Advances in Automatic Control
Using Genetic Algorithms to Solving the Allocation Problem of Loading/Unloading Ramps from a Warehouse Olteanu Sergiu, Petrescu Victoria Relly Transport, Traffic and Logistics University POLITEHNICA of Bucharest Splaiul Independentei nr.313, ,Bucharest ROMANIA
[email protected],
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Abstract: The paper presents a genetic algorithm used to solving the problem of allocation loading-unloading ramps to a warehouse. It is known that goods stores have the main functions receipt, storage, sorting and shipping the merchandises. Logistics companies found that the storage and sorting of goods is done with some costs. This led to a strategy that minimizes the storage and sorting of goods and default costs. This strategy is based on the philosophy of "Just in time" which eliminates functions of storage and sorting of goods and deposits while other functions are developed. Currently following the unloading of each truck is assigned a landing immediately available and each truck load is found to assign a specific loading dock. Arranging ramps for loading and unloading and the allocation of destinations for loading ramps are a difficult combinatorial optimization problem. The main purpose of this report is to present the issue of allocation of unloading/loading ramps, problem involving the allocation of destinations to loading ramps of cross-docking centers, so technically cargo handling equipment to minimize the number of moves made for achieving the loading / unloading process. The efficiency of a cross-docking center is conditioned practically by finding an allocation and an optimal arrangement of ramps. Key-words: genetic, logistics, loading, unloading, generation, ramp.
1 Introduction
2 Problem Formulation
It is known that goods stores have the main functions receipt, storage, sorting and shipping the merchandises. Logistics companies found that the storage and sorting of goods is done with some costs. This led to a strategy that minimizes the storage and sorting of goods and default costs. This strategy is based on the philosophy of "Just in time" which eliminates functions of storage and sorting of goods and deposits while other functions are developed. Currently following the unloading of each truck is assigned a landing immediately available and each truck load is found to assign a specific loading dock.
Arranging ramps for loading and unloading and the allocation of destinations for loading ramps are a difficult combinatorial optimization problems. The main purpose of this report is to present the issue of allocation of unloading/loading ramps, problem involving the allocation of destinations to loading ramps of cross-docking centers, so technically cargo handling equipment to minimize the number of moves made for achieving the loading / unloading process. The efficiency of a crossdocking center is conditioned practically by finding an allocation and an optimal arrangement of ramps.
ISBN: 978-960-474-383-4
311
Advances in Automatic Control
downloading and 4 ramps of uploading, presented schematically in the below figure.
3 Problem Solution - Genetic algorithms Genetic algorithms are adaptive heuristic search techniques based on the principles of genetics and natural selection Darwin stated (survives who is better suited (adapted)). The mechanism is similar to the biological process of evolution. This process has a feature that only the species that are better adapted to the environment are able to survive and evolve over generations, while those less adapted fail to survive and in time disappear, as a result of natural selection. The probability that species to survive and evolve over generations becomes greater the degree of adaptation increases, as the optimization terms means that the solution approaches of optim. A genetic algorithm is a computer model that emulates biological evolutionary model to solve problems of optimization or search. It comprises a set of individual elements represented in the form of binary strings (population) and a set of biological operators defined on population. With the aid of operators, the genetic algorithms handling the most promising strings, evaluated according to an objective function, seeking better solutions. Genetic algorithms have begun to be recognized as optimization techniques with the work of John Holland. Genetic algorithms are considered by specialists an application of artificial intelligence. As practical applications, genetic algorithms are often used to solve optimization problems, planning or search. The essential condition for the success of an application with intelligent agents is the problem to be solved not to seek to obtain the optimal solution, but to be sufficient and as a solution close to optimum. To make this optimization mechanism and to solve the "problem ramps Allocation discharge / charge a deposit" was used as the main tool for work Visual C++ programming language release 6.0 in addition with optimization techniques work based on genetic algorithms. This mechanism was created in several steps. The base model from which we started was a warehouse equipped with 8 ramps, 4 ramps of
Fig. 1 The structure with 8 loading/unloading ramps
Step1 At first, through a sub-functions implemented in C + + have a randomly generated 18 possible solutions. Step 2 Then through the objective function it was possible to calculate, for each solution, the number of moves performed by cargo handling machinery. Step3 After the previous step calculations we selected the last two solutions listed as the weakest of the 18 possible, and we have reintroduced a new cycle of random generation thus obtaining 18 more possible solutions to each of the two weak solutions. For each of the 36 solutions obtained new objective function is computed by selecting the best solutions. These two solutions are introduced in the initial population of solutions instead of two weak solutions. Step 3 is taken 100 times reaching finally to solutions that tend to be constant work we show that the optimal solution was found. Then this mechanism was tested on a wider field, namely a warehouse with 16 ramps, eight ramps for loading and eight ramps for unloading, and each ramp has a capacity of two trucks(a total of 32 trucks).
Fig. 2 The structure with 16 loading/unloading ramps
ISBN: 978-960-474-383-4
312
Advances in Automatic Control
Y nj is the total quantity of goods, to
We have obtained good results in this case too. The results are presented in the next chart:
the n
destination, that needs to be loaded at the j ramp.
4 Conclusion Genetic algorithms have many practical aplications and they are more and more used in various domains. The power of genetic algorithms comes from their simplicity and from the fact that even if they do not give the optimal solution, certainly the proposed solution is always close to the best results. For the allocation problem of loading/unloading ramps, relative to the initial solution at 100th generation of solutions, the total number of movements has been reduced with almost 11%.
Fig. 3 Modelling results
As we can observe from the Fig.3, for the 100th generation of solutions , the total number of movements done by the handling equipment has been significantly reduced. This mechanism is reduced to a mathematical model which involves the minimization of following function: I
J
M
References:
[1] Banzhaf W., Nordon P., Keller R.E., Francone F.D., Genetic Programming – An introduction, Morgan Kaufmann Publishiers, San Francisco, 1998. [2] Mateescu, G. D., Optimization by Using Evolutionary Algorithms with Genetic Acquisitions, Romanian Journal of Economic Forecasting, 2005. [3] Oltean, M. – Proiectarea si implementarea algoritmilor, Editura Computer Libris Agora, Cluj, 1999. [4] Andonie, R., Garbacea, I., Algoritmi fundamentali, o perspectiva C++, Editura Libris, Cluj, 1995. [5] Dumitrescu, D., Algoritmi genetici si strategii evolutive-aplicatii in inteligenta artificiala si in domenii conexe, Editura Albastra, Cluj Napoca, 2000.
N
d i 1 j 1 m 1 n 1
ij
wmn X miYnj where,
M is the number of origins; N is the number of destinations; I is the number of unloading ramps; J is the number of loading ramps; wij is the number of paths that have to be made by the handling equipment from the ramp i to the ramp j;
d ij is the distance from the ramp i to the ramp j; X mi is the total quantity of goods, from the m origin, that needs to be unloaded at the i ramp.
ISBN: 978-960-474-383-4
313
Advances in Automatic Control
ANNEX /*C++ SCRIPT*/ # include # include # include # include # include int A[9][3][20],dist[5][5],cant[9][9]; int i,rampa1,rampa2,camion_sosire,camion_expediere; int max1,max2,poz1,poz2; int matrice1[9][3][20],matrice2[9][3][20]; void initializari() { for(int k=0;k
