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Reports on a feasible direction method for solving Linear Programming problems followed by a procedure for purifying a non-basic solution to an improved extreme point solution. Design of the algorithm; Termination of the interior search step at a boundary point which is usually non-basic; Possible applications of the method.

AbstractSwap practices in the oil industry have been mostly ad-hoc, with no theoretical foundation, the main objective being to swap products on an as-needed basis. This research, using goal programming (GP), proposes a multiple objective methodology to solve the swap problem of the firms in the oil industry. The proposed model offers attractive alternatives and various practical GP-based scenarios, allowing the managers in the oil industry to consider viable options which take into consideration preferences, tradeoffs and outcomes when planning their logistics strategies and supply chain management activities. The swap strategies offered in this research have been developed with close cooperation of the officials from the oil industry—thus have practical implications and can be readily implemented.

This paper proposes and examines several swap strategies for the oil industry to create win-win situations for companies supplying oil to their customers. A realistic data from a Kuwaiti oil company and its competitor, in another part of the world, is used to build a number of Linear Programming models of the strategies under investigation. The optimal solutions of these models are analyzed to identify the strategies' advantages or disadvantages.The success of swap strategies relies on alliances and partnerships between the oil companies. They, however, seem to advocate very attractive alternative policies, create potentials for substantial cost savings and assure more reliable lead-time to delivery.

The aim of this research is to use Taguchi's loss function to assess the loss associated with a solution provided by a particular Multi-Criteria Decision Making (MCDM) method. Although the idea proposed in this paper, derived from Taguchi's philosophy and his idea of social loss, can be invariably applied to any MCDM method, the paper utilises Goal Programming (GP) to illustrate the applicability of the proposed method.