Ossama Kettani

Goal programming model: A glorious history and a promising future

Abstract In the last 40 years, there has been a marked transformation in the development of new methodologies to assist the decision-making process, especially in the development of procedures in multi-criterion decision-making and in multi-objective programming (MOP). Goal programming (GP) is the most commonly known model of MOP and it is today alive more than ever, supported by a network of researchers and practitioners continually feeding it with theoretical developments and applications, all of these with resounding success. This paper paints a picture summarizing the history of GP and suggests a few areas of research in this era of globalization.

On the optimization of supply chain networking decisions

Companies strive to position themselves to maximize the value they add to the supply chains in which they are embedded. This raises strategic questions such as: Which durable resources should be developed to enhance current core competencies? Which activities should be externalized and to which potential partner should they be given? Which internal activities should be preserved and developed? How should the resources of the enterprise be allocated to activities? The aim of this paper is to propose a mathematical programming model of the extended enterprise which can be used to investigate this type of strategic networking issues. A number of general network modeling constructs are first proposed. A model to optimize the supply chain structure under specific assumptions on the nature of production, cost and value functions in typical production/distribution companies is then derived. A heuristic to obtain solutions from the model is also presented. Finally, an example based on a refrigerator company is used to illustrate the usefulness of the approach. ” 2001 Elsevier Science B.V. All rights reserved.

A linearization procedure for quadratic and cubic mixed-integer problems

Several techniques of linearization have appeared in the literature. The technique of F. Glover, which seems to be the most efficient, linearizes a binary quadratic integer problem of n variables by introducing n new continuous variables and 4n auxiliary linear constraints. The new technique proposed in this paper is not only useful in linearizing binary quadratic and cubic integer problems, but also applicable to the case of quadratic and to a certain class of cubic “mixed-integer” problems. It is shown that the new technique further reduces the number of auxiliary linear constraints from 4n to n, while keeping the number of new continuous variables at n for the binary quadratic integer problem of n variables. And, it requires, in the case of a certain class of cubic mixed-integer problems having 2n of 0–1 variables, only 3n auxiliary linear constraints and the same number of new continuous variables. The analytical superiority of the new linearization technique has also been observed, in terms of the nu...

The facets of the modeling and validation process in operations research

Abstract The present paper suggests a way of exploring the process of modeling and validation in Operations Research (OR). This will be achieved by providing an interpretation for each facet of the modeling-validation tetrahedron formed by the quartet ‘managerial situation’, ‘conceptual model’, ‘formal model’, and ‘decision’. Such an approach not only leads to a contextual classification of OR problems, albeit in general terms, but also helps to identify the types of validation needed and their relative importance. The real world problems which OR is currently trying to tackle are rather complex in nature and vast in scope. This inevitably forces OR scientists and practitioners to position themselves somewhere on the ‘scientific perspective’ - ‘practice perspective’ spectrum. The proposed tetrahedron of the modelling-validation process is also instrumental in positioning OR workers with respect to the nature of their work.

An estimation model for country risk rating

Abstract Several statistical models, such as multiple regression, logistic regression (LOGIT), classification and regression tree (CART), etc. have been suggested in the literature and used in practice to explain and predict country risk ratings as a function of some selected social, political, but mostly economic factors or indicators. Such models, however, seem to have some important shortcomings. First, the same set of parameter values are usually assumed to apply to all countries, regardless of whether a particular political-economic factor carries more weight in the case of some countries. Second, the level of data adjustability is achieved only within the context of the optimization techniques inherent in the statistical models chosen a priori. This paper proposes, and applies to a group of 70 countries, a procedure that employs a generalized logit model (G-LOGIT) to link country risk rating and political-economic indicators. The estimates for the parameters of the G-LOGIT model are obtained through an independently developed mathematical programming model, rather than relying on classical optimization techniques as do most statistical models. The performance results of the proposed procedure are compared with two widely used statistical models: LOGIT and CART. The results indicate that the new procedure is superior to the statistical models, with respect to both estimation and validation errors.

AN EMPIRICAL STUDY ON ANALYZING THE PRODUCTIVITY OF BANK BRANCHES

Abstract Productivity analysis and its strategic implications are not only important for manufacturing sector but equally essential for other sectors as well. Branch banking sector is no exception in this sense and banks have to operate more efficiently and effectively in an increasingly competitive environment to sustain or improve their relative positions. This paper discusses the methodology of an empirical study that was employed in analyzing the operating productivities of a set of 44 bank branches of a major commercial bank offering relatively homogeneous products in a multi-market business environment. The methodology was based on the concepts and principles of Data Envelopment Analysis (DEA). The results of the study have indicated that this kind of productivity analysis is not only complementary to traditionally used financial ratios but also is a useful bank management tool in reallocating resources between the branches in order to achieve higher efficiencies.

Project evaluation and selection in a network of collaboration: A consensual disaggregation multi-criterion approach

Abstract Project evaluation and selection are usually complex processes in large organizations, for they involve several stakeholders who are to evaluate competing alternatives with respect to a certain set of criteria and then make a choice as to which projects are to be implemented. This is particularly more so in the case of international organizations where the competing projects are proposed by units or divisions having different values and preferences. This paper discusses a project evaluation and selection methodology based on multi-criteria disaggregative approach used as an instrument rather than as a descriptive tool, as it is often the case in the literature. The proposed methodology has been developed for an international organization which has more than a dozen country members and provides them with a platform to maximize the level of consensus among the member countries, subject to some certain budgetary constraints and resentment-avoiding principles.

A Multiple Criteria Analysis Model For Real Estate Evaluation

Real estate evaluation is of great importance and interest to many socio-economic agents, especially to property buyers and sellers for personal benefits, municipalities for tax purposes, financial institutions for loan policies, and to real estate brokerage firms for marketing activities. Although these agents are motivated in their actions by different objectives, even conflicting at times, they all desire to have a realistic description of the real estate market behavior in order to make right and timely decisions. This article presents an estimation model to describe the behavior of real estate markets. The model is based on certain observable real estate market data as well as on the perceptions of real estate agents who are active in the market. The parameters that describe the behavior of the real estate market are estimated, through the estimation model, using mathematical programming tools within a multiple criteria analysis context. The usefulness and applicability of the approach is empirically shown through an implementation using the data of the City of Edmonton, Alberta, Canada.

Reformulating nonlinear combinatorial optimization problems for higher computational efficiency

Abstract It is important to develop computationally efficient algorithms to solve combinatorial optimization problems. Equally important, if not more so, is to find a way to reformulate the original combinatorial optimization problem, provided this is possible, so that the resulting equivalent problem can be solved easily and efficiently using commercially available codes. This paper proposes an equivalent formulation to deal basically with the linearization of nonlinear expressions in 0–1 variables. The equivalent formulation technique proposed in this paper linearizes a binary quadratic integer problem of n variables by introducing only n new linear constraints, whereas the most economical method in the literature requires the addition of 2n of such constraints. The same technique is extended to linearize the binary cubic expression of n variables, this time requiring the addition of at most 3n auxiliary linear constraints and 3n continuous variables. Also discussed in the paper is the computational superiority of the proposed method over the existing ones in the literature through a series of randomly generated test problems.

A new mixed-integer linear programming model for rescue path planning in uncertain adversarial environment

Efficient vehicle path planning in hostile environment to carry out rescue or tactical logistic missions remains very challenging. Most approaches reported so far rely on key assumptions and heuristic procedures to reduce problem complexity. In this paper, a new model is proposed to solve the discrete rescue path planning problem for a single agent navigating in uncertain adversarial environment. It relies on a novel and simplified mathematical mixed-integer linear programming formulation aimed at minimizing traveled distance and threat exposure. Exploiting a user-defined survivability function approximation and survivability threshold, the approximate model allows constructing a solution providing an adjustable optimality gap interval on the optimal solution. Experimental results show the value of the proposed approach in computing near optimal solutions reasonably fast for various problem instances.