Abstract
In some formulations of the vehicle replacement problem, in particular those leading to repair limit type models, the alternative policies are evaluated and compared over a fixed planning horizon. Although it has been widely recognised that the optimal policies derived under these formulations depend critically on the length of the horizon, no method has been presented so far to set appropriately this parameter. In this paper. the authors describe a method which overcomes this shortcoming. Once the best policy has been derived from a given finite horizon with length H, such a policy is repeated indefinitely over time and an equivalent annual rent is computed. The parametrisation of H leads to the definition of an annual rent function with a sequence of nearly equidistant local minima. It is suggested that in practice the second local minimum of this function leads to an adequate choice of the parameter H. The method can be applied both to stochastic and deterministic cost modelling situations. The method was tested using both real data from large samples of different types of passenger vehicles and artificially generated data. (C) 1997 Elsevier Science B.V.

Abstract
Assortment selection problems with cutting policies play an important role in several industries but, possibly due to their combinatorial characteristics, they did not receive as much attention as cutting stock problems did, though the two problems are closely related. In this paper we graph several examples of cost functions of one and two-dimensional problems which reveal that many local optima with cost close to optimum exist. Several implementations of known meta-heuristics are tested with a real problem. Two different neighbourhood structures are considered and the different performance of the implemented heuristics is briefly discussed.

Abstract
In this paper, we analyse a complex production planning problem in a Make-To-Order company, involving quoting due dates, along with production scheduling, some plant layout decisions and line balancing issues. A general framework has been developed that identifies the main levels for decision making, and tackles these problems in a hierarchical fashion, the resulting interactions being carefully taken into consideration. This framework, based on considering discretised planning horizons, is implemented on a Decision Support System developed around an interface specially designed to involve the various participants in the planning process. In practice, the system is composed by a package of software products used as add-ons to the main management information system of the company. A comprehensive and detailed description of the approach, techniques used and developed algorithms is presented. The experience in using a first prototype of the system shows this may become a highly valuable computer tool in production planning, layout design and assignment of orders.

Abstract

Abstract
We consider the formulation of non-preemptive single machine scheduling problems using time-indexed variables. This approach leads to very large models, but gives better lower bounds than other mixed integer programming formulations. We derive a variety of valid inequalities, and show the role of constraint aggregation and the knapsack problem with generalised upper bound constraints as a way of generating such inequalities. A cutting plane/branch-and-bound algorithm based on these inequalities has been implemented. Computational experience on small problems with 20/30 jobs and various constraints and objective functions is presented.

Abstract
The author describes a man-computer interactive mass transit crew scheduling module which was developed as a component of a Decision Support System (DSS) implemented in a personal computer at the Oporto Urban Transport Authority (STCP). The problem of crew scheduling is briefly discussed and set in the context of the broader process of the planning and control of urban transport services. The general philosophy and the structure of the module are analysed. A crew scheduling heuristic based method is presented. Particular attention is paid to the interactive nature of the approach adopted. Results of the actual implementation process at STCP are given.