Linear Programming

Increased maritime transport due to global trade has a significant impact on the ports, which are the gateways of countries to trade. Ports make investment plans in order to maintain their competitiveness in the face of increasing freight traffic and also apply various measures in order to store more containers in their storage areas. In the Kocaeli region, the primary method for ports that are stuck in a narrow area is to gain space by filling the sea. However, it is thought that the dry port application, which is becoming more widespread in the world, can be a remedy for Kocaeli container terminals that might suffer from lack of space. The benefits of a dry port application in a circumstance when the seaport has capacity constraints have been examined by developing an optimization model provided that the seaport has a railway connection and is collaborating with that dry port. As a result of this study, it has been understood that all actors involved in container transportation can benefit to a certain level. It is thought that the developed mathematical model in this study can help the decision-making process of port operators. ÖZET Küresel ticarete bağlı olarak artan denizyolu taşımacılığı, ülkelerin ticarete açılan kapıları olan limanları önemli derecede etkilemektedir. Limanlar, artan yük trafiği karşısında rekabet güçlerini muhafaza edebilmek için yatırım planları yapmakta, ayrıca istif alanlarında daha çok konteyner depolayabilmek için çeşitli tedbirlere başvurmaktadırlar. Kocaeli bölgesinde, dar alana sıkışmış durumdaki limanlar için öncelikli yöntem, denizin doldurulması yöntemiyle alan kazanılmasıdır. Bununla birlikte, dünyada yaygınlaşmakta olan kuru liman uygulamasının da, yer kısıtlaması olan Kocaeli konteyner terminalleri için bir çare olabileceği düşünülmektedir. Bir deniz limanı açısından kapasite sorunu söz konusu olduğunda, demiryolu bağlantısına sahip olması ve bir kuru liman ile işbirliği yapması halinde, kuru liman uygulamasının sağlayacağı faydalar, bir optimizasyon modeli geliştirilerek incelenmiştir. Bu çalışmanın neticesinde, konteyner taşımacılığında rol alan tüm aktörlerin belli seviyede fayda sağlayabilecekleri anlaşılmıştır. Geliştirilen matematiksel modelin, liman operatörlerinin karar verme süreçlerinde yardımcı olabileceği düşünülmektedir. Anahtar Kelimeler: Kuru liman, konteyner taşımacılığı, optimizasyon modeli, deniz işletmeciliği.

Maximization of flow through the network has remained core issue in the field of optimization. In this paper a new advanced network problem is introduced, i.e., a multi-commodity network with a separator. This network consists of several sub-networks linked through a commodity separator. The objective is to maximize the flow of the commodity of interest from the commodity mixture at the output of the commodity separator, while observing the capacity constraints of all sub-networks. Such networks are present in Oil and Gas development fields. Such networks are also conceptual representation of material flows of many other manufacturing systems. In this paper an algorithm is developed for maximization of flow in these networks. Maximization of flow in such networks has direct practical relevance and industrial application. The developed algorithm brings together two distinct branches of computer science i.e., graph theory and linear programming to solve the problem.

This paper shows that managerial questions are not answered satisfactorily with the mathematical interpretation of sensitivity analysis when the solution of a linear programing model is degenerate. Most of the commercially available software packages provide sensitivity results about the optimality of a basis and not about the optimality of the values of the decision variables. The misunderstanding of the shadow price and the validity range information provided by a simplex based computer program may lead to wrong decision with considerable financial losses and strategic consequences. The paper classifies the most important types of sensitivity information, graphically illustrates degeneracy, and demonstrates its effect on sensitivity analysis. A production planning example is provided to show the possibility of faulty production management decisions when sensitivity results are not understood correctly. Finally the recommendations for the users of linear programing models and for software developers are provided.