Jan Telgen

Outranking methods in support of supplier selection

Initial purchasing decisions such as make-or-buy decisions and supplier selection are decisions of strategic importance to companies. The nature of these decisions usually is complex and unstructured. Management Science techniques might be helpful tools for this kind of decision making problems. So far, however, the application of outranking methods in purchasing decisions has not been suggested in purchasing or operations research literature. In this paper we show by means of a supplier selection example, that an outranking approach may be very well suited as a decision-making tool for initial purchasing decisions.

Minimal representation of convex polyhedral sets

A system of linear inequality and equality constraints determines a convex polyhedral set of feasible solutionsS. We consider the relation of all individual constraints toS, paying special attention to redundancy and implicit equalities. The main theorem derived here states that the total number of constraints together determiningS is minimal if and only if the system contains no redundant constraints and/or implicit equalities. It is shown that the existing theory on the representation of convex polyhedral sets is a special case of the theory developed here.

Public procurement : international cases and commentary

In many countries and sectors, public procurement is developing from a functional orientation to an effective socio-economic policy lever. There is a great interest among managers and academics to learn from other countries’ and other sectors’ change initiatives and how they dealt with the challenges they encountered. This text provides such learning opportunities, presenting case studies of public procurement, covering diverse nations, sectors and issues. The cases are combined with editorial commentary and contextualizing chapters to assist the student reader in understanding this complex topic. The text combines descriptions of cases of public procurement with cross case analysis to draw out the key dimensions to enable further examination of the central themes. Each case study concludes with three questions to aid its use as a teaching and training text. Edited by a team of internationally recognised experts in the field this innovative text illustrates the strategies and innovations within public procurement on a global scale and highlights common problems that all countries encounter. Public Procurement is vital reading for anyone with an interest in this topical area.

Unfair allocation of gains under the Equal Price allocation method in purchasing groups

Certain purchasing groups do not flourish. A supposed reason for this is a creeping dissatisfaction among various members of a group with the allocation of the cooperative gains. In this paper, we analyze unfairness resulting from using the commonly used Equal Price (EP) method for allocating gains under the assumption of continuous quantity discounts. We demonstrate that this unfairness is caused by neglecting a particular component of the added value of individual group members. Next, we develop two fairness ratios and tie these to fairness properties from cooperative game theory. The ratios show among other things that being too-big a player in a purchasing group can lead to decreasing gains. They can be used to assess if EP is an unfair method in specific situations. Finally, we discuss measures a purchasing group could consider in order to attenuate perceived unfairness. Thereby, the group may improve its stability and prosperity.

Public procurement in perspective

Focus on public procurement has never been at a higher level. Yet public procurement still lags far behind private sector procurement in scientific analysis and accumulated knowledge. Papers about public procurement are usually either in documentary form (explaining the situation in a certain country, e.g. the international section in the Journal of Public Procurement) or limited to a specific aspect (legal, e.g. Public Procurement Law Review, or administrative, e.g. Journal of Public Budgeting, Accounting and Financial Management).

Shake-and-bake algorithms for generating uniform points on the boundary of bounded polyhedra

We present a class of shake-and-bake algorithms for generating (asymptotically) uniform points on the boundary of full-dimensional bounded polyhedra. We also report results of simulations for some elementary test problems.

CHOOSING THE OPEN OR THE RESTRICTED PROCEDURE: A BIG DEAL OR A BIG DEAL?

The legislation in the European Union (EU) regarding contracts to be awarded to third parties allows for a free choice by public agencies between the open and restricted procedure. Empirical evidence shows a high variance in the preference for one of the procedures exists between countries. This preference may be based on cultural phenomena only. Here we develop a quantitative model to calculate which procedure is the most economic. With insights from this model guidelines are given for an efficient policy regarding the choice for the open or restricted award procedure.

A basis for modelling the costs of supplier selection: the economic tender quantity

In this paper, we consider the decision a purchaser must make regarding the number of suppliers that should be invited to submit a tender for a certain purchase. On the one hand, the costs of sending invitations to tender, the costs of evaluating the tenders received, and the costs of communicating the outcome to the suppliers that were not selected, all increase with the number of suppliers that are invited to tender. On the other hand, with every additional tender, the purchaser might obtain a better bid. We present a theoretical decision model, the Economic Tender Quantity (ETQ) model, that under certain conditions may assist the purchaser in finding the number of tenderers that minimises the expected total costs of the tender process, that is the sum of the expected costs of sending, evaluating and communicating, and the expected bid price. We discuss these conditions and possible extensions, as well as future research opportunities in this area.

Randomly generated polytopes for testing mathematical programming algorithms

Randomly generated polytopes are used frequently to test and compare algorithms for a variety of mathematical programming problems. These polytopes are constructed by generating linear inequality constraints with coefficients drawn independently from a distribution such as the uniform or the normal.It is noted that this class of ‘random’ polytopes has a special property: the angles between the hyperplanes, though dependent on the specific distribution used, tend to be equal when the dimension of the space increases.Obviously this structure of ‘random’ polytopes may bias test results.

On relaxation methods for systems of linear inequalities

Abstract In their classical papers Agmon and Motzkin and Schoenberg introduced a relaxation method to find a feasible solution for a system of linear inequalities. So far the method was believed to require infinitely many iterations on some problem instances since it could (depending on the dimension of the set of feasible soltions) converge asymptotically to a feasible solution, if one exists. Hence it could not be used to determine infeasibility. Using two lemmas basic to Khachians polynomially bounded algorithm we can show that the relaxation method is finite in all cases and thus can handle infeasible systems as well. In spite of more refined stopping criteria the worst case behaviour of the relaxation method is not polynomially bounded as examplified by a class of problems constructed here.