مشکل حمل و نقل: مورد خاص برای مشکلات برنامه ریزی خطی در مهندسی معدن

In real world applications the supply, the demand and the transportation cost per unit of the quantities in a transportation problem are hardly specified precisely because of the changing economic and environmental conditions. It is also important that the time required for transportation should be minimum. In this paper a method has been proposed for the minimization of transportation costs. Supply and transportation costs per unit of the quantities are also determined. The present study was carried out to evaluate the quality of gravel to know its suitability for aggregate (raw material for concrete and road). The samples of gravel were analyzed for petrographic, physical, mechanical and chemical properties. Samples were categorized as quartzite group and carbonate group according to ASTM standard 295. Among these, samples of quartzite group were found dominant. The petrography examination of gravels which was carried out constituted of opal, tridymite, chalcedony, crystobalite and alkali carbonates rocks. Those minerals react with alkalis in cement leading to expansion and cracking of concrete. Other components such as sulfides, sulfates, halites, iron oxides, clay minerals and anhydrites are examined, which might be present as coating and impurities. The present study indicated that all samples are suitable for concrete making and obtain the optimum solution for transporting these materials from quarries to cities with minimum cost according to Egyptian Code.

Transportation problem one of the most important and successful applications of quantities analysis to solve business problems has been in the physical distribution of products, commonly referred to as transportation problems. Basically, the purpose is to minimize the cost of shipping goods from one location to another so that the needs of each arrival area are met and every sipping location operates within its capacity. Although the transportation problem can be solved using the regular simplex methods, its specials structure offers a more convenient procedure for solving this type of problem. This procedure is based on the same theory as that of the simplex method, but it makes use of some short cuts which yield a simpler computational scheme as discussed in Gass [1]. In the case of rapid increasing population or development growth such as the Sohag governorate in Egypt, new infrastructures are necessary to meet the increasing of requirements. Construction materials in general and aggregate in particular are important components of infrastructure. Construction materials resources in Sohag retain to quaternary sediments as discussed in Omara [2]. Gravels are considered the most important raw materials in all building construction in this study area. Gravels are accumulations which exist in terraces occupying the area between the old cultivated and the foot slopes of Eocene. Quaternary sediments are mainly repeated by siliceous or calcareous associated with washed deposits such as clay. Sources of the gravel may be from the neighboring middle Eocene. To select the type of aggregate suitable for different purposes, the physical and chemical properties are determined. The study area lies along Sohag governorate on both sides of River Nile [3] and [4].

From the present work, it is concluded that: (1) All quarries gravel in the area under investigation is used in construction and building materials. Materials were classified according to their physical, chemical, petrographical properties for different uses. (2) The application of the optimum solution will give the minimum costs of transportation, as shown in Table 3 and Table 4. Results were obtained by the Premium Solver Platform program for gravel according to the given mathematical models of the problem (Sohag). This program is one of the simplest programs for such problems. (3) This study can be applied to the evaluation of the transportation problems for all locations of construction and building materials at any location. (4) The optimum solution means that, the production of gravel quarries in the studied area cover exactly the requirements of all construction sites, from one side and that these materials are totally consumed within the governorates borders. (5) This problem can be formulated when the availabilities are greater than requirements or the requirements are greater than the availabilities.