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A Heuristic Approach to the Multi-Period Single-Sourcing Problem with Production and Inventory Capacities and Perishability Constraints

Department of Industrial and Systems Engineering, University of Florida, P.O. Box 116595, Gainesville, Florida 32611-6595, USA
Innovative Scheduling, Gainesville Technology Enterprise Center (GTEC), 2153 Hawthorne Road Suite 128, Gainesville, Florida 32641, USA
Department of Industrial and Systems Engineering, University of Florida, P.O. Box 116595, Gainesville, Florida 32611-6595, USA
Saïd Business School, University of Oxford, Park End Street, Oxford OX1 1HP, United Kingdom
ahuja{at}ufl.edu
huang{at}innovativescheduling.com
romeijn{at}ise.ufl.edu
Dolores.Romero-Morales{at}sbs.ox.ac.uk

The multi-period single-sourcing problem that we address in this paper can be used as a tool for evaluating logistics network designs in a dynamic environment. We consider the assignment of retailers to facilities, taking into account the timing, location, and size of production and inventories, in the presence of various types of constraints. We formulate the problem as a nonlinear assignment problem, and develop efficient algorithms for solving the capacitated lot-sizing subproblems that form the objective function of this formulation. We propose a greedy heuristic, and prove that this heuristic is asymptotically optimal in a probabilistic sense when retailer demands share a common seasonality pattern. In addition, we develop an efficient implementation of the very-large-scale-neighborhood-search method that can be used to improve the greedy solution. We perform extensive tests on a set of randomly generated problem instances, and conclude that our approach produces very high quality solutions in limited time.

Key words: production and inventory planning; capacity constraints; heuristics
History: received April 2003; revised March 2005; accepted April 2005.