Ordering and pricing of service products in an advance sales system with price-dependent demand

This investigation addresses a service inventory control problem in which a firm orders and sells a service which will be used or consumed by customers on a specific future date. The firm sells the product through an advance booking system, aiming to optimize product price to maximize the total expected profit. Considering situations in which product demand is price-dependent and customers with reservations may cancel advance orders, this work develops a continuous-time model to simultaneously determine the order quantity and selling prices. The analytical results reveal that the optimal ordering quantity and prices are derived via closed-form solutions. In addition, sensitivity analysis of the optimal prices with respect to the system parameters is also conducted to illustrate optimal decision characteristics.     

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.     

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.     

Optimal selling price and lotsize with time varying deterioration and partial backlogging

The article deals with an EOQ (economic order quantity) model over an infinite time horizon for perishable items where demand is price dependent and partial backorder is permitted. The rate of deterioration is taken to be time proportional and it is assumed that shortage occurs at starting of the inventory cycle. Based on the partial backlogging and lost sale cases, the author develops the criterion for the optimal solution for the replenishment schedule, and proves the optimal ordering policy is unique. Moreover, the article suggests to new functions regarding price-dependent demand and time varying deterioration rate. Finally, numerical examples are illustrated to test the model in various issues.     

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.     

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。     

A newsvendor model with fuzzy price-dependent demand

Price-dependence is an important characteristic for some inventory problems. This paper proposes a newsvendor model with fuzzy price-dependent demand, and discusses the conditions to determine the optimal pricing and inventory decisions jointly so that the expected profit could be maximized. Then an algorithm combining the method of ranking fuzzy numbers is developed to tackle the problem. Furthermore, comparison is made between the fuzzy model and the deterministic model to study the effect of the uncertain price-dependent demand, and the sensitivity properties of the joint optimal decisions are illustrated through numerical examples.     

基于Backroom Effect的生鲜品零售库存决策优化

本文基于传统的Backroom Effect,考虑生鲜品零售中普遍存在的现象——仓库较之货架具有更为优越的腐损控制和保鲜能力,重新定义了仓库在保管生鲜品过程中存在的数量与保鲜方面的双重Backroom Effect。基于此,面向生鲜品零售商,研究包括仓库-货架补给决策以及订货补给的库存决策优化问题,并利用数值算例剖析了Backroom Effect下,货架与仓库存在的腐损率差异对零售商库存决策和相应利润的影响。文章的主要结论包括:生鲜零售商应在零售库存决策中充分考虑Backroom Effect的影响,借助其提高生鲜品的最优订货量,从而带来单位时间平均利润的提升;随着Backroom Effect效果的提升,零售商的最优订货量和对应的平均利润也随之增加;不同品类的生鲜品对Backroom Effect的敏感程度不同,零售商在进行仓库保鲜投资时应优先投资更易腐损且具有更高边际利润的生鲜品品种。     

需求依赖价格下港口存货质押业务中质押率研究

港口与银行合作办理质押贷款业务,不仅能增加港口的存储收入和金融收入,同时也能吸引更多的客户,从而增加其主营业务收入。在银行统一授信港口情况下,本文分析了质押物品的需求依赖价格条件下,风险中性的港口质押贷款业务中的最优质押率计算方法。并分别分析了在乘积型和加型随机需求函数条件下,质押产品价格、企业违约概率和质押物品数量以及质押期限对最优质押率和港口最大期望收益的影响,并通过数值分析验证了所有结论。     

不确定性对混合CVaR约束库存系统的影响

运用应用概率中的随机占优研究需求不确定性对混合CVaR约束库存系统最优订购量和最优利润的影响。引入刻画决策者风险态度的“风险偏好系数”,得到系统最优订购量和最优利润关于风险偏好系数的单调性。研究表明随机大需求总会导致系统较高的最优订购量和最优利润;在割准则序意义下,最优订购量可能随需求可变性的增加而增加也可能随需求可变性的增加而减少;在二阶随机占优且风险偏好系数大于等于1的情况下系统最优利润具有随机单调性,然而当风险偏好系数小于1时最优利润在二阶随机占优意义下的结论不一定成立,我们通过一个数值例子来说明。     

An inventory model for a deteriorating item with displayed stock dependent demand under fuzzy inflation and time discounting over a random planning horizon

An inventory model for a deteriorating item (seasonal product) with linearly displayed stock dependent demand is developed in imprecise environment (involving both fuzzy and random parameters) under inflation and time value of money. It is assumed that time horizon, i.e., period of business is random and follows exponential distribution with a known mean. The resultant effect of inflation and time value of money is assumed as fuzzy in nature. The particular case, when resultant effect of inflation and time value is crisp in nature, is also analyzed. A genetic algorithm (GA) is developed with roulette wheel selection, arithmetic crossover, random mutation. For crisp inflation effect, the total expected profit for the planning horizon is maximized using the above GA to derive optimal inventory decision. On the other hand when inflationary effect is fuzzy then the above expected profit is fuzzy in nature too. Since optimization of fuzzy objective is not well defined, the optimistic/pessimistic return of the expected profit is obtained using possibility/necessity measure of fuzzy event. Fuzzy simulation process is proposed to determine this optimistic/pessimistic return. Finally a fuzzy simulation based GA is developed and is used to maximize the above optimistic/pessimistic return to get optimal decision. The models are illustrated with some numerical examples and some sensitivity analyses have been presented.     

Keep or return? Managing ordering and return policies in start-up companies

Start-up companies are considered an important factor in the success of a nation’s economy. We are interested in the decisions for long-term survival of these firms when they have considerable cash restrictions. In this paper we analyse several inventory control models to manage inventory purchasing and return policies. The Markov decision models are formulated for both established companies that look at maximising average profit and start-up companies that look at maximising their long-term survival probability. We contrast both objectives, and present properties of the policies and the survival probabilities. We find that start-up companies may need to be riskier if the return price is very low, but there is a period where a start-up firm becomes more cautious than an established company and there is a point, as it accumulates capital, where it starts behaving as an established firm. We compare the various models and give conditions under which their policies are equivalent.     

The multi-period newsboy problem

We will try to generalize the so-called newsboy model so that we can deal with unsatisfied demand or unsold quantity. Consider the time interval that consists of multiple ordering cycles. Assume that the probability density function of demand is given for each cycle. Then our problem is to make the ordering plan with which we can maximize the expected profit. In the classical newsboy model ordering quantity is always equal to the (planned) initial inventory level. But if we take account of unsatisfied demand and unsold quantity, the (desired) ordering quantity must be determined by a proper stochastic rule. Then, in stead of determining the ordering quantity of each cycle, we must plan the initial inventory level so that the expected profit may be maximized. If unsold exists in present cycle, the ordering quantity of next cycle becomes smaller than the planned inventory level. And if unsatisfied demand exists in the present cycle, the ordering quantity of next cycle becomes larger than the planned inventory level.     

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.

     

退货情形下基于替代率的两产品联合订货决策研究

研究了一类在产品订货模型中考虑客户退货和产品间替代的两产品联合最优订货决策问题.假定客户以一概率退回其所购产品,退货产品经修复后可重新在市场上进行销售,销售期末未售出的商品只能在二级市场上降价处理,且不同产品间存在替代关系,销售商以自身利润最大化为目标确定两产品的订货量,得到其最优订货量及一些性质.研究结果表明:在允许退货的背景下,替代策略的采用将会进一步提高销售商利润.     

Integrated inventory model with quantity discount and price-sensitive demand

Quantity discount has been a subject of study for a long time; however, little is known about its effect on integrated inventory models when price-sensitive demand is placed. The objective of this study is to find the optimal pricing and ordering strategies for an integrated inventory system when a quantity discount policy is applied. The pricing strategy discussed here is one in which the vendor offers a quantity discount to the buyer. Then, the buyer will adjust his retail price based on the purchasing cost, which will influence the customer demand as a result. Consequently, an integrated inventory model is established to find the optimal solutions for order quantity, retail price, and the number of shipments from vendor to buyer in one production run, so that the joint total profit incurred has the maximum value. Also, numerical examples and a sensitivity analysis are given to illustrate the results of the model.     

Optimal spot market inventory strategies in the presence of cost and price risk

We consider a firm facing random demand at the end of a single period of random length. At any time during the period, the firm can either increase or decrease inventory by buying or selling on a spot market where price fluctuates randomly over time. The firm’s goal is to maximize expected discounted profit over the period, where profit consists of the revenue from selling goods to meet demand, on the spot market, or in salvage, minus the cost of buying goods, and transaction, penalty, and holding costs. We first show that this optimization problem is equivalent to a two-dimensional singular control problem. We then use a recently developed control-theoretic approach to show that the optimal policy is completely characterized by a simple price-dependent two-threshold policy. In a series of computational experiments, we explore the value of actively managing inventory during the period rather than making a purchase decision at the start of the period, and then passively waiting for demand. In these experiments, we observe that as price volatility increases, the value of actively managing inventory increases until some limit is reached.     

Quantity discounts based on the previous order in a two-period inventory model with demand uncertainty

We examine quantity discount contracts between a manufacturer and a retailer in a stochastic, two-period inventory model. The retailer places an order in each of the two periods to meet stochastic demands. The manufacturer gives the retailer a price discount on purchases in the second period in excess of the first-period order quantity (incremental QDP) or a price discount for all units ordered in the second period if the retailer orders more in the second period than in the first period (all-units QDP). We show that the retailer's optimal ordering decision in the second period depends on the sum of initial inventory and previous order quantity. Our computational study suggests that the QDP contract induces the retailer to buy more in the second period but less in the first period, while the increase of the total order quantity may not be significant; and that it increases the manufacturer's profit only when the wholesale margin is large relative to the retail margin.     

Coordinating order quantity decisions in the supply chain contract under random demand

In this paper, we are concerned with the coordinating quantity decision problem in a supply chain contract. The supply chain contract is composed of one manufacturer and one retailer to meet the random demand of a single product with a short lifecycle. Our analysis show that the retailer expects to obtain higher profit under proper ordering policies, which can also maximize the expected profit of the supply chain. The manufacturer may induce the retailer to order the coordinated quantity by adjusting the unit return price. As a result, the supply chain is expected to achieve the optimal expected profit.     

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.