Issuing for perishable inventory management with a minimum inventory volume constraint

We study a perishable inventory system that requires to maintain a minimum inventory volume at all times, where the minimum amount in the constraint is significant with respect to regular market demand and the traditional Economic Manufacturing Quantity (EMQ) models do not suffice. The problem is motivated by applications in homeland security, which are related to the management of pharmaceuticals in the Strategic National Stockpile (SNS) for emergency preparedness. We use a modified EMQ model to represent the system and consider the issuing policy given a fixed ordering quantity, as well as the joint ordering and issuing policy problem. We aim to maximize the profit of the system under a linearly-decreasing price structure assumption. We first present the optimal issuing policy with a given ordering quantity for this modified EMQ model. Then we demonstrate that maximizing the revenue of the ordering policy with FIFO (first-in, first-out) and LIFO (last-in, first-out) issuing policies can be formulated as a non-convex non-smooth unconstrained optimization problem. The properties of both problems (e.g. optimizing issuing policy with a fixed ordering quantity and optimizing ordering policy with a fixed issuing policy) is analyzed and an efficient exact algorithm is presented to solve the joint ordering and issuing problem. We show that the LIFO issuing policy is optimal with a linearly-decreasing price structure that deteriorates with the age of the item.     

Optimal ordering policies for deteriorating items using a discounted cash-flow analysis when a trade credit is linked to order quantity

In today’s competitive market, in order to obtain a competition advantage, the supplier often offers the purchaser a longer permissible delay in payments or a price discount if the order quantity is greater than or equal to a predetermined quantity. As a result, in this paper, we establish an inventory model for the purchaser in which the supplier provides different trade credits. We then solve the inventory problem by using a discounted cash-flow (DCF) approach, characterize the optimal solution, and obtain some theoretical results to find the optimal order quantity and the optimal replenishment time. Finally, we provide several numerical examples to illustrate the results.     

The optimal retailer's ordering policies with trade credit financing and limited storage capacity in the supply chain system

The traditional economic order quantity model assumes that the retailer's storage capacity is unlimited. However, as we all know, the capacity of any warehouse is limited. In practice, there usually exist various factors that induce the decision-maker of the inventory system to order more items than can be held in his/her own warehouse. Therefore, for the decision-maker, it is very practical to determine whether or not to rent other warehouses. In this article, we try to incorporate two levels of trade credit and two separate warehouses (own warehouse and rented warehouse) to establish a new inventory model to help the decision-maker to make the decision. Four theorems are provided to determine the optimal cycle time to generalise some existing articles. Finally, the sensitivity analysis is executed to investigate the effects of the various parameters on ordering policies and annual costs of the inventory system.     

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.     

Trade credit financing in the vendor–buyer inventory system with ordering cost reduction,transportation cost and backorder price discount when the received quantity is uncertain

Previous ordering cost reduction vendor–buyer inventory models with backorder price discount usually assumed that the buyer must pay to the vendor for the ordered items as soon as the items are received, the received quantity is same as the ordered quantity and the transportation cost is independent of the shipment lot-size. In practice, however, the vendor is willing to offer the buyer a certain credit period without interest to promote market competition as well as the buyer's quantity received may not match with the ordered quantity due to unavailability of the raw material, worker's strike, human errors in counting, transcribing, etc. Furthermore, the discounts are offered for the transportation cost of large ordered quantities. This paper derives a single-vendor single-buyer supply chain model for the ordering cost reduction inventory system with backorder price discount, taking into consideration the effect of transportation cost discount and the condition of permissible delay in payments include the case where the buyer's received quantity does not necessarily match the quantity requisitioned. We take the transportation cost as a function of the shipment lot-size and it is taken to be in an all-unit-discount cost format. Thus we incorporate transportation cost explicitly into the model and develop optimal solution procedures for solving the proposed inventory problem. Numerical example and sensitivity analyses are given to demonstrate the applications and performance of the proposed methodology.     

Heuristic solutions for transshipment problems in a multiple door cross docking warehouse

Cross docking is a practice in logistics with the main operations of unloading products from an incoming truck, regrouping them with respect to their destinations and loading them directly into an outbound truck with minimum storage in between these operations. In this article, we study the transshipment scheduling problem in a multiple inbound and outbound dock configuration. The operations manager has several decisions to make: he can decide to transship products directly from inbound to an outbound truck, if an outbound truck is available; he can temporarily store certain products and have them loaded later on; or he can replace an outbound truck to facilitate direct loading. The objective is to find the best schedule of transshipment operations to minimize the sum of inventory holding and truck replacement costs. In this article, we present several heuristics to attain this objective. Numerical experiments are presented and the results are compared with the optimal solution to evaluate the performance of the heuristics.     

Computation of approximate optimal policies in a partially observed inventory model with rain checks

This paper proposes a new methodology to solve partially observed inventory problems. Generally, these problems have infinite-dimensional states that are conditional distributions of the inventory level. Our methodology involves linearizing the state transitions via unnormalized probabilities. It then uses an appropriate functional basis to represent the state. Considering the speed and stability of computations, we choose truncated Chebyshev polynomials as the basis. We use Fast Fourier Transforms along with an appropriate discretization of inventory levels to speed up the computations. These main ideas are blended to obtain an iterative algorithm to solve a partially observed inventory model with rain checks. In this model, the inventory manager (IM) does not know the inventory level when it is positive. Otherwise, the IM fully observes it. This model provides a context to illustrate our methodology, which applies to other such models. Although this model has been studied mathematically in the literature, the use of our algorithm provides a numerical approximation of the optimal order quantities. These are compared to the orders released under a base mean-stock policy, where the IM replaces the unobserved inventory level with its mean and applies the well-known base stock policy. We show numerically that the optimal order quantity is very close to the base mean-stock order quantity, when the variance of the inventory distribution is small. When the mean of the inventory distribution is large, the optimal order quantity is more than the base mean-stock quantity, and it is the other way around when the mean is small or negative. These insights are explained via uncertainty and information effects and their interplay. We expect this interplay to show up in other partially observed inventory models.     

Integrated inventory and transportation decision for ubiquitous supply chain management

We consider price-dependent demand and develop an integrated inventory and transportation policy with strategic pricing to maximize the total profit for a ubiquitous enterprise. The proposed policy provides the optimal ordering, shipment and pricing decision. We first assume that demand for a product is a linear function of the price. A mathematical model for the total profit under quantity based dispatch is developed in consideration of ordering, shipment and pricing variables. Optimality properties for the model are then obtained and an efficient algorithm is provided to compute the optimal parameters for ordering, shipment and pricing decision. Finally, we extend our results to a more general case where demand for the product is a convex or a concave function of the price.     

A study on an inventory model for items with weibull ameliorating

This paper is concerned with the development of ameliorating inventory models. The ameliorating inventory is the inventory of goods whose utility increases over the time by ameliorating activation. The term ameliorating inventory is used in this paper at least, since the terminology is not standard well known. This study is performed according to areas; one is an economic order quantity(EOQ) model for the items whose utility is ameliorating in accordance with Weibull distribution, and the other is a partial selling quantity(PSQ) model developed for selling the surplus inventory accumulated by ameliorating activation. The proposed models cannot be solved directly in a closed form, thus we used a computer program and a graphical solution method to obtain the optimal ordering and selling quantity in this paper. Numerical examples to illustrate the effect of ameliorating rate on inventory polices are shown at the end of this paper.     

Joint replenishment policy with backordering and special sale

In this paper, an inventory control model with a joint replenishment policy and a temporary discount is developed. We assume that shortage is allowed and buyer uses an economic order quantity inventory control model. Different cases based on ordering policies for the first joint replenishment if the special order is not taken, and coincidence of a special period length with a positive or negative inventory level of the last regular period length, are investigated. Furthermore, several theorems are proved through which closed-form solutions are obtained. At the end, two numerical examples illustrate the different situations that the buyer may face and sensitivity analyses for both examples are reported.     

An integrated vendor–buyer inventory model with backorder price discount and effective investment to reduce ordering cost

The single-vendor single-buyer integrated production inventory system has been an object of study for a long time, but little is known about the effect of investing in reducing ordering cost on the integrated inventory models with backorder price discount and variable lead time. The purpose of this article is to investigate in the continuous review model with backorder price discount and variable lead time to effectively increase investment and to reduce the joint expected annual total cost. The integrated strategy discussed here is one in which the buyer orders a quantity, then the vendor produces n times order quantity in each production cycle, in order to reduce setup cost. In addition, the buyer offers backorder price discounts to the customers that may motivate the customers’ desire for backorders, and buyer ordering cost can be reduced through effective investment. An integrated inventory model is established to find the optimal solutions of order quantity, ordering cost, backorder price discount, lead time, and the number of shipments from the vendor to the buyer in one production run, so that the joint expected annual total cost incurred has the minimum value. Furthermore, numerical examples are used to demonstrate the benefits of the model.     

Sole versus dual sourcing under order dependent lead times and prices

In this paper, we consider a dual-sourcing model with constant demand and stochastic lead times. Two suppliers may be different in terms of purchasing prices and lead-time parameters. The ordering takes place when the inventory level depletes to a reorder level, and the order is split among two suppliers. Unlike previous works in the order splitting literature, the supply lead time between vendor and buyer as well as unit purchasing prices is considered to be order quantity dependent. The proposed model finds out the optimal reorder point, order quantity and splitting proportion, using a solution procedure. Numerical results show that neglecting the relationship between ordering batch size and lead times is a shortcoming that hides one of order splitting advantages. Moreover, connecting unit prices to order quantity can decrease the percentage saving from dual sourcing compared to sole sourcing. Furthermore, sensitivity analysis shows some managerial insights.     

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.     

Single period stochastic inventory problems with ordering or returns policies

In recent years, there has been an increasing adoption of returns policies in the coordination of the supply chain, where market demand is always assumed to be satisfied by manufacturing or by ordering from suppliers. However, many industries face the important decision of how to balance their inventory level. This problem has long been studied in financial institutions such as banks. This study presents an optimal inventory policy under a given stochastic demand such as a uniformly distributed demand, single-item, and single period review inventory system. The optimal inventory control policy obtained in this study is called a four-point policy: that is, when the entity’s inventory level is below a reorder point, the entity must increase his stock level by ordering and order up-to a fixed level (second point); when the entity’s inventory level is over a return point (third point); the stock level must be decreased by returns and decreased to a fixed level (fourth point); otherwise, nothing should be done. We also analyze the (K, S)-convex properties of the inventory cost function.     

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 bi-objective continuous review inventory control model: Pareto-based meta-heuristic algorithms

In this paper, a bi-objective multi-product (r,Q) inventory model in which the inventory level is reviewed continuously is proposed. The aim of this work is to find the optimal value for both order quantity and reorder point through minimizing the total cost and maximizing the service level of the proposed model simultaneously. It is assumed that shortage could occur and unsatisfied demand could be backordered, too. There is a budget limitation and storage space constraint in the model. With regard to complexity of the proposed model, several Pareto-based meta-heuristic approaches such as multi-objective vibration damping optimization (MOVDO), multi-objective imperialist competitive algorithm (MOICA), multi-objective particle swarm optimization (MOPSO), non-dominated ranked genetic algorithm (NRGA), and non-dominated sorting genetic algorithm (NSGA-II) are applied to solve the model. In order to compare the results, several numerical examples are generated and then the algorithms were analyzed statistically and graphically.     

基于Simulink的库存系统的动态建模与仿真

该文首先通过将随机的、不可控的需求控制问题转化为安全库存设置问题的方法,建立了库存系统的仿真模型。然后基于MATLAB／Simulink软件对多组策略值进行仿真,动态实时模拟了（t,s,S）策略的库存系统的入库、出库时机和数量。最后选择库存总费用的日平均值最低的一组为最优库存策略,从而使企业能够合理规划和安排仓库及各类设施、资源,文现库存成本的最小化。仿真结果清晰、直观,为现代经营者做出正确的库存决策提供了有价值的参考。     

Mathematical programming approach to inventory control

In many production systems inventory cost is the major element of investment. It is essential in these systems to hold inventory at a near optimal level to minimize the total costs of the system. This paper presents a procedure for developing an optimal inventory control plan which can be solved by mathematical programming. Input to the model includes demand forecasts, ordering costs, carrying costs, shortage costs, price break data, space constraints, and probability of usage. Most of the factors affecting this plan are investigated in order to simplify the way of handling all the input values.     

Modelling and analysis of inventory replenishment for perishable agricultural products with buyer–seller collaboration

In this article, we study the inventory replenishment model for perishable agricultural products in a simple two-level supply chain. Collaborative forecasting is introduced into the inventory replenishment decisions to avoid overstocking and understocking of agricultural products, and to maximise profits. We analyse the model with ordering cost, holding cost, shortage cost, deterioration cost and opportunity lost cost of perishable agricultural products. Extensive numerical analysis is carried out to study the performance of the inventory policy. The optimal replenishment policy that minimises the total cost can be obtained from the model. It has demonstrated that the supply chain cost decreases with supplier and retailer's collaborative forecasting.     

供应链环境下的装备多级库存优化研究

研究了一个战役级、多个战术级仓库组成的树型多级库存系统,建立了战役级仓库分别采用等量等间隔、不等量等间隔订货策略的模型。采用自适应遗传算法实现了模型的求解,并用实例验证了算法的有效性。