existence of specific characteristic features of macroeconomic inventory investment are justified, hence it makes sense to study the factors influencing these features. We then examine the contribution of various sectors to the production of in the countries involved and the relationship between sectoral structure and inventory intensity (annual inventory change/Gross Value Added). We find that the high share of agriculture and manufacturing increases inventory intensity, that the increasing share of services has a negative effect and that the role of construction and trade is not obvious. The relatively low stability of the statistical results warns us to be cautious with our judgements. Further, case-by-case analysis would be required to obtain more solid results.     

An inventory control model with consideration of remanufacturing and product life cycle

This paper investigates inventory control policies in a manufacturing/remanufacturing system during the product life cycle, which consists of four phases: introduction, growth, maturity, and decline. Both demand rate and return rate of products are random variables with normal distribution; the mean of the distribution varies according to the time in the product life cycle. Closed-form formulas of optimal production lot size, reorder point, and safety stock in each phase of the product life cycle are derived. A numerical example is presented with sensitivity analysis. The result shows that different inventory control policies should be adopted in different phases of the product life cycle. It is also found that the optimal production lot size and reorder point are not sensitive to the phase length and the demand changing rate.     

Derivation of confidence intervals of service measures in a base-stock inventory control system with low-frequent demand

We explore a base-stock system with backlogging where the demand process is a compound renewal process and the compound element is a delayed geometric distribution. For this setting it holds that the long-run average service measures order fill rate (OFR) and volume fill rate (VFR) are equal in values. However, though equal ex ante one will ex post observe differences as actual sample paths are different. By including a low-frequency assumption in the model, we are able to derive mathematical expressions of the confidence intervals one will get if OFR and VFR are estimated in a simulation using the regenerative method. Through numerical examples we show that of the two service measures it is OFR that in general can be estimated most accurately. However, simulation results show that the opposite conclusion holds if we instead consider finite-horizon service measures, namely per-cycle variants of OFR and VFR.     

The uniform distribution as a first practical approach to new product inventory management

It is common sense that the premises usually considered in inventory models have little applicability to new product inventory management. This paper develops a first practical approach to deal with this issue: the solution to the (Q, r) inventory model for uniform demand forecasts and lead-times. Based on the fact that the uniform distribution is defined by two parameters that are easy to estimate—maximum and minimum—this paper shows that such a premise may comprise a helpful and accurate decision support tool for managers until they begin to learn about the distribution characteristics of the demand during the lead-time.     

An inventory and order admission control policy for production systems with two customer classes

In this paper we examine a Markovian single-stage system producing a single item to satisfy demand of two different customer classes. A simple threshold type heuristic policy is proposed for the joint control of inventories and backorders. Explicit forms of the steady-state probabilities under this policy are derived and used to assess the average profit rate of the system and determine the optimal control parameters. Certain properties of the average profit rate are established and used to develop computationally efficient algorithms for finding the optimal control parameter values. Numerical results show that the proposed policy is a very good approximation of the optimal policy and outperforms other commonly used policies.     

Private production and income distribution in a Chinese commune

This article is concerned with the extent of inequality between production teams and between households in one commune in the People's Republic of China, and particularly with the effect of income from private production on the distribution of total household income. The authors briefly describe the history and role of private production within the commune system, and report the findings of household a survey conducted to discover the flows of food commodities from both private and collective sources. The authors conclude that private production is not a source of inequality in this commune.     

A vendor managed inventory supply chain with deteriorating raw materials and products

Fast deteriorating raw materials such as raw milk, fruit and vegetables are commonly used to produce slowly deteriorating finished products such as milk powders, cheeses, and pastas. This paper studies a Vendor Managed Inventory (VMI) type supply chain where the manufacturing vendor decides how to manage the system-wide inventories of its fast deteriorating raw material and its slowly deteriorating product. The decision variables are a common replenishment cycle of the product and the replenishment frequency of the raw material. We assume the deteriorating rates are known constants and every retailer's demand is deterministic. We develop an integrated model to calculate the total inventory and deterioration cost for such a system. We prove the convexity of the cost functions, and based on this a golden search algorithm is developed to find the optimal solution of the model. Our numerical results show that the deteriorating rate of the product may increase the total cost by more than 40% compared to the zero-deteriorating rate, while the deteriorating raw material has less impact on the total cost (commonly less than 5% in our numerical examples). This indicates that more attention should be paid to the product than the raw material. Further, an increase in the number of retailers can make the replenishment frequency of the raw material increase significantly but the common replenishment cycle of the product decreases a little. This indicates that adding a new retailer would not be felt strongly by the other retailers but would be felt by the supplier of the raw material.     

Joint pricing and inventory control for non-instantaneous deteriorating items with partial backlogging and time and price dependent demand

In this paper, a joint pricing and inventory control for non-instantaneous deteriorating items is developed. We adopt a price and time dependent demand function. Shortages is allowed and partially backlogged. The major objective is to determine the optimal selling price, the optimal replenishment schedule and the optimal order quantity simultaneously such that, the total profit is maximized. We first show that for any given selling price, optimal replenishment schedule exists and unique. Then, we show that the total profit is a concave function of price. Next, we present a simple algorithm to find the optimal solution. Finally, we solve a numerical example to illustrate the solution procedure and the algorithm.     

The deterministic EOQ and EPQ with partial backordering at a rate that is linearly dependent on the time to delivery

Our original models for the EOQ and EPQ with partial backordering assumed that the backordering rate, β, is a constant. In this paper we extend those models to allow β to increase linearly as the time until delivery decreases. We show how those previous models can be adapted to find the optimal decision variable values for this new assumption and develop, for each model type, a condition that the initial value of β must meet for partial backordering to be optimal.     

Optimization of a vendor managed inventory supply chain with guaranteed stability and robustness

In this work we address the steady state optimization of a supply chain model that belongs to the class of vendor managed inventory, automatic pipeline, inventory and order based production control systems (VMI-APIOBPCS). The supply chain is optimized with the so-called normal vector method, which has specifically been developed for the economic optimization of uncertain dynamical systems with constraints on dynamics. We demonstrate that the normal vector method provides robust optimal points of operation for a number of scenarios. Since the method strictly distinguishes economic optimality, which is treated as the optimization objective, from dynamical requirements, which are incorporate by appropriate constraints, it provides a measure for the cost of stability and robustness as a desired side-effect.     

随机需求下横向并购供应链网络整合优化策略研究

本文从系统优化视角,针对增设集散中心的横向并购供应链网络整合策略,利用变分不等式建立了随机需求下的整合优化模型。以市场链为主线,以供应链网络均衡理论为基 础,构建了以横向并购供应链网络活动总成本最小为目标的数学模型,通过转换成变分不等式采用改进的欧拉算法进行模型求解。通过数值算例进一步说明了模型的适用性和灵活性,得出了增设集散中心的并购整合策略能够降低供应链网络的平均运营成本的结论,通过对比不同市场紧密程度下产生的供应链网络平均成本协同效应,发现随着市场紧密程度的增加其协同效应更明显,为横向并购供应链网络整合优化提供理论依据与方法。     

Unimodality of price-setting newsvendor's objective function with multiplicative demand and its applications

We present a general solution framework for the price-setting newsvendor problem with a multiplicative stochastic demand. Under mild assumptions, such as increasing price elasticity on the mean demand function and increasing generalized failure rate on the distribution of the random factor, we first prove that both the profit function with respect to price and its derived function with respect to order quantity are quasi-concave. Three applications are then studied under our solution framework: (1) We consider a wholesale price only contract by which a manufacturer sets a wholesale price and a newsvendor determines an order quantity and the retail price, and show that the manufacturer's profit function is unimodal with respect to retailing price or stocking factor under certain conditions. (2) We consider a newsvendor problem in which the demand depends on both the retail price and the level of sales effort, and the cost exerting the sales effort is proportional to the order quantity; we prove that there exists a unique pair of price and sales-effort levels that maximize the total profit. This result is established under a set of mild assumptions on the demand and cost functions. (3) We identify a property in the single-period profit function that satisfies Condition 1 of Huh and Janakiraman (2008), which in turn guarantees the optimality of (s, S) policy for an infinite stationary dynamic inventory-price control system with lost sales and fixed order costs. Finally, the unimodality of the newsvendor problem with a general stochastic and price-sensitive demand is studied.