Abstract
The problem of transport management in a distributed logistics system "suppliers – consumers" is considered. Under the assumption of a random nature of transportation costs, an exact algorithm for solving this problem by a probabilistic criterion has been developed. This algorithm is implemented by an iterative procedure for sequential improvement of the transportation plan. The rate of convergence of a computational procedure to an exact solution depends significantly on the dimension of the problem and is unacceptably low in real problems. In this regard, an alternative method is proposed, based on reducing the original problem to solving a nontrivial problem of fractional-nonlinear programming. A method for solving this problem has been developed and substantiated. The corresponding computational algorithm reduces the fractional-nonlinear model to the quadratic one. The resulting problem is solved by known methods. Further, the original problem is supplemented by considering a situation that is important for practice, when in the conditions of a small sample of initial data there is no possibility of obtaining adequate analytical descriptions for the distribution densities of the random costs of transportation. In this case, the available volume of statistical material is sufficient only to estimate the first two moments of unknown distribution densities. For this marginal case, a minimax method for finding the transportation plan is proposed. The first step is to solve the problem of determining the worst distribution density with the given values of the first two moments. In the second step, the transportation plan is found, which is the best in this most unfavorable situation, when the distribution densities of the random cost of transportation are the worst. To find such densities, let’s use the modern mathematical apparatus of continuous linear programming
Highlights
In the system of management tasks for the multifunctional logistics complex «production – delivery – consumption», transport tasks take the central place
There are m suppliers of a homogeneous product and n consumers of this product. It is known the vector A = (a1a2...ai...am), the components of which fix the capabilities of suppliers, (2021), «EUREKA: Physics and Engineering» Number 2 the vector B = (b1b2...bj...bn), the components of which specify the demand of consumers, and the matrix C =, which determines the cost of delivery of a product unit from suppliers to consumers
It is shown that the problem of finding a plan that minimizes this criterion and satisfies the system of constraints belongs to the class of fractional nonlinear programming problems
Summary
In the system of management tasks for the multifunctional logistics complex «production – delivery – consumption», transport tasks take the central place. There are m suppliers of a homogeneous product and n consumers of this product. It is known the vector A = (a1a2...ai...am), the components of which fix the capabilities of suppliers,. (2021), «EUREKA: Physics and Engineering» Number 2 the vector B = (b1b2...bj...bn), the components of which specify the demand of consumers, and the matrix C = (cij), which determines the cost of delivery of a product unit from suppliers to consumers. It is necessary to find a nonnegative matrix X = (xij) that defines a plan for transporting a product from suppliers to consumers, minimizing the total cost of transportation: mn ∑ ∑ L1(X) = cij xij (1).
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