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| Analysis of Serial Inventory Systems with Batch Ordering and Nested Replenishment Schedule |
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| Abstract: |
We consider an $N$-stage serial inventory system
where material is produced/ordered in batches. Inventory replenishment between
stages follows a nested schedule. Stochastic customer demand occurs at the most
downstream stage. There are two types of fixed costs considered in this system:
setup costs and order costs. The former is associated with each batch
produced/ordered; the latter is incurred for each replenishment cycle. We study
two models. The first (resp., second) assumes that batch sizes (resp.,
replenishment cycles) are fixed. The objective is to determine optimal reorder
points and replenishment cycles (resp., batch sizes). These models represent two
variants of the deterministic model (e.g., Maxwell and Muckstadt 1985 and Roundy
1985). For both models, we use the same approach to construct a lower bound on
optimal cost and to develop an optimization algorithm. Since the algorithm is
computationally infeasible for large systems, we further propose a heuristic
that generates near-optimal solutions by solving at most $N$ single-stage
systems with the original problem data. We find, among other insights, that
managing these two systems is quite similar indeed.
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| Keyword: |
Multi-echelon inventory model
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