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A column generation algorithm for a stochastic location-inventory network design problem
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DOI：10.1016/j.orl.2025.107386.png)
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Abstract
En 中文
We consider a distribution network design problem where decisions on location, assignment and inventory management must be made concurrently. The model must simultaneously determine which from among a set of candidate warehouses to set up, which retailers to assign to each open warehouse for stock replenishment, and what the replenishment policy of each facility must be in order to minimize an infinite-horizon two-echelon inventory cost function. This last decision component is based on a one-warehouse multiretailer (OWMR) problem with stochastic demand: retailers replenish stocks from the central warehouse they are assigned to, which in turn replenishes from an outside supplier. Retailer demand is independent and normally distributed with given (nonidentical) means and variances. Safety stock must be kept both at retailer sites and at the warehouse in order to maintain certain required Type-I service levels. We consider power-of-two (POT) periodic ordering policies. The goal is to minimize long-term average fixed and holding costs. We design a set-partitioning reformulation for the overall network design problem whose linear relaxation is solved via column generation. In doing so, we leverage tools for the OWMR problem to design an algorithm for the pricing problem used to generate columns for the set-partitioning formulation. Computational experiments show that the formulation exhibits strong tightness properties, and that the proposed method returns good solutions for moderately-sized systems within reasonable computational times.
Keywords:
Joint location-inventory problems
One-warehouse multiretailer systems (OWMR)
Stochastic demand
Piecewise linearization
Set-partitioning
Column generation
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