Closed-form approximations for optimal (r, q) and (S, T) policies in a parallel processing environment
We consider a single-item continuous-review (r, q) inventory system with a renewal demand process and independent, identically distributed stochastic lead times. Using a stationary marked-point process technique and a heavy-traffic limit, we prove a previous conjecture that inventory position and inventory on-order are asymptotically independent.We also establish closed-form expressions for the optimal policy parameters and system cost in heavy-traffic limit, the first of their kind, to our knowledge. These expressions sharpen our understanding of the key determinants of the optimal policy and their quantitative and qualitative impacts. For example, the results demonstrate that the well-known square-root relationship between the optimal order quantity and demand rate under a sequential processing environment is replaced by the cube root under a stochastic parallel processing environment. We further extend the study to periodic-review (S, T) systems with constant lead times.
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Related Subject Headings
- Operations Research
- 3507 Strategy, management and organisational behaviour
- 1503 Business and Management
- 0802 Computation Theory and Mathematics
- 0102 Applied Mathematics
Citation
Published In
DOI
EISSN
ISSN
Publication Date
Volume
Issue
Start / End Page
Related Subject Headings
- Operations Research
- 3507 Strategy, management and organisational behaviour
- 1503 Business and Management
- 0802 Computation Theory and Mathematics
- 0102 Applied Mathematics