Effective network formulations for lot sizing with backlogging in two-level serial supply chains. Issue 2 (1st February 2016) - Solyali, Oguz; Denizel, Meltem; Süral, Haldun
ABSTRACT: This study considers the serial lot sizing problem with backlogging in two-level supply chains to determine when and how much to order at a warehouse and ship to a retailer over a T -period planning horizon so that the external known demand occurring at the retailer is satisfied and the total cost at all levels is minimized. In particular, the uncapacitated two-level serial lot sizing problem with backlogging and the two-level serial lot sizing problem with cargo capacity and backlogging are formulated using effective shortest-path network representations, which define the convex hull of their feasible solutions. These representations lead to efficient algorithms with O ( T 3 ) time for the uncapacitated problem and O ( T 6 ) time for the capacitated problem. Furthermore, a tight reformulation with O ( T 3 ) variables and O ( T 2 ) constraints (resp.  O ( T 6 ) variables and O ( T 5 ) constraints) is proposed for the uncapacitated (resp. capacitated) problem.