基于不同交货期决策权下的供应链交货期和定价决策研究

基于对价格和交货期敏感的需求,针对一个制造商与一个零售商构成的两阶段供应链,以最大化期望利润为目标,分别建立供应链交货期由制造商和零售商控制的决策模型,以得到相应的最优解和最大期望利润.通过比较,探讨了不同交货期决策权对供应链最优交货期和最大期望利润的影响,得到了为实现期望利润最大化,针对顾客需求特性,供应链系统应在保证一定交货期服务水平的基础上选择由制造商控制供应链交货期的结论.     

The benefit of VMI strategies in a stochastic multi-product serial two echelon system

We consider a multi-product serial two echelon inventory system with stochastic demand. Inventories at the downstream location are replenished periodically using an automatic ordering system. Under vendor managed inventory strategies the upstream stage is allowed to adapt these orders in order to benefit from economies of scale. We propose three different VMI strategies, aiming to reduce the order picking cost at the upstream location and the transportation costs resulting in reduced total supply chain costs. In a detailed numerical study the VMI strategies are compared with a retailer managed inventory strategy for two different demand models suitable for slow moving products. It is shown that if inventory holding costs are low, compared to handling and transportation costs, efficiencies at the warehouse are improved and total supply chain costs are reduced.     

A single-period inventory model with fuzzy demand

The single-period inventory models have wide applications in the real world in assisting the decision maker to determine the optimal quantity to order. Due to lack of historical data, the demand has to be subjectively determined in many cases. In this paper, a single-period inventory model for cases of fuzzy demand is constructed. The costs considered include the procurement cost, shortage cost, and holding cost. For different fuzzy total cost resulted from different order quantity, a method for ranking fuzzy numbers is adopted to find the optimal order quantity in terms of the cost. When the profit gained from selling one item is less (greater) than the loss incurred due to one unsold item, the optimal order quantity lies in the range defined for the left-shape (right-shape) function of the fuzzy demand. If the unit profit is equal to the unit loss, then all quantities with a membership grade 1 are optimal to be ordered. The methodology of this paper can be applied to construct other inventory models with fuzzy demand.     

季节性产品零售商的网络订单履行策略研究

以一个销售季节性产品的零售商为研究对象,该零售商拥有两个实体店,分别位于两个独立的地区,通过Drop-shipping方式接收网上的订单,以扩大销量。初始库存量是确定的,产品卖给网上顾客为零售商带来的收益要比卖给店内顾客的收益少（履行网上订单获得的收益是零售商与订单提供者共享）;因此,每当网上订单到达时,零售商需要在接收该订单、还是把产品留给能带来更高收益的未来的店内顾客间做决策;如果接收该订单,还要决策将由哪个实体店来履行订单效益更好;以最大化未来期望收益为目标,建立动态规划模型,并从实体店对单个产品期望收益的角度为这两个问题的决策提供依据;分别在两个实体店处于平等地位和其中一个实体店被确定为优先供应商两种不同的情况下,研究零售商决策结果的差异。     

库存水平影响需求下变质品订购、定价和保鲜技术投资的联合决策

研究变质品的订购、定价和保鲜技术投资联合决策问题.假设产品需求同时受价格和库存水平的影响,系统不允许缺货并放松期末库存水平为零的约束,零售商拥有有限的货架空间或存储空间,同时考虑零售商可以通过投资保鲜技术减低产品的变质率,以平均利润最大化为目标构建库存水平影响需求下变质品的订购、定价和保鲜技术投资联合决策模型.首先证明最优策略的存在性和唯一性,并给出零售商建立期末库存的条件;然后利用最优解的相关性质设计一个求解模型的多阶段迭代算法;最后通过具体算例验证展示模型和算法的可行性和实用性,并完成相关参数的敏感性分析,获得一定的管理启示.     

Joint pricing and replenishment policies for non-instantaneous deteriorating items with imprecise deterioration free time and credibility constraint

This study develops an inventory model for non-instantaneous deteriorating items with imprecise deterioration free time and credibility constraint. The model assumes price sensitive demand when the product has no deterioration and price and time dependent demand when the product has deterioration. Under these considerations, the study attempts to offer best policy for selling price and replenishment cycle for the retailer that aims at maximizing the total profit per unit time. Making use of nearest interval approximation and interval arithmetic, the single objective problem is transformed to multi objective problem. Employing Weighted Sum Method, an analytical approach along with simple algorithm is developed to identify Pareto optimal solution. Finally, the behavior of the model with varied parameters is illustrated in numerical examples.     

Joint quantity flexibility for multiple products in a decentralized supply chain

In this study, we analyze a decentralized supply chain with a single retailer and a single manufacturer where the retailer sells multiple products in a single period. The products differ in terms of a limited number of features only. The retailer places initial orders based on preliminary demand forecasts at the beginning of the period and has an opportunity to modify its initial order after receiving perfect demand information. However, the final orders of the retailer are constrained by its initial orders. The manufacturer has two options for procurement. The first procurement option is regular delivery at the beginning of the period, after the initial orders of the retailer. The next one is expedited delivery, after the updated orders are received. In this setting, our objective is to characterize the optimal policies for the retailer and the manufacturer, and assess the benefits of flexibility.     

A decision rule for coordination of inventory and transportation in a two-stage supply chain with alternative supply sources

This paper deals with a two-stage supply chain that consists of two distribution centers and two retailers. Each member of the supply chain uses a (Q,R) inventory policy, and incurs standard inventory holding and backlog costs, as well as ordering and transportation costs. The distribution centers replenish their inventory from an outside supplier, and the retailers replenish inventory from one of the two distribution centers. When a retailer is ready to replenish its inventory that retailer must decide whether it should replenish from the first or second distribution center. We develop a decision rule that minimizes the total expected cost associated with all outstanding orders at the time of order placement; the retailers then repeatedly use this decision rule as a heuristic. A simulation study which compares the proposed policy to three traditional ordering policies illustrates how the proposed policy performs under different conditions. The numerical analysis shows that, over a large set of scenarios, the proposed policy outperforms the other three policies on average.     

Two-Stage Stochastic Integer Programming Model for Multiperiod Sea Cargo Mix Problem in Container Shipping Industry

In this paper, we consider the cargo mix problem under uncertainty in the container shipping industry. We seek to determine the optimal cargo mix in a multiperiod planning horizon with the objective of maximizing the total expected profit derived from all freight bookings received in the planning horizon. We present a two-stage stochastic integer programming model and propose a heuristic algorithm for multiperiod sea cargo mix problem under uncertainty. Finally, numerical experiments on a wide range of randomly generated problem instances are conducted to demonstrate the efficiency of the algorithm.      

A numerical solution for a two-stage production and inventory system with random demand arrivals

This paper is about the study of a production lot sizing problem consisting of customers, one retailer, and one manufacturer. Demand from customers arrives randomly at a retailer one unit at a time. The retailer replenishes inventory from the manufacturer upon receiving a customer's order after its inventory depleted to zero. The manufacturer's production rate is assumed to be a finite constant. A production cycle starts when the manufacturer's inventory falls to or below zero and stops when its on-hand inventory reaches its optimal level. During the uptime in a production cycle, inventory is being built while randomly arriving orders from retailer are being fulfilled. The order arrival times from customers are independently and identically distributed, hence the inventory processes at both the manufacturer and the retailer become a renewal process that is difficult to solve analytically for a general distribution of order arrival time. Therefore, a numerical approach is used in developing a search procedure to obtain the optimal solution to the problem. Employing such a numerical approach, we also investigate how optimal solutions in different cases will change over the spectrum of some key parameters of the problem.     

基于购买行为的随机生命周期易逝品库存策略

研究需求和商品生命周期均为随机的零售商库存管理问题,提出按照购买行为特征对需求进行分类,在不同类型的客户之间进行库存分配并允许缺货的库存策略.通过构建动态规划模型,求解出零售商最优库存策略,包括补货策略和库存分配策略.与先到先服务策略相比,该策略能显著提升零售商的利润,减少商品损坏的损失.     

Ordering,wholesale pricing and lead-time decisions in a three-stage supply chain under demand uncertainty

This paper develops a game theoretic model of a three-stage supply chain consisting of one retailer, one manufacturer and one subcontractor to study ordering, wholesale pricing and lead-time decisions, where the manufacturer produces a seasonal/perishable product. We explicitly model the effects of the lead-time and the length of selling season on both demand uncertainty and inventory-holding costs. We present the equilibrium outcome of the decentralized supply chain. When the lead-time increases, we find that the retailer increases the order quantity, the manufacturer offers a lower unit-wholesale price and the subcontractor decreases its unit-wholesale price if the manufacturer subcontracts part of the retailer’s order. In the endogenous lead-time setting, we illustrate the effects of some factors such as unit holding cost and capacity on the equilibrium outcome. We find that a higher unit holding cost implies a lower optimal lead-time and order quantity while higher unit-wholesale prices; the basic demand uncertainty increases the optimal lead-time and order quantity while decreases the unit-wholesale prices. The effects of distribution form on equilibrium outcome/profits are investigated by employing a numerical example. The profit loss of decentralization decreases (increases) with the basic demand uncertainty and manufacturer’s capacity (mean demand).     

Single-period inventory model with a delayed incentive option for selling excess inventory

The single‐period problem (SPP) is to find the order quantity which maximizes the expected profit in a single period probabilistic demand framework. We extend the SPP to a case where a retailer uses delayed incentives in the form of cash mail‐in rebates to sell remaining inventory that did not sell at the regular price. The advantage of cash mail‐in rebates is that not all consumers will redeem them. We address three cases: (1) rebate value is predetermined and the order quantity is a decision variable; (2) order quantity is a decision variable and rebate value is set to the value needed to sell all excess inventory, and (3) order quantity is a decision variable and the rebate may be used to sell part of or all excess inventory. In the third case, any inventory remaining after the rebate offer is salvaged at reduced price. We provide analytical solutions for uniform and exponential demand distributions. In all cases, rebates can lead to significant increases in expected profit. We first maximize the expected profit. We then maximize the probability of achieving a target profit and show that the use of rebates can lead to a substantial increase in that probability.     

Combined optimal price and optimal inventory replenishment policies when a sale results in increase in demand

When a supplier reduces the price of a product temporarily a buyer might place a large order and offer a sale on these units to its customers. In most cases a price discount results in an increase in demand. In this paper we relax the constant demand assumption made in most studies of inventory systems with price changes. We analyze the options available to a buyer and develop profit functions for different combinations of sales period and replenishment time and present optimal ordering policies. The paper also presents a procedure to include any relationship between price and demand to determine the combined optimal price and optimal order quantity.     

Ordering and transferring model of dual-channel supply chain with delivery time difference

Customers with different delivery times in online and offline channels often lead to conflicts between two channels, which causes the loss of a large number of customers. Therefore, it is necessary to use the difference between the online and offline delivery to achieve the balance of inventory through order transferring. Aimed at this problem, a dual-channel supply chain system consisting of an online channel supplier and an offline retailer has been developed and sales stage has been expanded to two ones in order to explore the endogenous impact mechanism of different delivery periods on order transferring, and the structural properties of the order transferring threshold. Based on this, the optimal ordering strategy has been discussed at the beginning of the sales season by game theory. Secondly, the optimal threshold for order transferring of offline retailers in each stage by dynamic programming has been explored, and the relationship between the threshold and the sales stage has further been investigated in order to achieve a win-win co-operation by determining the optimal co-operative behavior. Finally, a numerical example has analyzed the influence of co-operation on ordering quantity, inventory quantity, and profit. Furthermore, we have also illustrated the existence of a stable interval when the delivery rate difference rate is lower, which simplifies the implementation of this strategy and improves its operability.     

随机需求随机补货间隔零售商补货控制策略研究

研究分销系统中零售商的补货控制策略．分销系统中各零售商可独立决定自己的补到水平．零售商需求率是随机变量．服从某一泊松分布;分销中心循环为各零售商送货．送货间隔是随机变量．认为所有未满足的需求销售机会都丢失,零售商既要支付库存持有费用．又要支付缺货损失费用．给出了收益数学期望值函数,求出了送货间隔是均匀分布随机变量时使收益数学期望值最大化的零售商补到水平控制策略．     

Optimal policy for profit maximising in an EOQ model under non-linear holding cost and stock-dependent demand rate

In this article, we integrate a non-linear holding cost with a stock-dependent demand rate in a maximising profit per unit time model, extending several inventory models studied by other authors. After giving the mathematical formulation of the inventory system, we prove the existence and uniqueness of the optimal policy. Relying on this result, we can obtain the optimal solution using different numerical algorithms. Moreover, we provide a necessary and sufficient condition to determine whether a system is profitable, and we establish a rule to check when a given order quantity is the optimal lot size of the inventory model. The results are illustrated through numerical examples and the sensitivity of the optimal solution with respect to changes in some values of the parameters is assessed.     

A fuzzy framework for coordinating pricing and inventory policies for deteriorating items under retailer partial trade credit financing

In this paper, we proposed a generalized economic order quantity (EOQ) – based inventory model using a trade credit policy in a fuzzy sense. 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, partially provides customers a permissible delay period N. This study considers fuzzy EOQ model to allow for: (1) selling price dependent demand rate which is imprecise in nature, (2) a profit maximization objective and (3) an imprecise holding cost, ordering cost, purchasing cost, interest earned and interest charged rate. Besides, the cases N ? M and N ? M are explored thoroughly. The objective function for the retailer in fuzzy sense is defuzzified using Modified Graded Mean Integration Representation Method. For the defuzzified objective function sufficient conditions for the existence and uniqueness of the optimal solution are provided. An efficient algorithm is designed to determine the optimal pricing and inventory policies for the retailer. Finally, numerical examples are presented to illustrate the proposed model and the effect of key parameters on optimal solution is examined.     

网上零售业多产品配送服务定价研究

随着越来越多的网上零售商开始实施有条件的免运费策略, 如何确定免运费的条件和运费成为电商企业面临的重要问题。该问题抽象成为一个两阶段的博弈模型：首先消费者根据效用最大化的原则确定购买决策, 然后零售商在考虑消费者购买决策的基础上依据利润最大化原则设定物流定价策略。通过算法设计和算例分析, 得到免运费阈值设定在产品价格组合边界时, 零售商利润会发生跳跃。     

Inventory and pricing strategies for deteriorating items with shortages: A discounted cash flow approach

In this article, we consider an infinite horizon, single product economic order quantity where demand and deterioration rate are continuous and differentiable function of price and time, respectively. In addition, we allow for shortages and completely backlogged. The objective is to find the optimal inventory and pricing strategies maximizing the net present value of total profit over the infinite horizon. For any given selling price, we first prove that the optimal replenishment schedule not only exists but is unique. Next, we show that the total profit per unit time is a concave function of price when the replenishment schedule is given. We then provide a simple algorithm to find the optimal selling price and replenishment schedule for the proposed model. Finally, we use a couple of numerical examples to illustrate the algorithm.