A branch-and-price algorithm for an integrated production and inventory routing problem

  • Bard J
  • Nananukul N
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With globalization, the need to better integrate production and distribution decisions has become ever more pressing for manufacturers trying to streamline their supply chain. This paper investigates a previously developed mixed-integer programming (MIP) model aimed at minimizing production, inventory, and delivery costs across the various stages of the system. The problem being modeled includes a single production facility, a set of customers with time varying demand, a finite planning horizon, and a fleet of homogeneous vehicles. Demand can be satisfied from either inventory held at a customer site or from daily product distribution. Whether a customer is visited on a particular day is determined by an implicit tradeoff between inventory and distribution costs. Once the decision is made, a vehicle routing problem must be solved for those customers who are scheduled for a delivery. A hybrid methodology that combines exact and heuristic procedures within a branch-and-price framework is developed to solve the underlying MIP. The approach takes advantage of the efficiency of heuristics and the precision of branch and price. Implementation required devising a new branching strategy to accommodate the unique degeneracy characteristics of the master problem, and a new procedure for handling symmetry. A novel column generation heuristic and a rounding heuristic were also implemented to improve algorithmic efficiency. Computational testing on standard data sets showed that the hybrid scheme can solve instances with up to 50 customers and 8 time periods within 1 h. This level of performance could not be matched by either CPLEX or standard branch and price alone. © 2010 Elsevier Ltd. All rights reserved.

Author-supplied keywords

  • Branch and price
  • Column generation
  • Inventory routing
  • Lot-sizing
  • Production planning

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  • Jonathan F. Bard

  • Narameth Nananukul

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