Optimal control approach to production systems withinventory-level-dependent demand

Demand occasionally depends positively on the amount of displayed stock, especially in the case of novelty or impulse purchase items. Such inventory-level dependence of demand rate has been incorporated into some continuous review inventory control models, but only ones with demand rate which does not vary with time, no shortages, infinite production rate and per-unit-time cost minimization. We propose an optimal control model which relaxes all these assumptions. That model generalizes a known optimal control model by adding inventory-level dependence of demand to the state dynamics. The framework is one of discounted profit maximization. We apply the maximum principle and obtain three possible singular regimes. The special case of time-invariant demand is solved explicitly. The uncapacitated case is analyzed in detail for a "wave-mode" time dependence of demand, and a numerical example is given     

On the performance of binomial and beta-binomial models of demand forecasting for multiple slow-moving inventory items

The paper deals with the lead-time demand forecasting for inventory management of multiple slow-moving items in the case when the available demand history is very short. Two stochastic models of demand are compared: (i) the first based on the “population-averaged” binomial distribution of requests (the traditional approach); and (ii) the second based on the beta-binomial probability distribution that assumes that the demand probabilities for the inventory items follow the beta distribution, and employs the Bayesian framework to forecast the lead-time demand (longitudinal statistical approach). The conducted simulation study shows that using the latter model leads to the significant decrease of the holding cost and higher inventory system reliability. Besides, as follows from the simulation results, the beta-binomial demand model is especially useful when the demand probabilities are low and have the U-shaped distribution.     

Analyzing a lost-sale stochastic inventory model with Markov-modulated demands: A simulation-based optimization study

A consumer demand that presents auto-correlated components is a class of demand commonly found in competitive markets in which consumers may develop preferences for certain products which influence their willingness to purchase them again. This behavior may be observed in inventory systems whose products are subject to promotion plans in which mechanisms that incentivize the demand are implemented. Inventory systems that ignore these dependency components may severely impair their performance. This paper analyzes a stochastic inventory model where the control review system is periodic, is categorized as a lost-sale case, and is exposed to this class of auto-correlated demand pattern. The demand for products is characterized as a discrete Markov-modulated demand in which product quantities of the same item may relate to one another according to an empirical probability distribution. A simulation-based optimization that combines simulated annealing, pattern search, and ranking and selection (SAPS&RS) methods to approximate near-optimal solutions to this problem is employed. Lower and upper bounds for a range of near-optimal solutions are determined by the pattern search step enhanced by ranking and selection—indifferent zone. Results indicate that inventory performance significantly declines as the autocorrelation increases and is disregarded.     

Detecting value-based scalar dependence

Precise value-based data dependence analysis for scalars is useful for advanced compiler optimizations. The new method presented here for flow and output dependence uses Factored Use and Def chains (FUD chains), our interpretation and extension of Static Single Assignment. It is precise with respect to conditional control flow and dependence vectors. Our method detects dependences which are independent with respect to arbitrary loop nesting, as well as loop-carried dependences. A loop-carried dependence is further classified as being carried from the previous iteration, with distance 1, or from any previous iteration, with direction <. This precision cannot be achieved by traditional analysis, such as dominator information or reaching definitions. To compute anti- and input dependence, we use Factored Redef-Use chains, which are related to FUD chains. We are not aware of any prior work which explicitly deals with scalar data dependence utilizing a sparse graph representation. A preliminary version of this paper appeared in theSeventh Anual Workshop on Languages and Compilers for Parallel Computing, August 1994. Supported in part by NSF Grant CCR-9113885 and a grant from Intel Corporation and the Oregon Advanced Computing Institute.     

The optimal integrated inventory policy with price-and-credit-linked demand under two-level trade credit

In this paper, we proposed a generalized, integrated, supplier–retailer inventory model using a trade credit policy. The trade credit policy adopted here is a two-level trade credit policy in which the supplier offers the retailer a permissible delay period M, and the retailer in turn provides customers a permissible delay period N. Cases where M > N and M ? N are explored thoroughly. In addition, the demand rate is assumed to be a function of both retail price and the customers’ credit period. Consequently, this paper deals with the problem of determining the optimal retail price, economic order quantity, and the number of shipments from the supplier to the retailer in one production run for an integrated inventory system under both two-level trade credit and price-and-credit-linked demand rate. Algorithms are developed in order to determine the joint optimal policies. Numerical examples are presented to illustrate the proposed models, as well as sensitivity analysis of key parameters.     

Pricing and inventory management in a system with multiple competing retailers under (r, Q) policies

We consider a multi-retailer system operated on an infinite horizon, in which each retailer faces stochastic demand following a Poisson process and adopts a continuous-review (r, Q) policy for replenishing inventory to satisfy customer demand. The system involves decisions of pricing and inventory management with the goal of maximizing profit, which equals the sales revenue minus the purchase and inventory costs. Taking Cournot competition into account, models are formulated to optimize simultaneously the expected sales volumes and (r, Q) policies of all retailers. An efficient approach is proposed to calculate the approximate inventory cost. Based on this approach, solution methods for centralized and decentralized scenarios are developed. A great number of numerical computations are provided to evaluate the efficiency of the solution methods, and their performance in the two scenarios. Moreover, system performance under sequential decisions (first pricing and then inventory management) is also investigated.     

A multi-warehouse inventory model for items with time-varying demand and shortages

This paper develops a deterministic replenishment model with multiple warehouses (one is an owned warehouse and others are rented warehouses) possessing limited storage capacity. In this model, the replenishment rate is infinite. The demand rate is a function of time and increases at a decreasing rate. The stocks of rented warehouses are transported to owned warehouse in continuous release pattern. The model allows shortages in owned warehouse and permits part of the backlogged shortages to turn into lost sales—which is assumed to be a function of the currently backlogged amount. The solution procedure for finding the optimal replenishment policy is shown. As a special case of the model, the corresponding models with completely backlogged shortages and without shortages are also presented. The models are illustrated with the help of numerical examples. Sensitivity analysis of parameters is given in graphical form.Scope and purposeIn practical inventory management, there exist many factors like an attracted price discount for bulk purchase, etc. to make retailers buy goods more than the capacity of their owned warehouse. In this case, retailers will need to rent other warehouses or to rebuild a new warehouse. However, from economical point of views, they usually choose to rent other warehouses. If there are multiple warehouses available, an important problem faced by the retailers is which warehouses to be selected to hold items replenished, when to replenish as well as what size to replenish. For such a problem, the existing two-warehouse models, based on an unrealistic assumption that the rented warehouse has unlimited storage capacity, presented some procedures for determining the optimal replenishment policy. This paper extends the existing two-warehouse models in three directions. Firstly, the traditional two-warehouse models assumed the storage capacity of the rented warehouse unlimited. The present paper relaxes this impractical assumption and considers the situation with multiple rented warehouses having a limited capacity. Secondly, the traditional two-warehouse models considered a constant demand rate or a linearly increasing demand rate. In this model, the demand rate varies over time and increases at a decreasing rate, which implies an increasing market going to saturation. Thirdly, we extend the two-warehouse models to the case with partially backlogged shortages. The purpose of this paper is to build a multi-warehouse replenishment model to help decision-makers solve the problem of which warehouses to be chosen to store items replenished and how to replenish.     

供电企业购电卡系统的研究与开发

本文针对目前供电企业电费管理现状,特提出电费购电卡收费方式的构想,与其他收费方式一起实现电费缴费方式的多样化。并对购电卡技术进行研究,在此基础上将系统划分为8个模块。最后通过对现有开发工具以及开发语言的分析比较,前端开发工具采用Visual Studio 2003及Java语言,后台数据库采用Oracle,开发了系统管理、购电卡领用存管理、收费票据领用存管理、购电卡管理、购电卡帐务管理、基本查询、统计汇总和短信管理模块。     

Two inventory systems with trapezoidal-type demand rate and time-dependent deterioration and backlogging

The demand rate for seasonable/fashionable products, in general, fluctuates through their life cycle, initially increases during the growth phase, then remains practically constant in the maturity phase, and finally decreases in the decline phase. Consequently, their demand rate can be reasonably depicted by a trapezoidal-type pattern, which includes constant, increasing, decreasing and ramp-type demand patterns as special cases. Recently, inventory models for deteriorating items with trapezoidal-type demand have been developed to minimize the total cost over the planning horizon (see Cheng & Wang, 2009; Skouri & Konstantaras, 2009; Cheng et al., 2011; Lin et al., 2014). However, in these models the purchasing cost is excluded from the total cost. As a result, this implies an underestimation of the lost sales cost. In the present paper, previous studies regarding inventory models with trapezoidal-type demand rate are extended and completed by (1) discussing two inventory systems starting with and without shortages, (2) including the purchasing cost into the total cost, (3) extending the deterioration rate to any time-varying rate, (4) taking into consideration the time value of money (5) maximizing the net present value of total profit. Therefore, many previous inventory models become special cases of the present model.     

Particle Swarm Optimization and Pure Adaptive Search in Finish Goods’ Inventory Management

Abstract

Inventory management deals with a tradeoff between the benefits of keeping stocks of goods that allows fulfillment of the customer’s demand, and the cost of carrying inventory. Inventory control techniques are very important components and the most organizations can substantially reduce their costs associated with the flow of materials. This paper presents new inventory management model based on particle swarm optimization and pure adaptive search global optimization algorithm in production-inventory system. The proposed model is focusing on planned level of demand for finished goods, production and raw materials cost, production capacity as the norm, change of the production cost and inventory capital cost, all of which are typical factors in automobile manufacture industry. The model determines different factors such as the minimizing inventory quantity, minimizing inventory value, and minimizing production cost based on demand for production items. The model is tested with original real-world dataset obtained from the automotive company Lear from US and its factory in Novi Sad, Serbia.     

Optimal policies for a finite-horizon batching inventory model

This paper is concerned with finding an optimal inventory policy for the integrated replenishment-production batching model of Omar and Smith (2002). Here, a company produces a single finished product which requires a single raw material and the objective is to minimise the total inventory costs over a finite planning horizon. Earlier work in the literature considered models with linear demand rate function of the finished product. This work proposes a general methodology for finding an optimal inventory policy for general demand rate functions. The proposed methodology is adapted from the recent work of Benkherouf and Gilding (2009).     

Joint optimisation of maintenance and production policies with subcontracting and product returns

This paper, an extension of our previous research, deals with the problem of jointly optimizing maintenance, production and inventory costs considering subcontracting and product returns. The manufacturing system, which fails randomly, has to satisfy a random product demand during a finite planning horizon under a required service level. The portion of products returned by the customers that are still in saleable condition are collected in the principle store from which customer demand is filled, while the portion that are non-conformal are collected in a second store and then remanufactured by a subcontractor. This study is validated by a real industrial case presented in this paper.     

Inventory systems for deteriorating items with shortages and a linear trend in demand-taking account of time value

This paper derives an inventory model for deteriorating items with the demand of linear trend and shortages during the finite planning horizon considering the time value of money. A simple solution algorithm using a line search is presented to determine the optimal interval which has positive inventories. Numerical examples are given to explain the solution algorithm. Sensitivity analysis is performed to study the effect of changes in the system parameters.Scope and purpose The traditional inventory model considers the ideal case in which depletion of inventory is caused by a constant demand rate. However, in real-life situations there is inventory loss due to deterioration. In a realistic product life cycle, demand is increasing with time and eventually reaching zero. Most of the classical inventory models did not take into account the effects of inflation and time value of money. But in the past, the economic situation of most of the countries has changed to such an extent due to large scale inflation and consequent sharp decline in the purchasing power of money. So, it has not been possible to ignore the effects of inflation and time value of money any further. The purpose of this article is to present a solution procedure for the inventory problem of deteriorating items with shortages and a linear trend in demand taking account of time value.     

Affinely adjustable robust optimization for a multi-period inventory problem with capital constraints and demand uncertainties

This study focuses on a multi-period inventory problem with capital constraints and demand uncertainties. The multi-period inventory problem is formulated as an optimization model with a joint chance constraint (JCC) requiring the purchase cost for each period not to exceed the available capital with a probability guarantee. To hedge against demand uncertainties, an affinely adjustable robust optimization approach is used to convert the developed model into a robust counterpart. By approximating the JCC under a budgeted uncertainty set to which the demands belong, the robust multi-period inventory model with the JCC is transformed into a linear programming model, which can be solved efficiently. Numerical studies are reported to illustrate the robustness, practicality, and effectiveness of the proposed model and the solution approach. The numerical results show that the proposed model and solution approach outperform the sample average approximation approach. Numerical studies are used further to analyze the impact of the budget coefficient and the upper bound parameter on the inventory costs and the realized capital constraint satisfaction rate. The proposed model and solution approach are further extended to the multi-product case.     

Stochastic model of production and inventory control using dynamic bayesian network

Bayesian Network is a stochastic model, which shows the qualitative dependence between two or more random variables by the graph structure, and indicates the quantitative relations between individual variables by the conditional probability. This paper deals with the production and inventory control using the dynamic Bayesian network. The probabilistic values of the amount of delivered goods and the production quantities are changed in the real environment, and then the total stock is also changed randomly. The probabilistic distribution of the total stock is calculated through the propagation of the probability on the Bayesian network. Moreover, an adjusting rule of the production quantities to maintain the probability of the lower bound and the upper bound of the total stock to certain values is shown. This work was presented in part at the 13th International Symposium on Artificial Life and Robotics, Oita, Japan, January 31–February 2, 2008     

按单装配系统中组件生产和库存分配控制策略研究

针对由两种组件、三类顾客需求组成的按单装配系统, 本文研究了其中的组件生产控制与库存分配问题. 在各类顾客需 求是泊松到达过程, 各种组件加工时间服从指数分布的假设下, 我们运用马尔科夫决策理论建立了无限期折扣总成本模型, 根据Lippman转换得到了相应归一化后的离散最优方程, 在此基础之上分析了生产和库存分配联合最优控制策略的结构性质. 本文证明了最优策略是依赖于系统状态的动态策略. 组件的最优生产策略是动态基库存策略, 其中基库存水平是关于系统中其他组件库存水平的非减函数. 而最优的分配策略是动态的阈值策略, 对于只需一种组件构成的顾客需求, 组件的分配阈值是系统中另一组件库存水平的增函数; 而对于同时需要两种组件组成的顾客需求, 其各组件的分配阈值是另一组件库存水平的减函数. 最后通过数值试验给出了各个参数对联合最优控制策略的影响, 并得到了相应的管理启示.     

基于改进神经网络的智能库存管理应用研究

随着电子技术的进步、世界经济一体化、全球化局面的出现,企业对知识和信息的有效管理已日益紧迫,可以说企业管理正进入新的理念。该文将改进的粒子群算法优化BP神经网络应用于库存管理系统中,建立库存预测模型为库存管理智能化提供辅助决策。从而使企业生产库存管理可以有效的对库存量进行控制,使库存量维持在一个比较合理的水平,将给企业带来巨大利益,因此对该方法的研究具有非常重要的现实意义。     

Construct validation of the Use, Abuse and Dependence on the Internet inventory

This study aims to validate the structure of the Use, Abuse and Dependence on the Internet (UADI) inventory on a sample of 1056 high school (n = 820) and university (n = 236) students. In particular, we performed exploratory and confirmatory factor analyses on sub-samples (cross-validation), tested the construct convergent validity, and tested correlations of UADI dimensions with HEXACO personality inventory (HEXACO-PI, where HEXACO stands for the six assessed dimensions: Honesty-Humility, Emotionality, eXtraversion, Agreeableness, Conscientiousness and Openness to experience) and external criteria (daytime internet use, etc.). Five dimensions (Compensatory Escape, Dissociation, Real Life Impact, Experience Making and Addiction) were best captured by a second-order factor structure with a factor reflecting Real Life Impact and Dependence saturated by the other four dimensions. This latter factor converged with other traditional measures of internet dependence. The results are discussed in light of the relationships with validity criteria.     

A newsvendor pricing game

This paper considers a horizontal market of multiple firms that face stochastic price-dependent demand. The firms make joint pricing/inventory decisions and use price to compete for market demand. With fairly general demand models that are price-dependent, stochastic, and substitutable among firms, we prove the existence and uniqueness of the pure-strategy Nash equilibrium. The market at the equilibrium exhibits a bias toward under-pricing caused by competition; specifically, raising prices at any equilibrium of the game increases the total system profit, and at any joint-optimal set of pricing levels each self-interested firm has an incentive to lower its price. This result closely parallels that obtained in the inventory competition games in which prices are fixed and the bias is toward overstocking.     

Exploring the economic consequences of letting a supplier hold reserve storage

We consider a single-item, periodic review inventory control problem with discrete non-stationary stochastic demand. The time horizon is finite and all shortages at the downstream level are backordered. There are two modes of supply: a normal supplier and a reserve storage supply. The reserve storage is capacitated and the downstream buyer can only order the entire inventory in the reserve storage or nothing. If the reserve storage is empty, it takes a fixed time interval before it is replenished again. Provided that the reserve storage is fully replenished it can be used at any time period, whereas orders to the normal supplier can only be issued at specific time periods. The lead time from the reserve storage is shorter than from the normal supplier, but using the reserve storage is more expensive than using the normal supplier. We use stochastic dynamic programming to specify an exact model of the problem. We also develop an approximate model which is computationally faster than the first model. The models are then used to analyze numerically the sensitivity with respect to key parameters like the reserve storage size and unit purchase cost. This paper is motivated by a problem presented during contacts with a leading Danish provider of communications solutions.