Abstract
We investigate M/M/1/∞-systems with inventory management, continuous review, exponentially distributed lead times and backordering. We compute performance measures and derive optimality conditions under different order policies. For performance measures, which are not explicitly at hand, we present an approximation scheme for all possible parameter combinations. Although we cannot completely determine analytically the steady state probabilities for the system we are able to derive functional relations between interesting probabilities and show surprising insensitivity properties of several performance measures. For the approximations we develop an algorithm adapted to the system structure which suggests easy adaption to other systems.
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Work supported by Deutscher Akademischer Austauschdienst and KBN, Poland, Project D/02/32206.
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Schwarz, M., Daduna, H. Queueing systems with inventory management with random lead times and with backordering. Math Meth Oper Res 64, 383–414 (2006). https://doi.org/10.1007/s00186-006-0085-1
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DOI: https://doi.org/10.1007/s00186-006-0085-1
Keywords
- Queueing systems
- Queue lengths
- Performance analysis
- Inventory systems
- Inventory policy
- Service level
- Inventory level