Maximin and maximal solutions for linear programming problems with possibilistic uncertainty

We consider linear programming problems with uncertain constraint coefficients described by intervals or, more generally, possi-bility distributions. The uncertainty is given a behavioral interpretation using coherent lower previsions from the theory of imprecise probabilities. We give a meaning to the linear programming problems by reformulating them as decision problems under such imprecise-probabilistic uncer-tainty. We provide expressions for and illustrations of the maximin and maximal solutions of these decision problems and present computational approaches for dealing with them

Manufacturing flow line systems: a review of models and analytical results

The most important models and results of the manufacturing flow line literature are described. These include the major classes of models (asynchronous, synchronous, and continuous); the major features (blocking, processing times, failures and repairs); the major properties (conservation of flow, flow rate-idle time, reversibility, and others); and the relationships among different models. Exact and approximate methods for obtaining quantitative measures of performance are also reviewed. The exact methods are appropriate for small systems. The approximate methods, which are the only means available for large systems, are generally based on decomposition, and make use of the exact methods for small systems. Extensions are briefly discussed. Directions for future research are suggested.National Science Foundation (U.S.) (Grant DDM-8914277

Capacity-expansion planning under uncertainty in the electric-utility industry

This document basically represents a comparison between theory and practice of capacity-expansion planning in the electric-utility industry. The purpose of the comparison is to provide avenues for further exploration in utility decision making. The focus of the Phase II study is upon the role of uncertainty in the decision-making process. The Phase I effort was directed at modeling the Averch-Johnson theory of the regulated utility. Part I of this report reviews the Anderson study (D. Anderson, Models for Determining Least-Cost Investments in Electricity Supply). The Anderson paper has become a standard reference for capacity-planning studies in the electric-utility industry. Part II examines uncertainty and the behavior of the firm. Part III reviews 5 models of electric-utility capacity planning under uncertainty, and Part IV is concerned with capacity-planning models in practice

Best and Worst optimum for linear programs with interval right hand sides

In optimization, it is used to deal with uncertain and inaccurate factors which make difficult the assignment of a single plausible value to each model parameters. Two approaches are possible: in the first one, a single nominal value is assigned to each parameter, the corresponding optimal solution is computed, then the interval in which each parameter can vary in order to preserve optimality solution is determined; the second approach consists in taking into account in the model to optimize, the possible variations of each parameter. In mathematical programming, the first approach is known as sensitivity analysis (see e.g. [6]). For the second approach, stochastic optimization may be applied for some problems in which parameters value can be described by probability laws (see for example [4]). When it is not possible nor relevant to associate probability laws to parameters, another way amounts to assign a set of possible values to each parameter. Two models may be considered: in the first one, a finite set of values is assigned to each uncertain model coefficient; in the second one, each uncertain model coefficient is associated with an interval number. In this paper, we only consider this second model called interval linear programming.ou

Sleeping position and upper airways bacterial flora: relevance to cot death.

The hypothesis that the prone sleeping position is associated with accumulation of upper airways secretions and increased bacterial growth was investigated in adults. Ten subjects with upper respiratory tract infection lay prone for one hour and then supine for one hour. Nasal swabs after the prone period yielded higher bacterial counts than swabs obtained after the supine period. This result could be relevant to sudden infant death syndrome (SIDS), as infants who sleep in the prone position are at increased risk of SIDS and one theory is that death is caused by toxins produced by bacterial overgrowth in the upper respiratory tract following a viral infection

Layered Formulation for the Robust Vehicle Routing Problem with Time Windows

Abstract. This paper studies the vehicle routing problem with time windows where travel times are uncertain and belong to a predetermined polytope. The objective of the problem is to find a set of routes that services all nodes of the graph and that are feasible for all values of the travel times in the uncertainty polytope. The problem is motivated by maritime transportation where delays are frequent and must be taken into account. We present an extended formulation for the vehicle routing problem with time windows that allows us to apply the classical (static) robust programming approach to the problem. The formulation is based on a layered representation of the graph, which enables to track the position of each arc in its route. We test our formulation on a test bed composed of maritime transportation instances