Product line selection and pricing analysis: Impact of genetic relaxations

A model for the product line selection and pricing problem (PLSP) is presented andthree solution procedures based on a genetic algorithm are developed to analyze the results based on consumer preference patterns. Since the PLSP model is nonlinear and integer, two of the solution procedures use genetic encoding to “relax” the NP hard model. The relaxations result in linear integer and shortest path models for the fitness evaluation which are solved using branch and bound and labeling algorithms, respectively. Performance of the quality of solutions generated by the procedures is evaluated for various problem sizes and customer preference structures. The results show that the genetic relaxations provide efficient and effective solution methodologies for the problem, when compared to the pure artificial intelligence technique of genetic search. The impact of the preference structure on the product line and the managerial implications of the solution characteristics generated by the genetic relaxations are also discussed. The models can be used to explicitly consider tradeoffs between marketing and operations concerns in designing a product line.     

Capacity planning with congestion effects

Important operational performance measures for a successful firm include not only price and quality, but also fast and on time delivery of customer orders. Capacity is a key issue in determining the lead time from customer order to delivery. However, capacity planning models seldom consider the impact of capacity levels on lead time performance. An important characteristic of this paper is the incorporation of congestion effects and their impact on lead time in making capacity acquisition decisions. It is especially important in a make-to-order environment, where customer orders arrive randomly and lead to high variability and congestion. This work was motivated by our observations of such tradeoffs at firms in several industries. We present a model to make equipment choice decisions in a multi-product, multi-machine, and single-stage production environment with congestion effects. The model is a nonlinear integer program. We present a heuristic solution procedure for this problem, which is based on a lower bound for the formulation that can be solved efficiently. The computational study shows that the solution procedure is quite effective in solving industry size problems. We illustrate the application of the model using data from a chemical-testing laboratory. We also discuss various extensions of the model.     

An integral LP relaxation for a drayage problem

This paper investigates a drayage problem, where a fleet of trucks must ship container loads from a port to importers and from exporters to the same port, without separating trucks and containers during customer service. We present three formulations for this problem that are valid when each truck carries one container. For the third formulation, we also assume that the arc costs are equal for all trucks, and then we prove that its continuous relaxation admits integer optimal solutions by checking that its constraint matrix is totally unimodular. Under the same hypothesis on costs, even the continuous relaxations of the first two models are proved to admit an integer optimal solution. Finally, the third model is transformed into a circulation problem, that can be solved by efficient network algorithms.     

集中通勤接送服务的最小化成本模型及算法

本文针对集中通勤接送服务业务流程中的车次分配与调度问题,建立了以最小化成本为目标的0-1混合整数规划模型,刻画了该问题所具有的多目标抵达地、多车协作、多行程车次等特征事实,同时考虑顾客满意度,以获得不同满意度下的近似最小成本。根据问题的复杂性和大规模性,设计开发了一种基于kNN思想的类标签启发式算法求解模型,拓展了构造路径的方法。算例数值结果表明,本文所设计模型和算法是有效性、可行的。     

The Delivery Man Problem with time windows

In this paper, a variant of the Traveling Salesman Problem with Time Windows is considered, which consists in minimizing the sum of travel durations between a depot and several customer locations. Two mixed integer linear programming formulations are presented for this problem: a classical arc flow model and a sequential assignment model. Several polyhedral results are provided for the second formulation, in the special case arising when there is a closed time window only at the depot, while open time windows are considered at all other locations. Exact and heuristic algorithms are also proposed for the problem. Computational results show that medium size instances can be solved exactly with both models, while the heuristic provides good quality solutions for medium to large size instances.     

竞争环境下截流设施选址问题

研究企业新建设施时,市场上已有设施存在的情况下,使本企业总体利润最大的截流设施选址问题。在一般截留设施选址模型的基础上引入引力模型,消费者到某个设施接受服务的概率与偏离距离及设施的吸引力相关,同时设施的建设费用与设施吸引力正相关,建立非线性整数规划模型并使用贪婪算法进行求解。数值分析表明,该算法求解速度快,模型计算精度较高。     

Efficient shift scheduling in the retail sector through two-stage optimization

Efficient workforce scheduling has an important impact on store profit and customer service. Standard scheduling problems do not recognize the effect of staff availability on customer sales, however, even though the latter is an important factor in the retail sector. In this paper a two-stage model is proposed for this purpose. In the first stage a sales response model is used to specify hourly staff requirements. The output of the sales response model is then used as the input of a mixed integer optimization model, which finds an optimum assignment of the staff to daily shifts. Simulations are used to validate the sales response function, and to revise the model for more accurate results. In the simulations, customer arrivals and sales response error values are generated using appropriate distribution functions. As a case study the proposed model is applied to a Turkish retailer in the apparel sector.     

Solving Planning and Design Problems in the Process Industry Using Mixed Integer and Global Optimization

This contribution gives an overview on the state-of-the-art and recent advances in mixed integer optimization to solve planning and design problems in the process industry. In some case studies specific aspects are stressed and the typical difficulties of real world problems are addressed. Mixed integer linear optimization is widely used to solve supply chain planning problems. Some of the complicating features such as origin tracing and shelf life constraints are discussed in more detail. If properly done the planning models can also be used to do product and customer portfolio analysis. We also stress the importance of multi-criteria optimization and correct modeling for optimization under uncertainty. Stochastic programming for continuous LP problems is now part of most optimization packages, and there is encouraging progress in the field of stochastic MILP and robust MILP. Process and network design problems often lead to nonconvex mixed integer nonlinear programming models. If the time to compute the solution is not bounded, there are already a commercial solvers available which can compute the global optima of such problems within hours. If time is more restricted, then tailored solution techniques are required.     

Tactical and strategic models for satellite customer assignment

In this paper we develop tactical and strategic models for assignments of customers to satellite channels. We solve this problem using mixed integer–linear programming, and study the managerial impacts of our models. As a managerial tool, the optimal placement of customer channels to minimize transponder re-balancing was found to have a real and observable profit potential in excess of $54 million for the GE Spacenet series geosynchronous orbit satellites. Further managerial findings and computational results are presented.     

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.     

模糊环境下动态供应商选择的混合整数非线性规划模型

基于供应商选择问题的动态性和模糊性,考虑在每个周期内生产商的需求能力及供应商的供应能力为模糊变量,本文将一个多阶段多商品多渠道的供应商选择问题视为一个0-1混合整数模糊动态非线性规划问题,目标函数为总成本最小化。然后建立了0-1混合整数模糊动态非线性规划模型。为了求解该模型,通过可信性理论把模型中模糊机会约束清晰化,将该模型转化为一个确定型的0-1混合整数动态非线性规划模型。最后给出了一个数值算例验证了模型的可行性。     

A closed-loop logistics model for remanufacturing

Recoverable product environments are becoming an increasingly important segment of the overall push in industry towards environmentally conscious manufacturing. Integral to the recoverable product environment is the recoverable manufacturing system that focuses on recovering the product and extending its life through remanufacture or repair. Remanufacturing provides the customer with an opportunity to acquire a product that meets the original product standards at a lower price than a new product. The flow of materials and products in this environment occurs both from the customer to the remanufacturer (reverse flow), and from the remanufacturer to the customer (forward flow). Since most of the products and materials may be conserved, essentially this forms a closed-loop logistics system. We present a 0–1 mixed integer programming model that simultaneously solves for the location of remanufacturing/distribution facilities, the transshipment, production, and stocking of the optimal quantities of remanufactured products and cores. We also discuss the managerial uses of the model for logistics decision-making.     

应急管理中车辆受限的生产_库存及配送整合模型

针对突发事件发生后,救灾物资不足、车辆数量及容量有限的情况,本文考虑了制造商生产、包装新的救灾物资,构造了车辆返回制造商需要等待订单完成生产的时间函数,建立了一个生产、库存及配送整合的混合整数规划模型。该模型由原材料供应商、制造商、配送中心及客户需求点四部分构成,以完成原材料的运输、制造商中的订单生产并运送到需求点及配送中心的库存订单运送到需求点的总花费时间最短为目标。本文将模型分为两层子模型进行求解:第一层模型采用改进的遗传算法求解;第二层模型采用隐枚举法求解。最后给出一个具体的案例以验证模型的合理性及算法的有效性。     

Asymptotically optimal staffing of service systems with joint QoS constraints

We consider the problem of staffing large-scale service systems with multiple customer classes and multiple dedicated server pools under joint quality-of-service (QoS) constraints. We first analyze the case in which arrival rates are deterministic and the QoS metric is the probability a customer is queued, given by the Erlang-C formula. We use the Janssen–Van Leeuwaarden–Zwart bounds to obtain asymptotically optimal solutions to this problem. The second model considered is one in which the arrival rates are not completely known in advance (before the server staffing levels are chosen), but rather are known via a probability distribution. In this case, we provide asymptotically optimal solutions to the resulting stochastic integer program, leveraging results obtained for the case of deterministic arrivals.     

Double-counting problem of the bonus–malus system

The bonus–malus system (BMS) is a widely used premium adjustment mechanism based on policyholder’s claim history. Most auto insurance BMSs assume that policyholders in the same bonus–malus (BM) level share the same a posteriori risk adjustment. This system reflects the policyholder’s claim history in a relatively simple manner. However, the typical system follows a single BM scale and is known to suffer from the double-counting problem: policyholders in the high-risk classes in terms of a priori characteristics are penalized too severely (Taylor, 1997; Pitrebois et al., 2003). Thus, Pitrebois et al. (2003) proposed a new system with multiple BM scales based on the a priori characteristics. While this multiple-scale BMS removes the double-counting problem, it loses the prime benefit of simplicity. Alternatively, we argue that the double-counting problem can be viewed as an inefficiency of the optimization process. Furthermore, we show that the double-counting problem can be resolved by fully optimizing the BMS setting, but retaining the traditional BMS format.     

客户发展关系的Markov链一般模型

根据客户发展关系的Markov链的转移概率矩阵，建立了客户发展关系的一般模型，它包含许多特殊模型。前人研究的一些模型正是该一般模型的特例。一般模型的建立不但刻画了各种客户发展关系，而且为企业对客户发展进行定量分析和管理奠定了基础。     

Chance constrained integer programming models for capital budgeting in fuzzy environments

This paper attempts to model capital budgeting problems by chance constrained integer programming in a fuzzy environment (rather than a stochastic environment). Some examples are also provided to illustrate the potential applications of new models. Finally, a fuzzy simulation based genetic algorithm is designed for solving chance constrained integer programming models with fuzzy parameters.     

The multi-commodity one-to-one pickup-and-delivery traveling salesman problem

This paper concerns a generalization of the traveling salesman problem (TSP) called multi-commodity one-to-one pickup-and-delivery traveling salesman problem (m-PDTSP) in which cities correspond to customers providing or requiring known amounts of m different commodities, and the vehicle has a given upper-limit capacity. Each commodity has exactly one origin and one destination, and the vehicle must visit each customer exactly once. The problem can also be defined as the capacitated version of the classical TSP with precedence constraints. This paper presents two mixed integer linear programming models, and describes a decomposition technique for each model to find the optimal solution. Computational experiments on instances from the literature and randomly generated compare the techniques and show the effectiveness of our implementation.     

面向顾客资产的三维顾客细分模型及其应用

简单依照顾客利润贡献对顾客细分未能充分考虑顾客的无形贡献,会低估顾客对企业的价值.从面向顾客资产的视角进行顾客细分,可以兼顾到顾客当前的利润贡献和顾客的潜在有形和无形贡献,从而提出基于顾客当前显性贡献、潜在显性贡献和潜在隐性贡献三维顾客细分模型及度量方法,并结合实证阐述顾客细分方法的实现过程.     

A comparison of strategies to develop a customer default scoring model

Behavioural scoring models are generally used to estimate the probability that a customer of a financial institution who owns a credit product will default on this product in a fixed time horizon. However, one single customer usually purchases many credit products from an institution while behavioural scoring models generally treat each of these products independently. In order to make credit risk management easier and more efficient, it is interesting to develop customer default scoring models. These models estimate the probability that a customer of a certain financial institution will have credit issues with at least one product in a fixed time horizon. In this study, three strategies to develop customer default scoring models are described. One of the strategies is regularly utilized by financial institutions and the other two will be proposed herein. The performance of these strategies is compared by means of an actual data bank supplied by a financial institution and a Monte Carlo simulation study.