Incorporating one-way substitution policy into the newsboy problem with imprecise customer demand

This paper presents an approach for solving an inventory model for single-period products with maximizing its expected profit in a fuzzy environment, in which the retailer has the opportunity for substitution. Though various structures of substitution arise in real life, in this study we consider the fuzzy model for two-item with one-way substitution policy. This one-way substitutability is reasonable when the products can be stored according to certain attribute levels such as quality, brand or package size. Again, to describe uncertainty usually probability density functions are being used. However, there are many situations in real world that utilize knowledge-based information to describe the uncertainty. The objective of this study is to provide an analysis of single-period inventory model in a fuzzy environment that enables us to compute the expected resultant profit under substitution. An efficient numerical search procedure is provided to identify the optimal order quantities, in which the utilization of imprecise demand and the use of one-way substitution policy increase the average expected profit. The benefit of product substitution is illustrated through numerical example.     

An alternative formulation for the fuzzy assignment problem

The existing assignment problems for assigning n jobs to n individuals are limited to the considerations of cost or profit measured as crisp. However, in many real applications, costs are not deterministic numbers. This paper develops a procedure based on Data Envelopment Analysis method to solve the assignment problems with fuzzy costs or fuzzy profits for each possible assignment. It aims to obtain the points with maximum membership values for the fuzzy parameters while maximizing the profit or minimizing the assignment cost. In this method, a discrete approach is presented to rank the fuzzy numbers first. Then, corresponding to each fuzzy number, we introduce a crisp number using the efficiency concept. A numerical example is used to illustrate the usefulness of this new method.     

考虑废旧品质量的闭环供应链混合回收渠道选择研究

为确定最优的回收渠道,对由单个制造商、零售商和第三方组成的闭环供应链系统进行研究。在该系统中,可能存在制造商和零售商、制造商和第三方、零售商和第三方以及制造商、零售商和第三方同时回收的四种渠道,并根据质量差异对废旧品进行翻新或再制造。在分散决策下建立了四种回收渠道模型。比较发现:站在制造商和系统收益最大化及社会效益角度,三渠道是最佳选择,此时得到的废旧品最多;制造商不进行回收时获利最低,且不利于提高废旧品的获取量。最后,通过算例剖析了废旧品再制造率对四种混合回收渠道下成员及系统利润的影响。结果表明:制造商应尽量将废旧品用于再制造。     

A Bayesian Approach to the Two-period Style-goods Inventory Problem with Single Replenishment and Heterogeneous Poisson Demands

This paper presents a model of the two-period style-goods inventory problem for a firm which stocks many hundreds of distinctive items having heterogeneous Poisson demands. The model uses a Bayesian procedure for forecast and probability revisions based on an aggregation-by-items scheme. These revised forecasts are then incorporated into a model which is used to derive the optimal inventory-stocking policies which maximize expected profit during the season. The model is illustrated using an actual case study of inventory planning for unframed poster art.     

A Crop Planning Problem with Fuzzy Random Profit Coefficients

The main purpose of this paper is to present a crop planning problem for agricultural management under uncertainty. It is significant that agricultural managers assign their limited farmlands to cultivation of which crops in a season. This planning is called the crop planning problem and influences their incomes for the season. Usually, the crop planning problem is formulated as a linear programming problem. But there are many uncertain factors in agricultural problems, so future profits for crops are not certain values. A linear programming model with constant profit coefficients may not reflect the environment of decision making properly. Therefore, we propose a model of crop planning with fuzzy profit coefficients, and an effective solution procedure for the model. Furthermore, we extend this fuzzy model, setting the profit coefficients as discrete randomized fuzzy numbers. We show concrete optimal solutions for each models.     

Incorporating market characteristics into physical distribution models

This paper is concerned with incorporating the interactive effects of location, price and demand into mathematical models of distribution systems. Equations for distribution costs, capital investment, demand and gross profit margin are introduced and from these, profit and return on investment equations are derived. For a given number of depots, a search procedure is derived to determine the locations of the depots which maximise the derived profit equation. A similar search procedure is derived to maximise return on investment. The maximum profit and maximum return on investment solutions are compared and it is deduced that for a fixed gross profit margin, these solutions will be almost identical. Finally, the search procedures are applied to real data and observations are made on how the type of location determined by the search procedures varies as the market characteristics vary.     

Differentiability of average profit as a function of the cycle-level period

It is proved that profit and average profit considered as level functions are continuously differentiable along the level cycle for a typical continuous control system on the circle with positive speeds and a differentiable profit density with finitely many critical points. __________ Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 38, Suzdal Conference-2004, Part 3, 2006.     

Modeling churn using customer lifetime value

The definition and modeling of customer loyalty have been central issues in customer relationship management since many years. Recent papers propose solutions to detect customers that are becoming less loyal, also called churners. The churner status is then defined as a function of the volume of commercial transactions. In the context of a Belgian retail financial service company, our first contribution is to redefine the notion of customer loyalty by considering it from a customer-centric viewpoint instead of a product-centric one. We hereby use the customer lifetime value (CLV) defined as the discounted value of future marginal earnings, based on the customer’s activity. Hence, a churner is defined as someone whose CLV, thus the related marginal profit, is decreasing. As a second contribution, the loss incurred by the CLV decrease is used to appraise the cost to misclassify a customer by introducing a new loss function. In the empirical study, we compare the accuracy of various classification techniques commonly used in the domain of churn prediction, including two cost-sensitive classifiers. Our final conclusion is that since profit is what really matters in a commercial environment, standard statistical accuracy measures for prediction need to be revised and a more profit oriented focus may be desirable.     

An instantaneous replenishment model under the effect of a sampling policy for defective items

We propose to study a EOQ-type inventory model with unreliable supply, with each order containing a random proportion of defective items. Every time an order is received, an acceptance sampling plan is applied to the lot, according to which only a sample is inspected instead of the whole lot. If the sample conforms to the standards, i.e. if the number of imperfect items is below an “acceptance number”, no further screening is performed. Otherwise, the lot is subject to 100% screening. We formulate an integer non-linear mathematical program that integrates inventory and quality decisions into a unified profit model, to jointly determine the optimal lot size and optimal sampling plan, characterized by a sample size, and an acceptance number. The optimal decisions are determined in a way to achieve a certain average outgoing quality limit (AOQL), which is the highest proportion of defective items in the outgoing material sold to customers. We provide a counter-example demonstrating that the expected profit function, objective of the mathematical program, is not jointly concave in the lot and sample size. However, we show that for a given sampling plan, the expected profit function is concave in the lot size. A solution procedure is presented to compute the optimal solution. Numerical analysis is provided to gain managerial insights by analyzing the impact of changing various model parameters on the optimal solution. We also show numerically that the optimal profit determined using this model is significantly higher when compared to the optimal profit obtained using Salameh and Jaber (2000)’s [1] model, indicating much higher profits when acceptance sampling is used.     

A heuristic for the one-dimensional cutting stock problem with usable leftover

A heuristic algorithm for the one-dimensional cutting stock problem with usable leftover (residual length) is presented. The algorithm consists of two procedures. The first is a linear programming procedure that fulfills the major portion of the item demand. The second is a sequential heuristic procedure that fulfills the remaining portion of the item demand. The algorithm can balance the cost of the consumed bars, the profit from leftovers and the profit from shorter stocks reduction. The computational results show that the algorithm performs better than a recently published algorithm.     

On stochastic management modeling with dependent variables

This paper presents an integrated framework for handling dependent random variables in a large class of stochastic management models, a class that includes stochastic break-even analysis and stochastic present-value analysis. We first demonstrate that the common approach of modeling dependent random variables is usually surprisingly inadequate, and a general “functional approach” is presented as a practical modeling alternative. Adopting this modeling approach, we then present a procedure for deriving the stochastic characteristics of the model's objective variable. In the context of stochastic breakeven analysis, this means determining the probabilities of achieving various profit levels and the expected utility of the stochastic profit. The procedure allows the model's random variables to assume diverse distribution and dependency forms, and the simplicity and reliability of the procedure is demonstrated by a numerical example.     

An iterative three-component heuristic for the team orienteering problem with time windows

This paper studies the team orienteering problem with time windows, the aim of which is to maximize the total profit collected by visiting a set of customers with a limited number of vehicles. Each customer has a profit, a service time and a time window. A service provided to any customer must begin in his or her time window. We propose an iterative framework incorporating three components to solve this problem. The first two components are a local search procedure and a simulated annealing procedure. They explore the solution space and discover a set of routes. The third component recombines the routes to identify high quality solutions. Our computational results indicate that this heuristic outperforms the existing approaches in the literature in average performance by at least 0.41%. In addition, 35 new best solutions are found.     

Stochastic Breakeven Analysis

This paper presents a practical approach for studying the profit probability distribution defined in stochastic breakeven analysis. After presenting a procedure for calculating the mean and the second to fourth central moments of the profit distribution, the several important uses of these four moments are discussed. A major application of the four moments is in the fitting of a Pearson's curve. Using a numerical example in conjunction with a set of published tables, we then demonstrate the simplicity of our proposed approach as well as the resultant high accuracy in estimating probabilities of various profit levels.     

求解最大利润流问题的一个算法

为了便于建立与最大利润流问题有关的决策支持系统，本给出了一个交易网络中求最大利润流的数值算法，证明了算法的理论依据，并举例了说明算法的应用。该算法能求得问题的最优解，并具有易于编程实现、收敛性好等优点，大量数值实验表明该算法非常实用有效。     

虚拟企业收益分配问题博弈研究

收益分配是虚拟企业的一个敏感而关键的问题，制订合理的收益分配方案对虚拟企业无疑是重要的。本分析了虚拟企业收益分配过程应考虑的因素，在此基础上应用博弈论建立了虚拟企业收益分配的博弈模型，并进行了相关分析，所得出的结论可用于虚拟企业的收益分配策略的制订，最后，论证了在虚拟企业中进行合作机制设计和应用的必要性。     

生猪生产的最优利润

线性规划（ＬＰ）用于确定饲料最低费用配比已有多年的历史。但确定饲料配比仅是农场主所关心的一件事，他们的主要目的是为了从生产中获取最大的利润。本文提出了基于ＬＰ的饲料规划方案，以便使猪是佳地生长，同时也使养猪者获取更大的生产利润。在最大利润模型中，售价和重量的乘积作为收入，饲料费和间接费作为成本。解中包括猪饲料的总量和猪应有的最佳重量。为了把猪的生长模式引入到ＬＰ模型中，我们用数学生长函数来表达生长率和猪龄之间的关系。该函数是经过适当的转化，用回归方法估算出来的。猪在不同生长阶段的营养需求是依据其生长模型和饲料转化率分析的。把上述结果全都引用到ＬＰ模型中，这样可以使利润最优化。实际数据的检验表明：在实践中，ＬＰ模型的结果是合理的。     

正交试验设计在麦白霉素高产菌株选育中的应用

本文应用正交试验设计改进了麦白霉素的生产工艺，在四个关键环节上选出了比对照组高出７００μ／ｍｌ以上的高产稳定菌株。该法使试验次数减少，选育周期缩短，既节省了人力物力和降低了生产成本，又增加了麦白霉素药粉的产量，取得了可观的经济效益。     

Strategic oscillation for the quadratic multiple knapsack problem

The quadratic multiple knapsack problem (QMKP) consists in assigning a set of objects, which interact through paired profit values, exclusively to different capacity-constrained knapsacks with the aim of maximising total profit. Its many applications include the assignment of workmen to different tasks when their ability to cooperate may affect the results. Strategic oscillation (SO) is a search strategy that operates in relation to a critical boundary associated with important solution features (such as feasibility). Originally proposed in the context of tabu search, it has become widely applied as an efficient memory-based methodology. We apply strategic oscillation to the quadratic multiple knapsack problem, disclosing that SO effectively exploits domain-specific knowledge, and obtains solutions of particularly high quality compared to those obtained by current state-of-the-art algorithms.     

A Simple Algorithm for the Nucleolus of Airport Profit Games

In this paper we present a procedure for calculating the nucleolus for airport profit games which are a generalization of the airport cost games.     

Customer rebates and retailer incentives in the presence of competition and price discrimination

Promotions are important tools for matching supply and demand in many industries. In the United States automotive industry, promotions are frequently offered, which may be given directly to customers (rebates) or given to dealers (incentives) to stimulate demand. We analyze the performance of customer rebate and retailer incentive promotions under competition. We study a setting with two manufacturers making simultaneous pricing and promotion decisions, and with two price-discriminating retailers as Stackelberg followers making simultaneous order quantity decisions. In the benchmark case with no promotions, we characterize the equilibria in closed form. We find that retailer incentives can be used by manufacturers to simultaneously improve each of their profits but can potentially lead to lower retailer profits. When manufacturers use customer rebates, we show that a manufacturer is able to decrease the profit of her competitor while increasing her own profit, although she is also at risk for her competitor to use rebates in a similar fashion. Unlike the monopoly case where the manufacturers are always better off with retailer incentives, customer rebates can be more profitable under some cases in the presence of competition. Using numerical examples we generate insights on the manufacturers’ preference of promotions in different market settings.