Algorithms for the q-model clustering problem with application in switching cabinet manufacturing

The model configuration problem (MCP) is a combinatorial optimization problem with application in the telecommunications manufacturing industry. The product is a switching cabinet, defined by a number of positions (slots) in which specific circuit packs are installed according to the customer requirements (configurations). Variety of customer requirements leads to a relatively large number of distinct configurations. In order to streamline the manufacturing process, a large number of switching cabinets with identical configurations (model cabinets) are produced in advance. A customer order is then filled by selecting a model cabinet whose configuration is relatively close to the customer configuration and performing any necessary circuit pack exchanges to make its configuration identical to the customer requirement. The manufacturing costs are proportional to the number of these circuit pack exchanges, and the q-model configuration problem is to design q different model configurations so as to minimize the total number of exchanges for a given collection of customer orders. We propose three heuristic algorithms for solving the q-model configuration problem and carry out a computational experiment to evaluate their effectiveness.     

The bipartite margin shop and maximum red matchings free of blue–red alternating cycles

The margin shop arises as a model of margining investment portfolios in a batch, a mandatory end-of-day risk management operation for any prime brokerage firm. The margin-shop scheduling problem is the extension of the preemptive flow-shop scheduling problem where precedence constraints can be introduced between preempted parts of jobs. This paper is devoted to the bipartite case which is equivalent to the problem of finding a maximum red matching that is free of blue–red alternating cycles in a complete bipartite graph with blue and red edges. It is also equivalent to the version of the jump-number problem for bipartite posets where jumps inside only one part should be counted. We show that the unit-time bipartite margin-shop scheduling problem is NP-hard but can be solved in polynomial time if the precedence graph is of degree at most two or a forest.     

A risk-based model for the valuation of pension insurance

In the US, defined benefit plans are insured by the Pension Benefit Guaranty Corporation (PBGC). Taking account of the fact that the PBGC covers only the residual deficits of the pension fund the sponsoring company is unable to cover and that the plans can be prematurely terminated, we consider a model that accounts for the joint dynamics of the pension fund’s and sponsoring firm’s assets in order to effectively determine the risk-based pension premium for the insurance provided by the PBGC. We obtain a closed-form pricing formula for this risk-based premium. Its magnitude depends highly on the investment portfolio of the pension fund and of the sponsoring company as well as the correlation between these two portfolios.     

A matching approach for replenishing rectangular stock sizes

Consider a replenishment problem in which several different rectangular sizes of material are stocked. Customers order rectangles of the material, but the rectangles ordered have a range on specified width as well as on specified length. To satisfy the customer requirements, the stock material can be cut once longitudinally in order to satisfy two customer requirements or not cut at all, that is, an entire stock piece of material is used to satisfy one customer requirement. If an exact match is impossible in the current planning period, the unused material must be returned to stock— an expensive and undesirable situation. In this paper, a nonbipartite weighted matching problem formulation will be given for determining the replenishment requirements of rectangular stock sizes. Then, a hybrid solution approach, capable of solving real applications (typically up to 3000 nodes) efficiently, will be discussed. This solution was implemented in September 1998 and has operated successfully since then.     

Staffing a service system with appointment-based customer arrivals

Appointment systems are widely used to facilitate customers’ access to services in many industries such as healthcare. A number of studies have taken a queueing approach to analyse service systems and facilitate managerial decisions on staffing requirements by assuming independent and stationary customer arrivals. This paper is motivated by the observation that the queueing-based method shows relatively poor performance when customers arrive according to their appointment times. Because customer arrivals are dependent on their appointment times, this study, unlike queueing-based methods, conducts a detailed analysis of appointment-based customer arrivals instead of making steady-state assumptions. We develop a new model that captures the characteristics of appointment-based customer arrivals and computes the probability of transient system states. Through the use of this model, which relaxes stationary and independent assumptions, we propose a heuristic algorithm that determines staffing requirements with aims to minimizing staff-hours while satisfying a target service level. The simulation results show that the proposed method outperforms the queueing-based method.     

Robust production planning in a manufacturing environment with random yield: A case in sawmill production planning

This paper addresses a multi-period, multi-product sawmill production planning problem where the yields of processes are random variables due to non-homogeneous quality of raw materials (logs). In order to determine the production plans with robust customer service level, robust optimization approach is applied. Two robust optimization models with different variability measures are proposed, which can be selected based on the tradeoff between the expected backorder/inventory cost and the decision maker risk aversion level about the variability of customer service level. The implementation results of the proposed approach for a realistic-scale sawmill example highlights the significance of using robust optimization in generating more robust production plans in the uncertain environments compared with stochastic programming.     

A problem-solving approach to product design using decision tree induction based on intuitionistic fuzzy

Customer complaint problem is a product design used to understand customer requirements. Furthermore, product design corresponding to customer requirement does not feel adequately solved for a cause of problem. The cause of the problem affecting product design is solved to prevent customer complaint from reoccurring. However, the problems by customer may have observation uncertainty and fuzzy. Fuzzy concept considers not only the degree of membership to an accept set, but also the degree of non-membership to a rejection set. Therefore, we present a new approach for problem solving using decision tree induction based on intuitionistic fuzzy sets in this paper. Under this approach, we first develop the problem formulation for the symptoms and causes of the problem based on intuitionistic fuzzy sets. Next, we identify the cause of the problem using intuitionistic fuzzy decision tree by the problem formulation. We then provide the approach to find the optimal cause of the problem for the consideration of product design. A numerical example is used to illustrate the approach applied for product design.     

An evaluation approach to engineering design in QFD processes using fuzzy goal programming models

Quality function deployment (QFD) is a product development process used to achieve higher customer satisfaction: the engineering characteristics affecting the product performance are designed to match the customer requirements. From the viewpoint of QFDs designers, product design processes are performed in uncertain environments, and usually more than one goal must be taken into account. Therefore, when dealing with the fuzzy nature in QFD processes, fuzzy approaches are applied to formulate the relationships between customer requirements (CRs) and engineering design requirements (DRs), and among DRs. In addition to customer satisfaction, the cost and technical difficulty of DRs are also considered as the other two goals, and are evaluated in linguistic terms. Fuzzy goal programming models are proposed to determine the fulfillment levels of the DRs. Differing from existing fuzzy goal programming models, the coefficients in the proposed model are also fuzzy in order to expose the fuzziness of the linguistic information. Our model also considers business competition by specifying the minimum fulfillment levels of DRs and the preemptive priorities between goals. The proposed approach can attain the maximal sum of satisfaction degrees of all goals under each confidence degree. A numerical example is used to illustrate the applicability of the approach.     

Fuzzy goal programming for inventory management: A bacterial foraging approach

An efficient inventory planning approach in today’s global trading regime is necessary not only for increasing the profit margin, but also to maintain system flexibility for achieving higher customer satisfaction. Such an approach should hence be comprised of a prudent inventory policy and clear satisfaction of stakeholder’s goals. Relative significance given to various objectives in a supply chain network varies with product as well as time. In this paper, a model is proposed to fill this void for a single product inventory control of a supply chain consisting of three echelons. A generic modification proposed to the membership functions of the fuzzy goal-programming approach is used to mathematically map the aspiration levels of the decision maker. The bacterial foraging algorithm has been modified with enhancement of the algorithms’ capability to map integer solution spaces and utilised to solve resulting fuzzy multi-objective function. An illustrative example comprehensively covers various decision scenarios and highlights the underlying managerial insights.     

Procedures for the Time and Space constrained Assembly Line Balancing Problem

The Time and Space constrained Assembly Line Balancing Problem (TSALBP) is a variant of the classical Simple Assembly Line Balancing Problem that additionally accounts for the space requirements of machinery and assembled parts. The present work proposes an adaptation of the Bounded Dynamic Programming (BDP) method to solve the TSALBP variant with fixed cycle time and area availability. Additionally, different lower bounds for the simple case are extended to support the BDP method as well as to assess the quality of the obtained solutions. Our results indicate that the proposed bounds and solution procedures outperform any other previous approach found in the literature.     

Scheduling periodic customer visits for a traveling salesperson

The problem considered in this paper deals with determining daily routes for a traveling salesperson who provides customers in Upper Austria with product range information of a large, global food wholesaler. Each customer has to be visited at least once a year, with some customers requiring up to one visit per month. Further, some customers may not be visited each day of the week. Our decision support system uses a commercial GIS software to extract customer data for input into the optimization procedure and to visualize the results obtained by the algorithm. The optimization approach is based on the variable neighborhood search algorithm which assigns customers to days and determines routes for the salesperson for each day with the primary objective to minimize the total travel time of the salesperson. Another objective studied is to minimize the number of days needed by the salesperson to visit all customers in a given month. Further we analyze the effects of changes in the business environment like increases in the amount or flexibility of the salesperson’s working time and variations in the possible days for customer visits. Finally, we enrich the objective function by considering periodicity requirements for customer visits. Specifically, we penalize irregular schedules, where the time between two successive customer visits varies.     

A Simulated Annealing Approach to Bicriteria Scheduling Problems on a Single Machine

In this paper, we apply a simulated annealing approach to two bicriteria scheduling problems on a single machine. The first problem is the strongly NP-hard problem of minimizing total flowtime and maximum earliness. The second one is the NP-hard problem of minimizing total flowtime and number of tardy jobs. We experiment on different neighbourhood structures as well as other parameters of the simulated annealing approach to improve its performance. Our computational experiments show that the developed approach yields solutions that are very close to lower bounds and hence very close to the optimal solutions of their corresponding problems for the minimization of total flowtime and maximum earliness. For the minimization of total flowtime and number tardy, our experiments show that the simulated annealing approach yields results that are superior to randomly generated schedules.     

A fuzzy goal programming approach for mid-term assortment planning in supermarkets

We develop a fuzzy mixed integer non-linear goal programming model for the mid-term assortment planning of supermarkets in which three conflicting objectives namely profitability, customer service, and space utilization are incorporated. The items and brands in a supermarket compete to obtain more space and better shelf level. This model offers different service levels to loyal and disloyal customers, applies joint replenishment policy, and accounts for the holding time limitation of perishable items. We propose a fuzzy approach due to the imprecise nature of the goals’ target levels and priorities as well as critical data. A heuristic method inspiring by the problem-specific rules is developed to solve this complex model approximately within a reasonable time. Finally, the proposed approach is validated through several numerical examples and results are reported.     

Multi-source facility location–allocation and inventory problem

We consider a joint facility location–allocation and inventory problem that incorporates multiple sources of warehouses. The problem is motivated by a real situation faced by a multinational applied chemistry company. In this problem, multiple products are produced in several plants. Warehouse can be replenished by several plants together because of capabilities and capacities of plants. Each customer in this problem has stochastic demand and certain amount of safety stock must be maintained in warehouses so as to achieve certain customer service level. The problem is to determine number and locations of warehouses, allocation of customers demand and inventory levels of warehouses. The objective is to minimize the expected total cost with the satisfaction of desired demand weighted average customer lead time and desired cycle service level. The problem is formulated as a mixed integer nonlinear programming model. Utilizing approximation and transformation techniques, we develop an iterative heuristic method for the problem. An experiment study shows that the proposed procedure performs well in comparison with a lower bound.     

Fuzzy linear programming models for NPD using a four-phase QFD activity process based on the means-end chain concept

Quality function deployment (QFD) is a customer-driven approach in processing new product development (NPD) to maximize customer satisfaction. Determining the fulfillment levels of the “hows”, including design requirements (DRs), part characteristics (PCs), process parameters (PPs) and production requirements (PRs), is an important decision problem during the four-phase QFD activity process for new product development. Unlike previous studies, which have only focused on determining DRs, this paper considers the close link between the four phases using the means-end chain (MEC) concept to build up a set of fuzzy linear programming models to determine the contribution levels of each “how” for customer satisfaction. In addition, to tackle the risk problem in NPD processes, this paper incorporates risk analysis, which is treated as the constraint in the models, into the QFD process. To deal with the vague nature of product development processes, fuzzy approaches are used for both QFD and risk analysis. A numerical example is used to demonstrate the applicability of the proposed model.     

On Entire Moments of Self-Similar Markov Processes

We consider a risk-based asset allocation problem in a Markov, regime-switching, pure jump model. With a convex risk measure of the terminal wealth of an investor as a proxy for risk, we formulate the risk-based asset allocation problem as a zero-sum, two-person, stochastic differential game between the investor and the market. The HJB dynamic programming approach is used to discuss the game problem. A semi-analytical solution of the game problem is obtained in a particular case.     

Towards profitability: a utility approach to the credit scoring problem

Since credit scoring was first applied in the 1940s the standard methodology has been to treat consumer lending decisions as binary classification problems, where the goal has been to make the best possible ‘good/bad’ classification of accounts on the basis of their eventual delinquency status. However, the real goal of commercial lending organizations is to forecast continuous financial measures such as contribution to profit, but there has been little research in this area. In this paper, continuous models of customer worth are compared to binary models of customer repayment behaviour. Empirical results show that while models of customer worth do not perform well in terms of classifying accounts by their good/bad status, they significantly outperform standard classification methodologies when ranking accounts based on their financial worth to lenders.     

Measure-Valued Differentiation for Markov Chains

This paper addresses the problem of sensitivity analysis for finite-horizon performance measures of general Markov chains. We derive closed-form expressions and associated unbiased gradient estimators for the derivatives of finite products of Markov kernels by measure-valued differentiation (MVD). In the MVD setting, the derivatives of Markov kernels, called -derivatives, are defined with respect to a class of performance functions such that, for any performance measure , the derivative of the integral of g with respect to the one-step transition probability of the Markov chain exists. The MVD approach (i) yields results that can be applied to performance functions out of a predefined class, (ii) allows for a product rule of differentiation, that is, analyzing the derivative of the transition kernel immediately yields finite-horizon results, (iii) provides an operator language approach to the differentiation of Markov chains and (iv) clearly identifies the trade-off between the generality of the performance classes that can be analyzed and the generality of the classes of measures (Markov kernels). The -derivative of a measure can be interpreted in terms of various (unbiased) gradient estimators and the product rule for -differentiation yields a product-rule for various gradient estimators. Part of this work was done while the first author was with EURANDOM, Eindhoven, Netherlands, where he was supported by Deutsche Forschungsgemeinschaft under Grant He3139/1-1. The work of the second author was partially supported by NSERC and FCAR grants of the Government of Canada and Québec.     

Network revenue management with inventory-sensitive bid prices and customer choice

We develop an approximate dynamic programming approach to network revenue management models with customer choice that approximates the value function of the Markov decision process with a non-linear function which is separable across resource inventory levels. This approximation can exhibit significantly improved accuracy compared to currently available methods. It further allows for arbitrary aggregation of inventory units and thereby reduction of computational workload, yields upper bounds on the optimal expected revenue that are provably at least as tight as those obtained from previous approaches. Computational experiments for the multinomial logit choice model with distinct consideration sets show that policies derived from our approach can outperform some recently proposed alternatives, and we demonstrate how aggregation can be used to balance solution quality and runtime.