Customer retention: a behavioural model

One of the main problems currently facing CTedit-card issuersis the increasing number of cardholders who are using theircards less often (i.e. attrition) and/or returning their cards(closures). This problem is of particular concern as the totalnumber of credit cards held by consumers is declining (by approximately0.6 per cent per month in 1992) and the number of new applicantsis also running at an all time-low (less than 1 per cent permonth in 1992). Most of the published literature in the broad area of creditcards looks at credit scoring, rather than the need for cardissuers to identify and retain a profitable portfolio of cardcustomers. The overall objective of our research is ‘segmentationfor customer retention’, and this paper aims to identifythe characteristics of card customers who initiate the closureof their accounts Linear discriminant analysis is applied toa sample of approximately 17,000 UK holders of bank credit cards,using various behavioural and sociodemographic variables, andtested on a holdout sample of 10,000 cases.     

Minimizing earliness and tardiness costs in stochastic scheduling

We address the single-machine stochastic scheduling problem with an objective of minimizing total expected earliness and tardiness costs, assuming that processing times follow normal distributions and due dates are decisions. We develop a branch and bound algorithm to find optimal solutions to this problem and report the results of computational experiments. We also test some heuristic procedures and find that surprisingly good performance can be achieved by a list schedule followed by an adjacent pairwise interchange procedure.     

The concert queueing game: strategic arrivals with waiting and tardiness costs

We consider the noncooperative choice of arrival times by individual users, who seek service at a first-come first-served queueing system that opens up at a given time. Each user wishes to obtain service as early as possible, while minimizing the expected wait in the queue. This problem was recently studied within a simplified fluid-scale model. Here, we address the unscaled stochastic system, assuming a finite (possibly random) number of homogeneous users, exponential service times, and linear cost functions. In this setting, we establish that there exists a unique Nash equilibrium, which is symmetric across users, and characterize the equilibrium arrival-time distribution of each user in terms of a corresponding set of differential equations. We further establish convergence of the Nash equilibrium solution to that of the associated fluid model as the number of users is increased. We finally consider the price of anarchy in our system and show that it exceeds 2, but converges to this value for a large population size.     

Minmax scheduling with job-classes and earliness–tardiness costs

We address scheduling problems with job-dependent due-dates and general (possibly nonlinear and asymmetric) earliness and tardiness costs. The number of distinct due-dates is substantially smaller than the number of jobs, thus jobs are partitioned to classes, where all jobs of a given class share a common due-date. We consider the settings of a single machine and parallel identical machines. Our objective is of a minmax type, i.e., we seek a schedule that minimizes the maximum earliness/tardiness cost among all jobs.     

Scheduling projects with variable-intensity activities: The case of dynamic earliness and tardiness costs

This paper addresses the problem of resource-constrained multi-project scheduling with variable-intensity activities. Four dynamic models, based on four types of precedence relations are presented to minimize dynamic earliness and tardiness of project activities. The first two models are designed to cope with start-to-end precedence relations via unit step functions and specially constructed penalty functions respectively. Conditions are derived for the case when an optimal solution of the second model with relaxed start-to-end precedence relations is the global optimal solution of the first model. The third and the fourth models are dealing with overlapping precedence relations based on a milestone approach and on start-to-start precedence relations with lags respectively. The relationship between the four models is studied and a lower bound on the objective function is proposed. An efficient time-decomposition approach is adopted for solving the last three models. This approach is used to guide an effective search for the solution of the first model.     

Minmax earliness–tardiness costs with unit processing time jobs

The problem addressed in this paper is defined by M parallel identical machines, N jobs with identical (unit) processing time, job-dependent weights, and a common due-date for all jobs. The objective is of a minmax type, i.e. we are interested in minimizing the cost of the worst scheduled job. In the case of a non-restrictive (i.e., sufficiently large) common due-date, the problem is shown to have a solution that is polynomial in the number of jobs. The solution in the case of a restrictive due-date remains polynomial in the number of jobs, but is exponential in the number of machines. We introduce a lower bound on the optimal cost and an efficient heuristic. We show that the worst case relative error of the heuristic is bounded by 2 and that this bound is tight. We also prove that the heuristic is asymptotically optimal under very general assumptions. Finally, we provide an extensive numerical study demonstrating that in most cases the heuristic performs extremely well.     

Scheduling problems with random processing times under expected earliness/tardiness costs

This work is concerned with scheduling problems for a single machine. Taking earliness and tardiness of completion time and due–date value into consideration, the objective function with a common due date is considered. The processing time of each job is random. Sufficient conditions guaranteeing an optimal SEPT sequence are derived. Under exponential and normal processing times, further results are obtained     

Semantics for possibilistic answer set programs: Uncertain rules versus rules with uncertain conclusions

Although Answer Set Programming (ASP) is a powerful framework for declarative problem solving, it cannot in an intuitive way handle situations in which some rules are uncertain, or in which it is more important to satisfy some constraints than others. Possibilistic ASP (PASP) is a natural extension of ASP in which certainty weights are associated with each rule. In this paper we contrast two different views on interpreting the weights attached to rules. Under the first view, weights reflect the certainty with which we can conclude the head of a rule when its body is satisfied. Under the second view, weights reflect the certainty that a given rule restricts the considered epistemic states of an agent in a valid way, i.e. it is the certainty that the rule itself is correct. The first view gives rise to a set of weighted answer sets, whereas the second view gives rise to a weighted set of classical answer sets.     

Sequencing and due-date determination in the stochastic single machine problem with earliness and tardiness costs

This paper studies the problem of simultaneous due-date determination and sequencing of a set of n jobs on a single machine where processing times are random variables and job earliness and tardiness costs are distinct. The objective is to determine the optimal sequence and the optimal due-dates which jointly minimize the expected total earliness and tardiness cost. We present an analytical approach to determine optimal due-dates, and propose two efficient heuristics of order O(n log n) to find candidates for the optimal sequence. It is demonstrated that variations in processing times increase cost and affect sequencing and due-date determination decisions. Our illustrative examples as well as computational results show that the proposed model produces optimal sequences and optimal due-dates that are significantly different from those provided by the classical deterministic single machine models. Furthermore, our computational experiments reveal that the proposed heuristics perform well in providing either optimal sequences or good candidates with low overcosts.     

Manufacturing costs in serial production systems with rework

In this paper, we present a Markovian modelling framework that can describe any serial production system with rework. Each production stage is represented by a state in the Markov chain. Absorbing states indicate the events of scrapping a product at a production stage or the completion of the finished product. Generalizable formulae for the final absorption probabilities are derived that represent: (1) the probability that an unfinished product is scrapped at a certain production stage and (2) the yield of the system. We also derive various expected costs and quantities associated with all products ending in any absorbing state, as well as the equivalent costs and quantities for finished products. The applicability of our modelling framework is demonstrated in a real-life manufacturing environment in the food-packing industry.     

Hopf bifurcation in an open monetary economic system: Taylor versus inflation targeting rules

The main aim of the present work is to detect the Hopf bifurcation in policy relevant economic dynamical system. The study employs two deferent forms of monetary policy rules namely: Taylor rule and inflation targeting rule. The results show that there exists Hopf bifurcation between policy relevant variables in both types of rules in our open economic system.     

Single machine total tardiness maximization problems: complexity and algorithms

In this paper, we consider some scheduling problems on a single machine, where weighted or unweighted total tardiness has to be maximized in contrast to usual minimization problems. These problems are theoretically important and have also practical interpretations. For the total weighted tardiness maximization problem, we present an NP-hardness proof and a pseudo-polynomial solution algorithm. For the unweighted total tardiness maximization problem with release dates, NP-hardness is proven. Complexity results for some other classical objective functions (e.g., the number of tardy jobs, total completion time) and various additional constraints (e.g., deadlines, weights and/or release dates of jobs may be given) are presented as well.     

A model for allocated versus actual costs in assignment and transportation problems

We present a simple mathematical model which will relate the actual cost spent in accomplishing a task to the dollars budgeted for that task. In the specific instances of assignment and transportation problems we show how to minimize total dollars spent given total dollars allocated. We show furthermore how to quantitatively measure the work done along each arc in such problems. The total work, which will measure how fixed costs are realized across various arcs for a given prescribed effort, can then be minimized. It is shown that this, in general, leads to a third type of optimal solution which is different from those optimal solutions obtained by minimizing either total cost or total dollars allocated.     

Bi-criteria scheduling problems: Number of tardy jobs and maximum weighted tardiness

Consider a single machine and a set of n jobs that are available for processing at time 0. Job j has a processing time p_j, a due date d_j and a weight w_j. We consider bi-criteria scheduling problems involving the maximum weighted tardiness and the number of tardy jobs. We give NP-hardness proofs for the scheduling problems when either one of the two criteria is the primary criterion and the other one is the secondary criterion. These results answer two open questions posed by Lee and Vairaktarakis in 1993. We consider complexity relationships between the various problems, give polynomial-time algorithms for some special cases, and propose fast heuristics for the general case. The effectiveness of the heuristics is measured by empirical study. Our results show that one heuristic performs extremely well compared to optimal solutions.     

Customer lifetime value: stochastic optimization approach

Since the early 1980s, the concept of relationship marketing has been becoming important in general marketing, especially in the area of direct and interactive marketing. The core of relationship marketing is the maintenance of long-term relationships with the customers. However, the relationship marketing is costly and therefore, the determination of the customer lifetime value (CLV) is an important element in making strategic decisions in both advertising and promotion. In this paper, we propose a stochastic dynamic programming model with a Markov chain for the optimization of CLV. Both cases of infinite horizon and finite horizon are discussed. The model is then applied to practical data of a computer service company.     

Multiple-buyer multiple-vendor multi-product multi-constraint supply chain problem with stochastic demand and variable lead-time: A harmony search algorithm

In this paper, a multi-buyer multi-vendor supply chain problem is considered in which there are several products, each buyer has limited capacity to purchase products, and each vendor has warehouse limitation to store products. In this chain, the demand of each product is stochastic and follows a uniform distribution. The lead-time of receiving products from a vendor to a buyer is assumed to vary linearly with respect to the order quantity of the buyer and the production rate of the vendor. For each product, a fraction of the shortage is backordered and the rest are lost. The ordered product quantities are placed in multiple of pre-defined packets and there are service rate constraints for the buyers. The goal is to determine the reorder points, the safety stocks, and the numbers of shipments and packets in each shipment of the products such that the total cost of the supply chain is minimized. We show that the model of this problem is of an integer nonlinear programming type and in order to solve it a harmony search algorithm is employed. To validate the solution and to compare the performance of the proposed algorithm, a genetic algorithm is utilized as well. A numerical illustration and sensitivity analysis are given at the end to show the applicability of the proposed methodology in real-world supply chain problems.     

客户知识管理—概念与量表开发

通过文献分析,将客户知识管理的定义划分为三类。从客户知识管理的概念和客户知识活动的特性入手,以文献研究和已有相关问卷、量表为基础,结合半结构化问卷和人员访谈所获得的资料,编制客户知识管理量表。研究结果表明,客户知识管理具有多维度结构,其量表的开发具有较好的可信度和可靠性,客户知识管理包括五个维度,即客户知识获取、客户知识整合、客户知识共享、客户知识使用和客户知识创新。本文对概念的界定以及量表的开发可以为企业进行客户知识管理提供参考和借鉴。