FINDING ACCEPTABLE SOLUTIONS OF CONVEYOR SYSTEMS PROBLEM FOR FOUR AND MORE OPERATIONS APPLYING DIRECTIONAL SEARCH METHOD

When forming various production plans of short-term or long-term nature, managers often have to solve the problem of reducing the production time of a certain product or parts (blocks) of a single complex product. Solving such problems can be reduced to a mathematical formulation of combinatorial optimization problems - the so-called ordering problems, the methods of solving which have been developing and improving for several centuries. Many of these methods have their own application limitations. In particular, in order to formulate the problem of conveyor processing (producing a set of items, where each item passes through several technological operations, whose order is strictly determined and must not be violated) the early algorithm for obtaining the optimal launch program was developed only for the process with two technological operations (manufacturing stages). It was Bellman-Johnson’s algorithm. In the given example there are four operations, but the search logic will be the same for the larger number of operations. The proposed method for obtaining solutions to the combinatorial problem of determining the sequence of manufacturing a batch of products or components of one complex product at minimal time consumption is intuitive and simple. It does not require to use deep mathematical knowledge or special computer programs. At the same time, calculations have shown that such logical step-by-step approach allows to obtain solutions that are very close to optimal (or are optimal, in fact). The example given illustrates the search logic. Dimensions of the original matrix (the number of products and the number of technological operations for their manufacture) can be arbitrary. The complexity of the calculations does not depend on it. The algorithm can be used both for forming the changing production plans, and for the task of conveyor processing in various industries.