Continuous time control of make-to-stock production systems
Author(s)
Advisor
Fadıloğlu, M. MuratDate
2010Publisher
Bilkent University
Language
English
Type
ThesisItem Usage Stats
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Abstract
We consider the problem of production control and stock rationing in a make-tostock
production system with multiple servers –parallel production channels--, and
several customer classes that generate independent Poisson demands. At decision
epochs, in conjunction with the stock allocation decision, the control specifies
whether to increase the number of operational servers or not. Previously placed
production orders cannot be cancelled. We both study the cases of exponential and
Erlangian processing times and model the respective systems as M /M /s and M /Ek /s
make-to-stock queues. We characterize properties of the optimal cost function, and
of the optimal production and rationing policies. We show that the optimal
production policy is a state-dependent base-stock policy, and the optimal rationing
policy is of state-dependent threshold type. For the M /M /s model, we also prove
that the optimal ordering policy transforms into a bang-bang type policy when we
relax the model by allowing order cancellations. Another model with partial ordercancellation
flexibility is provided to fill the gap between the no-flexibility and the
full-flexibility models. Furthermore, we propose a dynamic rationing policy for the
systems with uncapacitated replenishment channels, i.e., exogenous supply systems. Such systems can be modeled by letting s --the number of replenishment channels--
go to infinity. The proposed policy utilizes the information on the status of the
outstanding replenishment orders.
This work constitutes a significant extension of the literature in the area of control
of make-to-stock queues, which considers only a single server. We consider an
arbitrary number of servers that makes it possible to cover the spectrum of the cases
from the single server to the infinite servers. Hence, our work achieves to analyze
both the exogenous and endogenous supply leadtimes.
Keywords
InventorySimulation
Optimal Control
Multiple Demand Classes
Multiple Servers
Make-toStock
Dynamic Rationing
Stock Rationing
Production