M (t) _j ~ (x_j,) / G_j Queues, As Well As Optimization Algorithm In Order Assembly In The Supply Chain

In recent years, the analysis for supply chain (SC) has been a new focus. In the field of operations research and an assemble-to-order (ATO) system is an important business model in managing a wide-ranging class of supply chains. To get the performance of ATO and realize optimal control, it is key to give mathematical model of system.In this thesis, the set of M(t)_j^X_j/G_j queues has been analyzed, and we introduce the set of M(t)_j^X_j/G_j queues and optimization algorithm into the assemble-to-order system.The main results are as follows:1. We consider set of queues M(t)_j^X_j/G_j/∞driven by common inhomogeneous Poisson batch arrival process. And we derive the multivariate generation functions for joint queue length process and joint output process, and give the analysis of relative properties between queuing systems.2. We introduce set of M_i^X_i/D_i/∞queues into an assemble-to-order system. We study an optimization problem to determine the optimal component base-stock levels: minimizing expected number of component backorders and the average component inventory on hand in steady state subject to an upper limit on the total component inventory investment and a components fill rate. We also give its corresponded numerical example by greedy-type algorithm.3. An assemble-to-order which is equal to the set of M_i^X_i/D_i queues with finite capacity based on (R_i,Q_i) policies is considered. Since the set of queues have finite capacity, not only the producer-based performance measures but also the supplier-based performance measures should be concerned. And we find a coordination mechanism using Stacklberg principal and subordinate game that allows assemble-to-order to perform just as well as a centralized one. Then the genetic algorithm is introduced to minimize the long run average cost with respect to the reorder points, order batch size and the extra capacity of suppliers in the numerical example.