Integrated Lot Sizing in Serial Supply Chains with Production Capacities

Abstract

We consider a model for a serial supply chain in which production, inventory, and transportation decisions are integrated in the presence of production capacities and concave cost functions. The model we study generalizes the uncapacitated serial single-item multilevel economic lot-sizing model by adding stationary production capacities at the manufacturer level. We present algorithms with a running time that is polynomial in the planning horizon when all cost functions are concave. In addition, we consider different transportation and inventory holding cost structures that yield improved running times: inventory holding cost functions that are linear and transportation cost functions that are either linear, or are concave with a fixed-charge structure. In the latter case, we make the additional common and reasonable assumption that the variable transportation and inventory costs are such that holding inventories at higher levels in the supply chain is more attractive from a variable cost perspective. While the running times of the algorithms are exponential in the number of levels in the supply chain in the general concave cost case, the running times are remarkably insensitive to the number of levels for the other two cost structures.lot sizing, integration of production planning and transportation, dynamic programming, polynomial time algorithms

A practical expected-value-approach model to assess the relevant procurement costs

“…Fortunately, these items, such as the direct material cost and the holding cost (Ghodsypour and O'Brien, 1998;Dahel, 2003;Kelle et al, 2003;Hoesel et al, 2005), the transportation cost (Hoesel et al, 2005;Hill and Galbreth, 2008), the order handling/receiving cost (Kelle et al, 2003), and the administrative (management) cost (Dahel, 2003;Chopra and ManMohan, 2004;Hong et al, 2005;Araz and Ozkarahan, 2007), have, already, been dispersedly mentioned or modelled by the researchers. These make the EOC assessment more grounded.…”

Coordinated production and delivery for an exporter

“…They developed a polynomial-time DP algorithm to solve the problem. Van Hoesel et al (2005) proposed a model for a serial supply chain, in which production, inventory, and transportation decisions are integrated in the presence of production capacities and concave cost functions. They generalized the uncapacitated serial single-item multilevel economic lotsizing model by adding stationary production capacities at the manufacturer level and presented DP algorithms with a running time that is polynomial in the length of the planning horizon when all cost functions are concave.…”

Optimal stationary policies in a 3-stage serial production-distribution logistic chain facing constant and continuous demand

“…He restricted his study to stationary nested policies. Some research has also been developed in discrete time environment (see [9] or [2] for heuristic techniques for examples). Recall that all these papers consider increasing holding costs along the chain and unlimited production capacity upstream.…”