An optimal replenishment model for inventory items with normally distributed deterioration

This paper deals with the inventory replenishment problem for deteriorating items with normally distributed shelf life, continuous time-varying demand, and shortages under the inflationary and time discounting environment. The reasons of choosing normal are twofold: it is one of the most important probability phenomena in the real world due to the classical central limit theorem, and it is also one of the most commonly used lifetime distributions in reliability contexts. The problem is formulated as a dynamic programming model and solved by numerical search techniques. The solutions of the model determine the optimal replenishment schedule over a finite planning horizon so that the present worth of the future costs associated with the system is minimized. In the extensive experiments, we validate the model, demonstrate the optimal replenishment schedule and lot-size, and carry out a comparative study to ascertain its contribution. In addition, sensitivity analysis was provided to help identify the most crucial factors that affect system performance. The experimental result shows that the deteriorating problem solved by an appropriate model (i.e. the proposed normal model) can save the total cost up to 2% approximately. It also identifies that the magnitudes of purchase cost per unit and demand rate are the most significant parameters that affect the replenishment decisions and cost.     

A quick response production strategy to market demand

The reason for considering the quick response production strategy to market demand is due to the rapid technology change, which results in decreasing market price and obsolescence. This study considers a production strategy of locating final production line in response to the changes in market demand and the continuous deterioration in stock. The demand rate is assumed to decrease exponentially with time while the price is assumed to decrease linearly with time. The purpose of this study is to derive the most economical site of final-production line that assembles products with short life cycle. The model considered in this research takes into account the sales revenue, the deteriorating cost, the carrying cost, the variable cost and the fixed cost of production. Although there is a higher labour and material cost when the production site is located near market point, the total profit increases due to quicker responsive time, smaller import tax, lower inventory and lesser deteriorating cost.     

An integrated supplier-buyer model for improving supply chain coordination

This study develops a decision support model that can be used by a supplier in making production and price decisions at contract renewal times in a supply chain environment. The supplier first makes aggregate production decisions with a special attempt to estimate buyer commitments, and then determines the price of the item so as to satisfy his own profit and buyer cost reduction expectations simultaneously. Mathematical programming models are designed to achieve these in accordance with the contract terms. The main emphasis is placed upon the conceptual and negotiation aspects of the models, and some solution procedures are cited from previous studies. Then the approach is implemented in the biggest electric motor manufacturer in Turkey which has a large number of buyers in household appliances sector, and it is shown to be a useful tool for developing fair partnership.     

A new EPQ model: integrating lower pricing,rework and reject situations

The economic production quantity (EPQ) is a well-known and commonly used inventory control technique. It has been used for well over 50 years to optimize lot sizes in transportation/production. The standard results are easy to apply but are based on a number of assumptions. A common assumption in the EPQ model is that all units produced are of perfect quality, this will underestimate the actual required quantity. Many researchers have studied the effects after relaxing this assumption on the EPQ model. The previous studies had considered that imperfect quality and defective items are either to be reworked instantaneously and kept in stock or rejected at a cost. The objective of this paper is to provide a framework to integrate lower pricing, rework and reject situations into a single EPQ model. A 100% inspection is performed in order to identify the amount of good quality items, imperfect quality items and defective items in each lot. This model assumes that items of imperfect quality, not necessarily defective, could be used in another production situation or sold to a particular purchaser at a lower price. The electronic and clothing industries give good examples for such situations. A mathematical model is developed and a numerical example is presented to illustrate the solution procedures. It is found that the time factor of when to sell the imperfect items is critical, as this decision will affect the inventory cost and the batch quantities.     

The effects of the warranty cost on the imperfect EMQ model with general discrete shift distribution

In this paper, we investigate the effect of the warranty cost on optimization of the economic manufacturing quality (EMQ). This is done for a deteriorating process where the production process shifts from the in-control state to the out-of-control state following a general discrete probability distribution. Once the production process goes out of control, the production process produces some defective items. The defective item cost includes reworking and warranty costs. Thus, in order to economically operate a production-inventory system with products sold under warranty, the tradeoffs among the production setup, inventory, and defective item cost, including the reworked cost before sale and the warranty cost after sale, needed to be analysed. This objective in this paper is to determine the production lot size while minimizing the total cost per unit of time per unit of time. Various special cases are presented. Two of them are extensions of results obtained previously in the literature. Finally, a numerical example is given which uses a discrete Weibull probability distribution. Sensitivity analysis of the model with respect to cost and time parameters is also performed.     

Shipping Fees or Shipping Free? A Tale of Two Price Partitioning Strategies in Online Retailing

In this article, we study the price partitioning decisions of online retailers regarding shipping and handling (S&H) fees. Specifically, we analyze two partitioning formats used by retailers in this context. In the first scenario, retailers present customers with a price that is partitioned into a product price and a separate S&H surcharge (the PS strategy); in the second, customers are offered free shipping through a non‐partitioned format where the product price already includes the shipping cost (the ZS strategy). We first develop a stylized game‐theoretic model that captures the competitive dynamics between (and within) these two formats. Analysis of the model provides insights into how both firm and product level characteristics drive a retailer's strategic choice regarding which partitioning format to adopt and, hence, determines the equilibrium market structure in terms of proportion of ZS and PS retailers. Subsequently, we conduct empirical analyses, based on product and S&H prices data for two different product categories (digital cameras and printers) collected from online retailers, to validate all the results of our theoretical model. We establish that PS retailers charge lower product prices than ZS ones, but the total price (product + S&H) charged is higher for the first group. The S&H charge for PS retailers can be significant—it is, on average, 5.4% (printers) and 3.0% (digital cameras) for our two product categories. Furthermore, retailers which are popular and/or face risky cost environment are more likely to opt for the ZS strategy, while retailers whose portfolio mostly includes large or heavy products with high cost (S&H)‐to‐price ratios usually choose the PS strategy. Lastly, our empirical study also illustrates that the price adjustment behavior of retailers is affected by their shipping‐fee policies—for example, ZS retailers change their product prices almost 1.5 times more frequently than PS ones.     

A simulated annealing algorithm for designing cellular manufacturing systems with productivity consideration

In this paper, we propose a productivity model for solving the machine-part grouping problem in cellular manufacturing (CM) systems. First, a non-linear 0-1 integer programming model is developed to identify machine groups and part families simultaneously. This model aims to maximize the system productivity defined as the ratio of total output to the total material handling cost. Second, an efficient simulated annealing (SA) algorithm is developed to solve large-scale problems. This algorithm provides several advantages over the existing algorithms. It forms part families and machine cells simultaneously. It also considers production volume, sales price, and maximum number of machines in each cell and total material handling cost. The proposed SA also has the ability to determine the optimum number of manufacturing cells. The performance of the developed models is tested on eight problems of different size and complexity selected from the literature. The results show the superiority of the SA algorithm over the mathematical programming model in both productivity and computational time.     

Coordinating replenishments in a supply chain with quality control considerations

We study the impact of coordinated replenishment, a popular supply chain initiative, on a quality control system. We use the (Q, S) policy to manage a two-item inventory control system. If the items are jointly replenished, the number ordered for each item varies from lot to lot. As the number varies, the sampling plan will also be changed. Companies have to determine sampling plans to minimize quality cost when the order is mixed with several items and the number of each item varies from order to order. Management's primary concern is to determine the optimal sampling sizes and acceptance numbers for all items in an order.     

Optimal Policy for a Reseller When the Supplier Offers a Temporary Reduction in Price*

A common practice in product distribution is the case in which the supplier offers a temporary reduction in price. It is suggested in the literature that in such situations, the reseller may engage in forward buying (i.e., purchasing additional stock at the reduced price offered by the supplier for later sale at the regular selling price). In this paper, a model is formulated of the reseller's response when the supplier offers a temporary reduction in price. It is assumed that the market demand for the product is elastic with respect to the selling price the reseller sets. A procedure for determining the optimal response of the reseller is developed. The model presented in this paper can easily be adapted to the case in which the reseller faces a permanent increase in the price charged by the supplier.     

Menu Costs,Multiproduct Firms,and Aggregate Fluctuations

Golosov and Lucas recently argued that a menu‐cost model, when made consistent with salient features of the microdata, predicts approximate monetary neutrality. I argue here that their model misses, in fact, two important features of the data. First, the distribution of the size of price changes in the data is very dispersed. Second, in the data many price changes are temporary. I study an extension of the simple menu‐cost model to a multiproduct setting in which firms face economies of scope in adjusting posted and regular prices. The model, because of its ability to replicate this additional set of microeconomic facts, predicts real effects of monetary policy shocks that are much greater than those in Golosov and Lucas and nearly as large as those in the Calvo model. Although episodes of sales account for roughly 40% of all goods sold in retail stores, the model predicts that these episodes do not contribute much to the flexibility of the aggregate price level.     

Price Setting With Menu Cost for Multiproduct Firms

We model the decisions of a multiproduct firm that faces a fixed “menu” cost: once it is paid, the firm can adjust the price of all its products. We characterize analytically the steady state firm's decisions in terms of the structural parameters: the variability of the flexible prices, the curvature of the profit function, the size of the menu cost, and the number of products sold. We provide expressions for the steady state frequency of adjustment, the hazard rate of price adjustments, and the size distribution of price changes, all in terms of the structural parameters. We study analytically the impulse response of aggregate prices and output to a monetary shock. The size of the output response and its duration both increase with the number of products; they more than double as the number of products goes from 1 to 10, quickly converging to the response of Taylor's staggered price model.     

The effects of component commonality in an infinite horizon inventory model

This paper studies the effects of component commonality in the context of an infinite horizon inventory model. Three models are proposed that are characterized by different degrees of component commonality. Assuming the three models all follow the same inventory policy, exact service level measures are derived and incorporated into cost optimization problems. With the infinite horizon assumption, potential setup cost reductions can be evaluated due to the inclusion of common components. The results indicate that, as expected, commonality incurs significant cost savings; what is new and unique is that setup cost may increase or decrease when commonality is present. In addition, when the behaviour of the optimal solutions is examined, it is found that some of the well-known properties suggested by the existing one-period models do not hold for this infinite horizon model.     

带学习效应的双渠道供应链库存策略研究

针对具有学习行为的双渠道供应链问题,本文研究了两种分销渠道并存下的最优库存策略。有限计划期内,分销商通过传统销售和在线销售来满足下游顾客的需求。两种分销渠道下的销售单价为时变不减线性函数,当系统中各周期的生产订购固定成本以一定的概率具有学习效应行为时,分别建立了非变质产品生产存贮问题的混合整数约束优化模型以及易变质产品存贮问题的无约束混合整数优化模型,所建立模型的目标为极大化分销商总利润函数。对于这两类模型,通过分析其最优解的性质,利用将生产订购次数松弛为连续变量的技巧证明了最优解存在的唯一性。给出了最优策略的求解方法并比较了两类模型最优利润函数值的大小。最后通过数值算例对上述模型进行了验证,数值结果表明当供应链系统中存在学习效应行为时,该系统能够获得更多的利润。     

The resource constrained single-item inventory problem with demand-dependent unit cost

In this paper, we present an economic order quantity (EOQ) with both demand-dependent unit cost and restrictions. An analytical solution of the EQO is derived using a recent and simple method, which isthe geometric programming approach. The EOQ inventory model with demand-dependent unit cost without any restriction and the classical EOQ inventory model are obtained.     

有限时域与采购价格上升情形下的最优订货策略

研究了有限时域下采购商面对价格上升时的订货策略问题.在分析问题的基础上提出一种新的最优采购策略,并分析了价格上升幅度对订货量的影响,以经典EOQ模型的总成本为基准,比较了本文提出的策略与文献已有策略在成本节约上的差异.本文对库存总成本的计算方法更加精确;分析表明在有限时域背景下采购商的临时订货量决定于价格上涨的幅度、在库库存以及时段长度.     

Emergency inventory ordering assuming Poisson demands

Abstract

Most business and industrial firms use some procedure for emergency ordering. If independent demand for low-volume, high-cost items is Poisson distributed, subsequent analyses reveal that emergency ordering may be less expensive than carrying extra safety stock. Emergency ordering reduces the out-of-stock cost as well as the required safety stock. Total cost is sensitive to the lead time required for emergency orders. The results are particularly applicable to maintenance inventory. Under the assumptions of this study, the conclusion may be drawn that an emergency ordering system may approach the theoretical minimum for operating an inventory system.     

Sourcing from Multiple Suppliers for Price‐Dependent Demands

We analyze a model that integrates demand shaping via dynamic pricing and risk mitigation via supply diversification. The firm under consideration replenishes a certain product from a set of capacitated suppliers for a price‐dependent demand in each period. Under deterministic capacities, we derive a multilevel base stock list price policy and establish the optimality of cost‐based supplier selection, that is, ordering from a cheaper source before more expensive ones. With general random capacities, however, neither result holds. While it is optimal to price low for a high inventory level, the optimal order quantities are not monotone with respect to the inventory level. In general, a near reorder‐point policy should be followed. Specifically, there is a reorder point for each supplier such that no order is issued to him when the inventory level is above this point and a positive order is placed almost everywhere when the inventory level is below this point. Under this policy, it may be profitable to order exclusively from the most expensive source. We characterize conditions under which a strict reorder‐point policy and a cost‐based supplier‐selection criterion become optimal. Moreover, we quantify the benefit from dynamic pricing, as opposed to static pricing, and the benefit from multiple sourcing, as opposed to single sourcing. We show that these two strategies exhibit a substitutable relationship. Dynamic pricing is less effective under multiple sourcing than under single sourcing, and supplier diversification is less valuable with price adjustments than without. Under limited supply, dynamic pricing yields a robust, long‐term profit improvement. The value of supply diversification, in contrast, mainly comes from added capacities and is most significant in the short run.     

非瞬时补货下改良品联合采购决策

联合采购往往使订货批量成倍增加,从而更易享受供应商提供的价格折扣,因此联合采购受到零售商们的青睐。考虑由单供应商与多零售商组成的二级改良品供应链中,供应商对零售商提供非瞬时补货,分别建立零售商独立采购与联合采购的单位时间成本函数,求解出两种采购模式的最小单位时间成本并对之进行比较,得到联合采购优于独立采购的必要条件。同时,以联合采购的联盟成本作为分摊对象,应用多人合作博弈理论,将联合采购的成本分摊问题构造成多人合作博弈问题,给出最小核心法的成本分摊思路。通过数值算例演示成本分摊过程,给出净改良率对订货参数及成本参数的敏感性分析,并对四种成本分摊算法的分摊结果作出比较。     

Multi-item inventory model with quantity-dependent inventory costs and demand-dependent unit cost under imprecise objective and restrictions: A geometric programming approach

A multi-item inventory model with constant demand and infinite replenishment is developed under the restrictions on storage area, total average shortage cost and total average inventory investment cost. These restrictions may be precise or imprecise. Here, it is assumed that inventory costs are directly proportional to the respective quantities, and unit purchase/production cost is inversely related to the demand. Restricted shortages are allowed but fully backlogged. First, the problem is formulated in crisp environment taking the deterministic and precise inventory parameters. It is solved by both geometric programming (GP) and gradient-based non-linear programming (NLP) methods. Later, the problem is formulated with fuzzy goals on constraints and objectives where impreciseness is introduced through linear membership functions. It is solved using the fuzzy geometric programming (FGP) method. The inventory models are illustrated with numerical values and compared with the crisp results. A sensitivity analysis on the optimum order quantity and average cost is also presented due to the variation in the tolerance of total average inventory investment cost and total average shortage cost following Dutta et al., 1993, Fuzzy Sets and Systems, 55, 133-142.     

Multi-item production lot-size inventory model with varying order cost under a restriction: A geometric programming approach

In this paper we present a geometric programming approach for determining the inventory policy for multiple items having varying order cost, which is a continuous function of the order quantity, and a limit on the total average inventory of all items. Our model is a generalization of that of Gupta and Gupta for unrestricted single-item order quantity model with varying order cost and assumes the same order cost function. This cost function relates well to real-life situations since it increases as the order quantity increases and, at the same time, it is easy to handle when deducing previous work as special cases of our model since it is easily reducible to a constant. An example is solved to illustrate the method.