Two-phase pricing and inventory management for deteriorating and fashion goods under trade credit

This study models a finite horizon inventory problem for deteriorating and fashion goods under trade credit and partial backlogging conditions. Demand may vary with price or time. The supplier can extend credit to the retailer. As a result, the retailer does not have to pay for goods immediately upon acquiring them, and can instead earn interest on the retail price of the goods between the time they are sold and the end of the credit period. The proposed model considers two-phase pricing and inventory decisions. In other words, it determines both the optimal prices and the lengths of the in-stock and stock-out period. This paper is the first to consider different price decisions for in-stock and stock-out periods under trade credit. We develop an algorithm to determine the optimal pricing and replenishment strategy while still maximizing the total profit. Further, this study shows that the proposed two-phase pricing strategy is superior to a one-phase pricing strategy in terms of profit maximization. Computational analysis illustrates the solution procedures and the impacts of the related parameters on decisions and profits. The results of this study can serve as references for business managers or administrators.     

Effect of declining selling price: profit analysis for a single period inventory model with stochastic demand and lead time

In this paper, considering the empirical trend for sales and price of fashion apparels as prototype, optimal ordering policy for a single period stochastic inventory model is investigated. The impact of the presence of random lead time and declining selling price on the profitability of the retailer is explored. Existence of unique optimal solutions for net profit functions is proved. Numerical examples are presented to illustrate the method of identifying profitable levels of inventory holding and penalty costs. Percentage profit per unit investment in inventory is obtained in order to assist managers in taking business decisions, specifically to the extent of whether or not to take up a particular business under known constraints. It is demonstrated that the optimal inventory policy in the absence of price decline and lead time differs considerably from that when lead time and price decline are simultaneously considered.     

A profit-based scoring system in consumer credit: making acquisition decisions for credit cards

Consumer credit scoring is one of the most successful applications of quantitative analysis in business with nearly every major lender using charge-off models to make decisions. Yet banks do not extend credit to control charge-off, but to secure profit. So, while charge-off models work well in rank-ordering the loan default costs associated with lending and are ubiquitous throughout the industry, the equivalent models on the revenue side are not being used despite the need. This paper outlines a profit-based scoring system for credit cards to be used for acquisition decisions by addressing three issues. First, the paper explains why credit card profit models—as opposed to cost or charge-off models—have been difficult to build and implement. Second, a methodology for modelling revenue on credit cards at application is proposed. Finally, acquisition strategies are explored that use both a spend model and a charge-off model to balance tradeoffs between charge-off, revenue, and volume.     

Economic Batch-Size Determination for Multi-Product Scheduling

In the determination of batch-sizes in batch production, different criteria can be used as guiding principles, depending on the specified objectives. In a production schedule consisting of several products, an optimum solution for the whole production schedule is sought. At the same time it is necessary to ensure that the total production costs of each individual product will not exceed a certain pre-determined value. Solutions for overall optimization of the schedule with respect to maximum profit per batch, or with respect to maximum return on the total cost of production of the batch, have already been published. This paper suggests a method for determining the economic batch-sizes when it is desirable to maximize the rate of return per unit time for a multi-product schedule.     

Comments on: A comparative analysis for determining optimal price and order quantity when a sale increases demand

Although the net present value (NPV) criterion is theoretically the correct approach to developing optimal inventory policies, in the classical EOQ case, the average profit criterion generates solutions that are practically identical to those resulting from the NPV criterion. Nevertheless, a recent paper suggests that, when the demand for a product is price-elastic and a wholesaler offers a one-time-only price discount, use of the average profit criterion may obtain policies that are drastically suboptimal compared to the policies obtained by using the NPV criterion. We show that this suggestion is based on inaccurate models and inconsistent comparisons. Although in cases of large one-time-only discounts, there may be significant differences in the policies and consequences resulting from the two criteria, such large discounts are unrealistic. Furthermore, the larger the discount, the less practicable are the optimal order quantities based on either one of these criteria. Thus, in most real-life situations, the use of the average profit criterion does not result in serious suboptimization. In these situations, what may be important is not whether a retailer uses the NPV criterion or the average profit criterion, but whether the retailer can and does implement the optimal decisions resulting from the use of either criterion.     

随机产出下考虑小微供应商成本利润率的供应链决策研究

小微型供应商由于产能、资金等限制,其目标可能是实现成本利润率最优,从而提高企业生存能力。基于该观察,区别于多数文献采用利润最优决策准则,本文研究由小微供应商和零售商组成的单周期供应链决策问题。小微供应商面临产出随机风险,以成本利润率最大为目标进行产能决策,零售商以利润最大为目标确定最优订购量。研究发现小微供应商的成本利润率受到自身成本偏重系数以及零售商盈利能力的共同影响,将出现亏损、合理盈利、超额盈利三种情况。并且,零售商采取不同订货策略也会对小微供应商盈利情况产生差异影响。保守(积极)订货策略下,零售商是否盈利取决于自身单位净利润能否弥补单位缺货损失(自身可盈利空间)。本文研究融合现实普遍存在的产出随机问题,为小微供应商和其他供应链成员的产能/订购决策问题提供有益的管理启示。     

Inventory models for defective items incorporating marketing decisions with variable production cost

This paper investigates the finite replenishment inventory models of a single product with imperfect production process. In this process, a certain fraction or a random number of produced items are defective. These non-conforming items are rejected or reworked or if they reached to the customer, refunded. Here, a generalised unit cost function is formulated incorporating the several factors like raw material, labour, replenishment rate and others factors of the manufacturing system. The rate of replenishment is considered to be a variable. The selling price of an unit is determined by a mark-up over the production cost. Optimum production of the product is suggested to have maximum profit using a gradient based mathematical programming technique for optimization. Finally, numerical examples are given to illustrate the results and the significant features of the production system. As a particular case, the result of the perfect system (without defective items) are obtained. Also, the effect of changes in the selling rate, defectiveness, production cost and other parameters on the optimal average profit are graphically presented. Some interesting decisions regarding production policy are established.     

Modelling to optimise consumptive use of game

There has been a rapid increase in the number of private game ranches established in South Africa in recent years. These ranches are good for conservation but many are driven by the profit motive. A number of models have been used to help managers formulate strategies for achieving their economic objectives. These models are discussed and their use illustrated.A detailed sex and age structured model is presented first with an illustration of its use in attaining two different management objectives. For a given management objective this model generates the returns per unit of food consumed for each species. These returns are then fed into a model to determine the relative abundance of each species in a multispecies herbivory that is required to maximise income.Finally, some problems with the use of these models are discussed. Suggestions and current modelling activities towards improving the tools available to African game ranch managers are presented.     

Unbalanced Highway Contract Tendering

This paper deals with a central and recurrent concern of managers responsible for highway tendering: formulating unit bids for Unit Price Proposals. Unit Price Proposals are prepared by the client and indicate contract items and (estimated) quantities deemed necessary to accomplish the proposal objective. The bidder is required to indicate unit prices or bids. These unit bids are multiplied by the indicated quantities and summed to arrive at the bid total. Virtually every tender (bid) is unbalanced in order to improve cash flow. Often the unbalancing is neither competent nor conscious. A linear programming model was devised to determine unit bids that maximize the present worth of future profit. The model characterizes the managerial environment with uncommon competence. Examples illustrate features of implementation. The model is especially useful for large and complicated contracts of long duration. These linear models have the remarkable feature that, for given project information, no other means of unbalancing will yield a greater present worth.     

Real R&D options and optimal activation of two-dimensional random controls

We value investments under uncertainty with embedded optional costly controls (impulse-type with uncertain outcome) that capture managerial intervention for value enhancement and/or information acquisition (exploration, R&D, advertising, marketing research, etc). Implementing real option models but neglecting such embedded managerial actions can severely underestimate investment opportunities and lead to erroneous investment decisions. Optimal decisions are solutions to a maximization problem where the trade-off between the control's cost and the value added by such actions is explicitly taken into consideration. In this paper, we generalize such a methodology from one dealing with the special case of actions affecting only one state-variable, to one with actions that affect several. Asset values follow geometric Brownian motion or jump-diffusion processes with multiple generating sources of jumps. The Markov-chain numerical methodology we provide can handle sequential controls. Although we report the results with open-loop policies, the approach can be readily extended to accommodate dependency among the controls.     

Bank branch sales evaluation using extended value efficiency analysis

This article results from our collaborative project with a Finnish bank aiming to evaluate the sales performance of bank branches. The management wishes to evaluate the branches’ ability to generate profit, which rules out the pure technical efficiency considerations. The branches operate in heterogeneous environments. We deal with the heterogeneity by subdividing the branches according to the bank specification into overlapping clusters and analyze each cluster separately. The prices of the branch outputs are hard to assess as the results from the sales efforts can only be observed with long delays. We employ benchmark units similarly as in value efficiency analysis (VEA). However, we extend VEA in two ways. First, in standard VEA the benchmark unit is assumed to yield the maximum profit among the set of feasible technologies; instead, our benchmark technology may or may not be in the feasible set. Second, we consider efficiency tests employing a benchmark with respect to both profit and return. We propose a solution strategy for these extensions. The bank uses the study to support decisions concerning new branches, changes in the operations of inefficient branches, and actions aiming to more flexible deployment of the staff.     

再制造中零件供应系统整合优化研究

再制造企业里,在决策购买新零件或修复旧零件时,经常面对有限的拆卸修复信息和不确定的订货提前期.为了得到科学的决策,人们试图尽早地掌握拆卸修复零件的确切信息,与有能力的供应商建立良好的关系,或在企业建立管理信息系统来统计分析废旧品的状态和数量等.根据市场需求和产品批发价,以满足市场需求所要购买新零件数和拆卸修复机器数为决策变量,并考虑拆卸修复成功的概率,建立企业期望利润的数学模型,求得可能情况下的最优解或现实满意解.洞察再制造企业取得最大利润的主要影响因数及这些因数间的关系,为制作生产计划提供理论依据.最后指出进一步的研究问题.     

Decentralized Business Strategies in a Multi-Unit Firm

In a multi-unit firm, such as a retail chain or a multi-plant manufacturer, we compare the business strategies developed by unit managers with the strategies that maximize corporate profit. The setting is one in which units face different markets and where learning spillovers between two units are enhanced if their strategies are more similar. When there is a small number of units, we find a tendency for managers' strategies to be excessively tailored to their local market. When the firm has many units, unit strategies can be either excessively or insufficiently standardized.     

A discrete long-term location–price problem under the assumption of discriminatory pricing: Formulations and parametric analysis

We consider a competitive location problem in which a new firm has to make decisions on the locations of several new facilities as well as on its price setting in order to maximise profit. Under the assumption of discriminatory prices, competing firms set a specific price for each market area. The customers buy one unit of a single homogeneous price-inelastic product from the facility that offers the lowest price in the area the consumers belong to. Three customer choice rules are considered in order to break ties in the offered prices. We prove that, considering long-term competition on price, this problem can be reduced to a problem with decisions on location only. For each one of the choice rules the location problem is formulated as an integer programming model and a parametric analysis of these models is given. To conclude, an application with real data is presented.     

Fuzzy profit measures for a fuzzy economic order quantity model

Changing economic conditions make the selling price and demand quantity more and more uncertain in the market. The conventional inventory models determine the selling price and order quantity for a retailer’s maximal profit with exactly known parameters. This paper develops a solution method to derive the fuzzy profit of the inventory model when the demand quantity and unit cost are fuzzy numbers. Since the parameters contained in the inventory model are fuzzy, the profit value calculated from the model should be fuzzy as well. Based on the extension principle, the fuzzy inventory problem is transformed into a pair of two-level mathematical programs to derive the upper bound and lower bound of the fuzzy profit at possibility level α. According to the duality theorem of geometric programming, the pair of two-level mathematical programs is transformed into a pair of conventional geometric programs to solve. By enumerating different α values, the upper bound and lower bound of the fuzzy profit are collected to approximate the membership function. Since the profit of the inventory problem is expressed by the membership function rather than by a crisp value, more information is provided for making decisions.     

MIP models for production lot sizing problems with distribution costs and cargo arrangement

This study presents mixed integer programming (MIP) models for production lot sizing problems with distribution costs using unit load devices such as pallets and containers. Problems that integrate production lot sizing decisions and loading of the products in vehicles (bins) are also modelled, in which constraints such as weight limits, volume restrictions or the value of the cargo loaded in the bins are considered. In general, these problems involve a trade-off between production, inventory and distribution costs. Lot sizing decisions should take into account production capacity and product demand constraints. Distribution decisions are related to the loading and transport of products in unit load devices. The MIP models are solved by the branch-and-cut method of an optimization package and the results show that these approaches have the potential to address different practical situations.     

Selective maintenance for support equipment involving multiple maintenance actions

Selective maintenance is the process of identifying a subset among sets of desirable maintenance actions. Previous works use mathematical programming models for making selective maintenance decisions for production equipment and military vehicles, which perform sequences of missions and are repaired only between missions. In this paper, extensions of these models are proposed. First, system component life is assumed to follow Weibull distributions. Second, the decision-maker is given multiple maintenance options: minimal repair on failed components, replacement of failed components, and replacement of functioning components (preventive maintenance).     

Optimizing pig marketing decisions under price fluctuations

In the manufacturing of fattening pigs, pig marketing refers to a sequence of culling decisions until the production unit is empty. The profit of a production unit is highly dependent on the price of pork, the cost of feeding and the cost of buying piglets. Price fluctuations in the market consequently influence the profit, and the optimal marketing decisions may change under different price conditions. Most studies have considered pig marketing under constant price conditions. However, because price fluctuations have an influence on profit and optimal marketing decisions it is relevant to consider pig marketing under price fluctuations. In this paper we formulate a hierarchical Markov decision process with two levels which model sequential marketing decisions under price fluctuations in a pig pen. The state of the system is based on information about pork, piglet and feed prices. Moreover, the information is updated using a Bayesian approach and embedded into the hierarchical Markov decision process. The optimal policy is analyzed under different patterns of price fluctuations. We also assess the value of including price information into the model.

     

Optimal inventory policies for profit maximizing EOQ models under various cost functions

In this paper, we establish and analyze three EOQ based inventory models under profit maximization via geometric programming (GP) techniques. Through GP, we find optimal order quantity and price for each of these models considering production (lot sizing) as well as marketing (pricing) decisions. We also investigate the effects on the changes in the optimal solutions when different parameters are changed. In addition, a comparative analysis between the profit maximization models is conducted. By investigating the error in the optimal price, order quantity, and profit of these models, several interesting economic implications and insights can be observed.     

基于双边市场理论的金融超市竞争定价策略研究

基于双边市场理论,重点分析金融超市在双寡头垄断情形下的竞争定价策略。即在在一般定价模型的基础上,构建起加入金融超市双边用户交易次数为歧视标准的价格歧视竞争模型。并且围绕金融超市追求长期利益和短期利益两种不同动机,对采取该策略均衡时最终用户的均衡进入价格、金融超市利润和市场份额进行比较分析。最后,给出金融超市实施价格歧视策略的对策和建议。