A distribution-free newsvendor problem with nonlinear holding cost

In this paper, we analyse a single-period newsvendor model to determine the optimal order quantity where the customers’ balking occurs.This scenario occurs when the customers are opposed to buy a product for various reasons, such as decreasing quality of product, product is not as good as fresh when it reaches under a threshold level, etc. The model is investigated by assuming that the holding cost function depends on order quantity and the inventory level at which customer balking occurs depends on holding cost. The model allows partial backlogging and permits part of the backlogged shortages to turn into lost sales. We develop the model without taking any specific distributional form of demand, only assuming the mean and the variance of the distribution of demand. Finally, we illustrate the model by numerical examples and compare our distribution-free model with the specific distributional form of demand.     

Joint management of finished goods inventory and demand process for a make-to-stock product: a computational approach

In this paper, we consider the joint management of finished goods inventory and demand for a product in a make-to-stock production system. The production process is random with controllable mean rate, and the demand process is stochastic with changeable mean rate dependent on the sale price being high or low. The management issue is how to dynamically adjust the production rate and the sale price to maximize the long run total discounted profit. We show that: 1) the optimal management of the finished goods inventory follows a base stock policy: when the inventory is above certain base stock level, the production is halted; otherwise the maximum production rate is deployed to raise the inventory to the base stock level; and 2) the optimal management of the demand process follows a price switch threshold policy: when the inventory is above the threshold, the low sale price is chosen to sell the product; and below it the high price is chosen to reduce the demand. We provide an algorithm to compute the base stock level and price switch threshold. Extension to multiple price choices is given with proofs highlighted.     

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.     

Inventory and investment in quality improvement under return on investment maximization

In this paper, we construct and analyze inventory and investment in quality improvement policies under return on investment (ROI) maximization. In our model, the level of quality is represented by the fraction of an order quantity meeting the quality requirements such as product specifications. The key contributions of this paper are the establishment of an ROI model and characterization of the unique global optimal solution. We also show how the inventory level is reduced when it is optimal to invest additional money in quality improvement. In addition, we derive the unique global optimal solutions in closed-form when the investment in quality improvement is a linear function of the quality. Various interesting managerial insights and a numerical example are provided.Scope and purposeQuality improvement and inventory reduction has been extensively studied in accordance with just-in-time (JIT) and/or total quality management (TQM). Meanwhile, for finished products, the return on investment (ROI) is widely used as an economic performance criterion. The purpose of this paper is to design and analyze inventory and investment in quality improvement policies under return on investment (ROI) maximization. Specifically, this paper shows how the level of inventory is reduced quantitatively when it is optimal to invest additional money in quality improvement. In addition, this paper shows how the optimal inventory and investment in quality improvement policies are derived and characterized analytically.     

An EOQ model for deteriorating items with price- and stock-dependent selling rates under inflation and time value of money

This study applies the discounted cash flow (DCF) approach for the analysis of a replenishment problem over a finite planning horizon. Thus, a deterministic economic order quantity (EOQ) inventory model taking into account inflation and time value of money is developed for deteriorating items with price- and stock-dependent selling rates. An efficient solution procedure is presented to determine the optimal number of replenishment, the cycle time and selling price. Then the optimal order quantity and the total present value of profits are obtained. Numerical examples are presented to illustrate the proposed model and particular cases of the model are also discussed.     

An accurate and reliable solution procedure for the EOQ model with deteriorating items under supplier credits linked to the ordering quantity

The inventory problem consists of two parts: (1) the modelling and (2) the solution procedure. The modelling can provide insight to solve the inventory problem and the solution procedure involves the implementation of the inventory model. Basically, the modelling and the solution procedure to the inventory problem are equally important. Chang et al.’s inventory model [Chang, C. T., Ouyang, L. Y., & Teng, J. T (2003). An EOQ model with deteriorating items under inflation when supplier credits linked to order quantity. Applied Mathematical Modelling, 27, 983–996] is correct and interesting. However, they ignore the explorations of the functional behaviors of the annual total relevant cost to locate the optimal solutions such that proofs of their solution procedures are not perfect from the viewpoint of logic. The main purposes of this paper are to provide accurate and reliable solution procedures to improve [Chang, C. T., Ouyang, L. Y., & Teng, J. T (2003). An EOQ model with deteriorating items under inflation when supplier credits linked to order quantity. Applied Mathematical Modelling, 27, 983–996].     

Mean-variance analysis and the single-period inventory problem

The classic single-period inventory problem, colloquially referred lo in the literature as the newsboy problem, is examined assuming the objective of maximizing a mean-variance utility function. This objective function is intended to reflect different attitudes of decision makers towards risk. The optimal order quantity is derived and it is shown that under risk aversion the amount that is ordered is less than the amount ordered under risk neutrality. On the other hand, it is shown that the optimal order quantity when the decision maker is a risk lover is greater than it would be were he risk neutral. The problem is also considered when the ordering cost includes a fixed cost component in addition to the purely variable quantity purchase cost. For this case, an optimal (s, Q) policy is derived (where s is the reorder point and Q is the order quantity).     

过度自信和需求不确定性对库存系统的影响

研究过度自信和需求不确定性对库存系统的影响。通过引入一个均值增加、方差缩小的变换来定量刻画决策者的过度自信水平,得到系统最优订货量和最优利润关于过度自信水平和单位缺货惩罚的单调性。证明随机大的需求会导致较高的最优订货批量,系统最优订货量在割准则序意义下具有随机单调性,并给出了比较系统最优订货量的充分或充分必要条件。进一步,运用标准化随机变量的变换证明了在高利润环境下系统利润将随着需求可变性的增加而减少。     

需求和回收品均随机的制造-再制造系统生产控制

需求及回收品数量和时间的不确定性, 导致制造-再制造系统的库存管理非常困难. 为控制库存尽可能位于某一合理区间内, 在假设库存水平变化由无负跳跃Lévy 过程描述条件下, 利用更新过程和鞅理论, 构建了系统期望折扣总费用模型, 并采用交叉熵法确定最优的生产速率和调整阈值. 最后, 通过仿真实验分析了回收品、需求和系统参数对最优控制策略和期望折扣费用的影响.     

Economic production quantity with rework process at a single-stage manufacturing system with planned backorders

In traditional inventory models such as the economic order quantity (EOQ) and the economic production quantity (EPQ) the sole objective is to minimize the total inventory-related costs, typically holding cost and ordering cost. These models do not consider the presence of defective products in the lot or rework of them. Recently, Jamal, Sarker, and Mondal (Jamal, A. A. M., Sarker, B. R., & Mondal, S., (2004). Optimal manufacturing batch size with rework process at single-stage production system. Computers and Industrial Engineering, 47(1), 77–89) proposed a model, which dealt with the optimum batch quantity in a single-stage system in which rework is done by addressing two different operational policies to minimize the total system cost, but their models do not consider planned backorders. In this direction, this paper develops an EPQ type inventory model with planned backorders for determining the economic production quantity for a single product, which is manufactured in a single-stage manufacturing system that generates imperfect quality products, and all these defective products are reworked in the same cycle. We also establish the range of real values of the proportion of defective products for which there is an optimal solution, and the close form for the total cost of inventory system. The use of the inventory model is illustrated with numerical examples. The classical EOQ, EPQ inventory models with or without planned backorders and Jamal, Sarker and Mondal’s model (Jamal, A. A. M., Sarker, B. R., & Mondal, S., (2004). Optimal manufacturing batch size with rework process at single-stage production system. Computers and Industrial Engineering, 47(1), 77–89) are shown to be special cases of the EPQ inventory model presented in this paper.     

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.     

需求不确定性对条件风险价值约束库存系统的影响

研究风险偏好和需求不确定性对库存系统的影响,证明最优订货量和最优利润关于缺货惩罚成本和风险水平的单调性。利用随机比较方法证明随机大需求导致较高的最优订货量,当不考虑缺货惩罚成本时随机大需求导致较高的最优利润;证明最优利润随需求可变性增加而减少,并给出相应的充分条件与充分必要条件;进一步证明存在一类需求分布,在一定条件下系统利润随需求可变性增加而增加。通过数值例子验证了所得研究结果。     

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.     

A fixed interval ordering policy for joint optimization of age replacement and spare part provisioning

A new policy is presented for the joint optimization of age replacement and spare provisioning. The policy, referred to as a fixed interval ordering policy, is formulated by combining an age replacement policy with a periodic review ( t₀,q) type inventory policy, where t0 is the order interval and q is the order quantity. It is generally applicable to any operating system with either a single item or a number of identical items. A SLAM based simulation model has been developed to determine the optimal values of the decision variables by minimizing the total cost of replacement and inventory. The behaviour of the policy has been studied for a number of case problems specifically constructed by five-factor second-order rotatory design and the effects of different cost elements and item failure characterisics have been highlighted. The performance of the proposed policy has also been compared with that of the stocking policy which incorporates a continuous review ( s, S) type of inventory policy, where s is the stock reorder level and S is the maximum stock level. Simulation results clearly indicate that the optimal fixed interval ordering policy is less expensive than the optimal stocking policy when the system consists of a large number of operating units.     

A joint model for cash and inventory management for a retailer under delay in payments

As retail companies continue to navigate through the economy downturn, it becomes critical to find innovative cost reduction methods. Cash management is a cost-intensive process for retailers, who are currently focusing on effective cash management, such as deciding on the maximum cash level to keep in their business accounts and how much to borrow to finance inventories and pay suppliers. In this paper, we consider the problem of finding the optimal operational (how much to order and when to pay the supplier) and financial decisions (maximum cash level and loan amount) by integrating the cash management and inventory lot sizing problems. We consider a supplier offering a retailer an interest-free credit period for settling the payment. Beyond this period, the supplier charges interest on the outstanding balance. Whenever the cash exceeds a certain limit, it will be invested in purchasing financial securities. At the time when the retailer pays the supplier for the received order, cash is withdrawn from the account, incuring various financial costs. If the cash level becomes zero or not sufficient, the retailer obtains an asset-based loan at interest. We model this problem as a nonlinear program and propose a solution procedure for finding the optimal solution. We perform a numerical study to analyze the impact of optimal cash management on the inventory decisions. The results indicate that the optimal order quantity decreases as the retailer’s return on cash increases. We compare our model to a model that ignores financial considerations of cash management, and show numerically that our model lowers the retailer’s cost. Also, we illustrate the effect of changing various model parameters on the optimal solution and obtain managerial insights.     

A supplier selection and order allocation problem with stochastic demands

We consider a system comprising a retailer and a set of candidate suppliers that operates within a finite planning horizon of multiple periods. The retailer replenishes its inventory from the suppliers and satisfies stochastic customer demands. At the beginning of each period, the retailer makes decisions on the replenishment quantity, supplier selection and order allocation among the selected suppliers. An optimisation problem is formulated to minimise the total expected system cost, which includes an outer level stochastic dynamic program for the optimal replenishment quantity and an inner level integer program for supplier selection and order allocation with a given replenishment quantity. For the inner level subproblem, we develop a polynomial algorithm to obtain optimal decisions. For the outer level subproblem, we propose an efficient heuristic for the system with integer-valued inventory, based on the structural properties of the system with real-valued inventory. We investigate the efficiency of the proposed solution approach, as well as the impact of parameters on the optimal replenishment decision with numerical experiments.     

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.     

Finite horizon EOQ model for non-instantaneous deteriorating items with price and advertisement dependent demand and partial backlogging under inflation

This paper deals with an economic order quantity (EOQ) model for non-instantaneous deteriorating items with price and advertisement dependent demand pattern under the effect of inflation and time value of money over a finite planning horizon. In this model, shortages are allowed and partially backlogged. The backlogging rate is dependent on the waiting time for the next replenishment. This paper aids the retailer in minimising the total inventory cost by finding the optimal interval and the optimal order quantity. An algorithm is designed to find the optimum solution of the proposed model. Numerical examples are given to demonstrate the results. Also, the effect of changes in the different parameters on the optimal total cost is graphically presented and the implications are discussed in detail.     

Mixture inventory model with back orders and lost sales for variable lead time demand with the mixtures of normal distribution

In recent papers by Ben-Daya and Raouf and by Ouyang et al. a continuous review inventory model is presented in which they considered both the lead time and the order quantity as decision variables. When the demands of the different customers do not have identical lead times, then we cannot use only a distribution (such as Ouyang et al. who used a normal distribution) to describe the demand of the lead time. Hence, we have extended the model of Ouyang et al. by considering the mixtures of normal distribution (see the book by Everitt and Hand). In addition, we also still assume that shortages are allowed. Moreover, the total amount of stock-out is considered as a mixture of back orders and lost sales during the stock-out period. Moreover, we also develop an algorithmic procedure to find the optimal order quantity and optimal lead time; the effects of parameters are also studied.     

缺货不补的随机存储系统的建模与仿真

基于(s,S)策略,讨论了缺货不通过到达的订货进行补充的随机存储系统.假定需求量、需求发生的间隔、以及提前时间都为随机变量,建立了系统的数学模型.给出库存总费用和缺货率的计算公式,将二者加权平均得到策略的综合系数.设计了系统仿真运行框图,在各种费用参数给定后,利用计算机仿真和综合系数来选定最优存储策略.