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Queueing with Inventory Models for Analysing Make-to-Order Systems

Saffari, Mohammad | 2010

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 42034 (01)
  4. University: Sharif University of Technology
  5. Department: Industrial Engineering
  6. Advisor(s): Hajji, Alireza
  7. Abstract:
  8. In this thesis, we consider various Make-to-Order systems as a version of integrated production-inventory systems. Most Make-to-order systems can be sufficiently modeled by a queueing system with inventory in which completing each service in the queueing system requires an on-hand inventory. Unlike most researches in this field, we present an analytical approach. In all systems we embed a stochastic process with joint state space that can entirely describe the state of system. Then steady state distributions are derived. Those distributions are applied to compute performance measures and long-run average cost function which can be used for optimization. In our Make-to-Order models, demands arrive according to a Poisson process and service/production times of single service/production unit are xponentially distributed random variables. These systems are modeled as an M/M/1 system with inventory. We consider such a model with lost sale situation in which system does not accept arriving demands during stockout. We first apply continuous review (r, Q) policy for the inventory system, and replenishment lead times are mixed exponentially distributed. We derive Steady state distribution of joint queue length and on-hand inventory using balance equations. As an extension of the previous model a similar model is developed when lead times can take every probability distribution. Deriving the steady state distribution for general lead times is a significant challenge in this model because continuous time markov process assumption of the embedded process will be vanished. We first prove that the stationary distribution is of product form f joint queue length and on-hand inventory. Then we derive marginal steady state distributions separately to conclude the joint stationary distribution.The remaining parts deal with the Make-to-Order system in a two echelon supply chain, in which Customers refer to retailer according to a Poisson process and retailer uses one for one inventory policy. The supplier has an inventory system and a service unit to process the orders received from the retailer. The supplier’s lead time and the service time of his service unit are exponentially distributed random variables. When the supplier has on-hand inventory, the retailer’s order joins the queue at the service unit. Otherwise the supplier does not accept retailer’s order. We first consider the model when supplier uses (r, Q) inventory management policy but in the subsequent chapter we assume that supplier uses one for one inventory policy. Steady state distributions of joint queue length of supplier, supplier’s on-hand inventory and retailer’s on-hand inventory are derived using balance equations. Finally computing performance measures and cost functions we conclude optimal inventory policies of the supply chains
  9. Keywords:
  10. Inventory Control ; Queueing System ; Make-to-Order ; Stationary Probabilities

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