Thursday, 14:15 - 14:40 h, Room: H 0104


Laurence Wolsey
The one warehouse multiple retailer problem with start-ups and constant capacities

Coauthors: Mathieu Van Vyve, Hande Yaman


For the uncapacitated OWMR problem with K clients and T periods,
a multi-commodity reformulation solves instances with K,T=100 to optimality. We consider a new relaxation
motivated by the Wagner-Whitin relaxation that is effective for single level problems. The relaxed solution set
X decomposes into X =∩t=1TYt, each set Yt having the same structure, denoted Y.

  1. When K=1 and uncapacitated at warehouse and client, we give a tight and compact extended formulation for conv(Y), an inequality description in the original space, and an O(T) separation algorithm.
  2. A similar result with start-up costs at both levels.
  3. With multiple clients (K>1), the convex hull of Y is essentially the intersection of the convex hulls for each client individually,
    providing an O(KT2) formulation for X and OWMR.
  4. When uncapacitated at the warehouse and constant capacity for each retailer, we give an extended formulation for Y
    that is conjectured to be tight.

For OWMR with start-ups, our formulation improves computationally on the multicommodity formulation, and with capacities it solves to optimality instances with K,T=25.


Talk 3 of the invited session Thu.2.H 0104
"Strong relaxations for stable set and lot sizing" [...]
Cluster 11
"Integer & mixed-integer programming" [...]


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