Solving Supply Planning Problem Under Uncertain Demands

It is very important for each enterprise in the joint of supply chain to make its supply plan under uncertain demands. A reasonable and feasible supply plan is an important factor for the success of an enterprise.Supply planning is a multi-objective optimization problem which tries to maximize gross profit, minimize cost and opportunity loss simultaneously. It is an uncertain problem owing to the random and variable market demands. The uncertainty of the problem directly affects some indices that enterprise cares about. The supply planning in mathematics is described correctly by a multi-objective stochastic optimization model. Thus, the results of the optimization model are more scientific and effective.The random demands are the first consider question. In this thesis, the market demands are simulated by some historical datum (e.g. mathematical expectations, deviations and correlation coefficients between them), which satisfy certain probability distribution. Then the Monte Carlo Simulation is introduced based on the market demands. The simulation of uncertain demands depends on a fine pseudorandom number generator in the interval [0,1]. The module 2~W pseudorandom number generator, which was presented in 1960's, has a quite great development. MT algorithm is one of Feedback Shift Register Generators, which has been applied into many fields widely, due to its long-period, high decision and good random performance in high-dimension. Thus, in this thesis, it is used to solve the supply planning problem too.Traditionally, there are several classic methods for solving multi-objective optimization, but it is hard to get an acceptable solution owing to the problem complexity caused by the stochastic of the problem. Thus, a multi-objective genetic algorithm by which several Pareto optimal solutions can be gotten is employed in this thesis. We adopt Monte Carlo simulation method, which makes the statistics amount of gross profit, cost and opportunity loss as fitness function. In this thesis, we present several strategies to decision-makers as alternatives based on the gross profit maximization, cost and opportunity loss minimization. Boundary initialization and random initialization of population are employed. Moreover, the boundary initialization of population is obtained by getting all the extreme points of the bounded convex polyhedron.We show the effect of our approach by one numerical experiment. The results show that this approach achieves a remarkable performance. Between the two different population initialization strategies, the boundary initialization makes the search more efficient thanrandom initialization. Further more, compared with consideration of gross profit and opportunity loss, the consideration of cost plays a greater role in the affection of the final results.