多周期报童模型在煤炭物资库存管理中的应用

为了降低煤炭企业物资库存管理成本,本文结合郑州煤电物资供销公司的实际情况,提出了考虑供过于求时,剩余物资对库存以及订货量影响的多周期库存模型。不同于经典报童模型中以订货量为自变量,本模型以期望利润为目标函数,以初始库存为自变量,在期望利润最大的情况下,得出每个周期的初始库存水平。通过郑州煤电物资供销公司的物资库存管理实例计算,结果表明可降低库存成本50%左右,说明该模型合理可行。     

A stochastic inventory problem with fuzzy shortage cost

Up to now, many inventory models have been considered in the literature. Some assume stochastic demands and others consider the deterministic case. Though they include a shortage cost due to lost sales, it is usually assumed to be known concretely and a priori. This paper introduces fuzziness of shortage cost explicitly into the classical newsboy problem. That is, we investigate the so-called fuzzy newsboy problem where its shortage cost is vague and given by an L shape fuzzy number. Then the total expected profit function also becomes a fuzzy number. Finally, we find an optimal ordering quantity realizing the fuzzy max order of the profit function (fuzzy min order considering the profit function) and compare it with the optimal ordering quantity of the non-fuzzy newsboy problem.     

三种可替代的Newsboy型产品最优订购模型

经典的报童(Newsboy)问题是在单周期内,商品的需求量是随机状态下,寻找一种商品订购数量,使系统预期利润最大.本文主要研究三种商品的相互替换问题:首先,我们建立三种商品相互替换的模型,根据实际的库存与缺货状况,将其分为八种情况,并求出这八种情况下利润函数,得到整个过程的总利润函数;最后,结合应用实例给出最优的数值解.     

可追加订购的报童问题

研究带有追加 (两次 )订购的报童模型 ,分析了此模型与经典 (一次订购 )报童模型的收益关系 ,服务水平评价 ,订购量与需求均值、方差、价格等的灵敏度及发现了在适当的条件下 ,最大追加订购量 M的最优解存在 ,且给出了求解的方法 .     

Analysis and design of returns policies from a supplier's perspective

This paper considers the problem of designing a returns policy in a supply chain from a supplier's perspective. The supply chain considered here is assumed to have one supplier and one retailer who serves a random demand of a product with a short life cycle. The retailer can return all the unsold products to the supplier with a partial refund. We found that if the retailer behaviour is rational, that is, ordering the optimal quantity to maximize its expected profit, then both retailer and supplier could benefit from the returns policy. Furthermore, we established that the optimal buyback price is independent of the mean of the random demand, but the variance of the demand has a significant impact on setting the optimal buyback price. The higher the variance the higher the optimal buyback price and the larger the profit gain of both parties. Numerical studies are employed to help understand the benefits of returns policies for the supplier, the retailer, and the whole supply chain.     

A multi-period ordering and clearance pricing model considering the competition between new and out-of-season products

The joint management of pricing and inventory for perishable products has become an important problem for retailers. This paper investigates a multi-period ordering and clearance pricing model under consideration of the competition between new and out-of-season products. In each period, the ordering quantity of the new product and the clearance price of the out-of-season product are determined as decision variables before the demand is realized, and the unsold new product becomes the out-of-season one of the next period. We establish a finite-horizon Markov decision process model to formulate this problem and analyze its properties. A traditional dynamic program (DP) approach with two-dimensional search is provided. In addition, a myopic policy is derived in which only the profit of the current period is considered. Finally, we apply genetic algorithm (GA) to this problem and design a GA-based heuristic approach, showing by comparison among different algorithms that the GA-based heuristic approach is more performance sound than the myopic policy and much less time consuming than the DP approach.     

需求依赖销售努力库存系统的随机比较

研究需求依赖销售努力库存系统中需求不确定性对系统最优订货量、利润和销售努力的影响.对一般需求模型给出期望利润关于订货量和努力水平为联合凹的充分条件,证明期望利润函数的超模性质.对加乘需求模型证明系统最优利润和最优努力水平都可由一类与需求分布有关的广义TTT变换来表示.通过引入定义在不同支撑分布集合上一阶、二阶和三阶随机占优,得到广义TTT变换之差与二阶和三阶随机占优之间的关系式,建立了比较库存系统最优利润或努力水平的理论基础.在一阶和二阶随机占优意义下对加乘需求模型得到比较系统最优利润和努力水平的充分条件或充分必要条件.进一步,证明存在一类需求分布当系统关键比(或市场价格)足够大时系统最优利润和努力水平随需求可变性的增加而增加.最后给出几个数值例子验证了研究结果.     

Dynamic pricing of inventory with cancellation demand

When an inventory item has such a limited selling period that only a single supply order can be placed to satisfy future demand, a decision-maker must determine the quantity of the order to meet future demand and how to price this stock. Although this problem has received considerable attention, related investigations typically view the demand and selling price as exogenous parameters and assume that customers cannot cancel an order or return the product after purchasing the item. Pricing is, however, an important pervasive marketing vehicle that affects demand, and customers indeed cancel or return their orders after placing them. The newsboy problem is extended here so that demand is price-dependent and customers may cancel their orders. This paper seeks to develop decision rules to maximize the total expected profit over a given planning period. Analysis results demonstrate the feasibility of applying the order-up-to structure to yield the order quantity.     

不完备质量下的报童问题及其评估机制

在产品质量不完备的环境下,考虑了需求依赖于质量水平的报童问题。本文主要利用马氏理论刻画质量水平与需求之间关联性的动态演变过程,并将“不完备质量”的决策理念纳入报童问题的理论框架,进而提出了新的随机库存系统的优化模型及其决策机制。同时,利用随机质量过程中的首达性、遍历性、不可约性等基本属性,构建了随机库存系统在运作和管理过程中的可靠性及其收益评估机制。模型的相关结论表明:在不完备质量的环境下,零售商的最优订购决策是由各个质量状态的转移概率所确定,若由质量水平的波动性所导出的随机过程为不可约遍历马氏链时,则库存系统的决策机制具有良好的稳定性。     

An EOQ model with stock and price sensitive demand

Many business practices show that the presence of a larger quantity of goods displayed may attract more customers than that with a smaller quantity of goods. This phenomenon implies that the demand may have a positive correlative with stock level. Under such a circumstance, a firm should seriously consider its pricing and ordering strategy since the demand for their goods may be affected by their selling prices and inventory level. This paper aims to develop a continuous inventory model for finding the strategy for a firm that sells a seasonal item over a finite planning time. The purpose of this firm is to maximize its expected profit by determining the optimal ordering quantity and price setting/changing strategy. Some sufficient conditions are found for finding the optimal decision rules.     

需求依赖于服务水平的易变质品库存策略研究

本文研究需求依赖于上一周期服务水平、缺货时订单部分损失的两周期易变质品库存问题。分别考虑一次订货和多次订货两种情况,以平均利润最大化为目标构建库存模型,证明了模型解的存在性和唯一性,得到了最优库存服务水平和最优补货策略。最后,通过算例给出两个模型的应用,对重要参数进行了灵敏度分析,并且将两种模型的结果进行了对比分析。结果表明:订单损失率的增加会提高服务水平,但会使得利润降低;顾客期望服务水平的提高会降低第一阶段的服务水平,同时使利润减少;单位库存持有成本或变质率的增加会降低服务水平和平均利润。通常情况,企业通过多次订货能获得更大的利润,而只有当库存持有成本极小时,一次订购才能够获得更大的利润。同时,结果也表明:服务水平对库存策略有较大的影响,因此在进行库存决策时考虑服务水平具有重要的作用。     

EOQ holds under stochastic demand,a technical note

We consider a variant of the economic order quantity (EOQ) model. Mainly, we assume that demand occurs at random, one unit at a time, and is characterized by independent and identically distributed times between two demand epochs. We also assume that the ordering policy is characterized by ordering the same amount whenever the inventory level drops to zero, and a demand occurs. Surprisingly, we show that the optimal order quantity that minimizes the expected inventory cost follows the familiar EOQ formula.     

Inventory and coordination issues with two substitutable products

This study considers a two level supply chain in a newsboy setting with two substitutable products. Demands for the two products are assumed independent as long as both are available. If, however, a product stocks out, some of its demand is transferred to the available one with a known probability which ultimately creates a dependence on the amount of purchased items. The retailer is allowed to return some or all of the unsold products to the manufacturer with some credit. The expected chain profit, the retailer’s and the manufacturer’s profit expressions are derived under general conditions. Special cases are inspected to investigate the conditions under which channel coordination is achieved. It is demonstrated that channel coordination can not be achieved if unlimited returns are allowed with full credit, a result that agrees with the findings of Pasternak [B.A. Pasternack, Optimal pricing and return policies for perishable commodities, Market. Sci. 4 (1985) 166–176] for the single item case. For the cases of unlimited returns with partial credit, the conditions for coordination are derived for one way full substitutions. For exponential demand explicit expressions for the channel and retailer’s expected profit functions are provided.     

Profit maximization in an inventory system with time-varying demand,partial backordering and discrete inventory cycle

In this paper, an inventory problem where the inventory cycle must be an integer multiple of a known basic period is considered. Furthermore, the demand rate in each basic period is a power time-dependent function. Shortages are allowed but, taking necessities or interests of the customers into account, only a fixed proportion of the demand during the stock-out period is satisfied with the arrival of the next replenishment. The costs related to the management of the inventory system are the ordering cost, the purchasing cost, the holding cost, the backordering cost and the lost sale cost. The problem is to determine the best inventory policy that maximizes the profit per unit time, which is the difference between the income obtained from the sales of the product and the sum of the previous costs. The modeling of the inventory problem leads to an integer nonlinear mathematical programming problem. To solve this problem, a new and efficient algorithm to calculate the optimal inventory cycle and the economic order quantity is proposed. Numerical examples are presented to illustrate how the algorithm works to determine the best inventory policies. A sensitivity analysis of the optimal policy with respect to some parameters of the inventory system is developed. Finally, conclusions and suggestions for future research lines are given.

     

考虑框架协议的动态报童模型强化学习建模研究

企业为了稳定货源和供货关系,常与供应商签订一定时期的框架性协议。为了解决零售商在框架协议下采购报童产品的问题,本文运用强化学习建立库存决策模型并使用Q学习算法求取较优订货策略。通过生成样本随机数来模拟需求量,对比研究Q学习算法订货和传统方法订货的差别。通过多次数值实验,发现使用强化学习方法订货相比于传统订货方法(定量订货法、移动平均预测、指数平滑法)平均利润提高约7%~22%,且多次实验下强化学习方法订货相比于理想状态的平均利润相差约8%。这些发现验证了强化学习解决库存问题的有效性和可行性。本文还研究了相关参数变化对总利润的影响,发现利润随着贪婪率(ε)增加而降低、随着学习率(α)的增加而增加。该结论能够为解决相关库存问题提供新的思路。     

A two-echelon supply chain of a returnable product with fuzzy demand

This study investigates the effects of the manufacturer’s refund on retailer’s unsold products for the two-echelon decentralized and centralized supply chains of a short life and returnable product with trapezoidal fuzzy demand, in which retailer returns the unsold and the customer’s unsatisfactory products to the manufacturer. For each returnable chain, we obtain the closed-form solution of order quantity to maximize the total expected profit of the supply chain, and confirm that demand fuzziness does indeed affect the order quantity and the members’ expected profits. We provide a number of managerial insights by comparing both chains and show that each chain is more advantageous to the members depending on certain condition. Our models are appropriate for a supply chain with a returnable product that lacks information about the demand.     

Inventory rationing for the News-Vendor problem with a drop-shipping option

We consider a single-period inventory model for a bricks-and-clicks business. Store inventory can be used to fulfill both store demand and internet demand. Drop-shipping is used as an additional option for internet sale. We analyze two rationing policies for store inventory: a threshold policy and a fixed-portion policy. We formulate the expected profit for both and prove concavity. There exists an optimal order quantity for store inventory and an optimal stock rationing level below which the manager starts to use drop-shipping for internet demand. Numerical examples show that considering the rationing problem for the single-period inventory model, which is ignored in some earlier works, can result in remarkable differences.     

A production planning model for an unreliable production facility: Case of finite horizon and single demand

We study a two-level inventory system that is subject to failures and repairs. The objective is to minimize the expected total cost so as to determine the production plan for a single quantity demand. The expected total cost consists of the inventory carrying costs for finished and unfinished items, the backlog cost for not meeting the demand due-date, and the planning costs associated with the ordering schedule of unfinished items. The production plan consists of the optimal number of lot sizes, the optimal size for each lot, the optimal ordering schedule for unfinished items, and the optimal due-date to be assigned to the demand. To gain insight, we solve special cases and use their results to device an efficient solution approach for the main model. The models are solved to optimality and the solution is either obtained in closed form or through very efficient algorithms.     

数量折扣契约下制造商与零售商库存合作联盟的稳定性

针对实际中存在的不同形式合作联盟,研究了零售商库存合作联盟,以及制造商与零售商库存合作联盟所形成混合合作联盟的稳定性。在随机需求情况下,制造商通过自身中心仓库向多个零售商提供数量折扣契约,首先证明了两个合作联盟的最优运作决策都存在且唯一,并给出了制造商向零售商库存合作联盟提供数量折扣契约的形式,然后分析了两种合作联盟的稳定性,并得出混合合作联盟的总期望利润要高于零售商库存合作联盟的结论。     

服务水平约束下动态定价与库存管理

本文研究服务水平约束下的动态定价与库存管理问题。企业在有限期内销售某种产品,产品的需求为随机需求,且期望需求依赖于产品价格。在每一期期初,企业需要在满足服务水平约束的条件下同时决定订货量和产品价格。本文首先构建了动态定价和订购联合决策的随机动态规划模型,并证明了最优解的存在性。进一步,通过对最优解的结构进行刻画,将原问题的求解转化为若干子问题的求解,降低了问题求解的难度。通过对最优解的分析发现,当期初库存增大时,产品最优价格降低。通过分析目标服务水平对利润的影响,证明了服务水平与利润之间存在权衡,实现高的服务水平需要承受利润损失。数值模拟表明,相对于传统的静态定价策略,采用动态定价策略可以降低追求服务水平所带来的利润损失,验证了动态定价策略的有效性。