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In this paper, we present a mathematical framework for the problem of minimizing the cash-out penalties of a natural gas shipper. The problem is modeled as a mixedinteger bilevel programming problem having one Boolean variable in the lower level problem. Such problems are difficult to solve. To obtain a more tractable problem we move the Boolean variable from the lower to the upper level problem. The implications of this change of the problem are investigated thoroughly. The resulting lower level problem is a generalized transportation problem. The formulation of conditions guaranteeing the existence of an optimal solution for this problem is also in the scope of this paper. The corresponding results are then used to find a bound on the optimal function value of our initial problem.

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Softcover reprint of the hardcover I st edition 2002No part of this work may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording or otherwise, without written permission from the Publisher, with the exception of any material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work.

One of the many complex problems that arise from the transmission and marketing of natural gas is when a shipper draws a contract with a pipeline company to deliver a certain amount of gas among several points. What is actually delivered is often different from the amount that had been originally agreed upon. This phenomenon is called an imbalance. When an imbalance occurs, the pipeline penalizes the shipper by imposing a cash-out penalty policy. Since this penalty is a function of the operating daily imbalances, an important decision-making problem for the shippers is how to carry out their daily imbalances so as to minimize their incurred penalty.In this paper, we introduce the problem of minimizing the cash-out penalty costs from the point of view of a natural gas shipping party. We present a mixed integer bilevel linear programming model and discuss its underlying assumptions. To solve it efficiently, we reformulate it as a standard mathematical program and describe a penalty-function algorithm functions for its solution. The algorithm is well-founded and its convergence is proved. Results of numerical experiments support the algorithm's robustness providing a valuable solution technique for this very important and complex problem in the natural gas market.Keywords Mixed integer bilevel programming . Penalty function . Natural gas market . Cash-out penalty policy