A polynomial algorithm for a lot-sizing problem with backlogging, outsourcing and limited inventory

Authors:
Chengbin Chu;Feng Chu;Jinhong Zhong;Shanlin Yang
Affiliations:
School of Economics and Management, Tongji University, China and Laboratoire Génie Industriel, Ecole Centrale Paris, France;Laboratoire IBISC, Université d'Evry-Val d'Essone, France;School of Management, Hefei University of Technology, China;School of Management, Hefei University of Technology, China
Venue:
Computers and Industrial Engineering
Year:
2013

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Abstract

This paper addresses a real-life production planning problem arising in a manufacturer of luxury goods. This problem can be modeled as a single item dynamic lot-sizing model with backlogging, outsourcing and inventory capacity. Setup cost is included in the production cost function, and the production level at each period is unbounded. The holding, backlogging and outsourcing cost functions are assumed to be linear. The backlogging level at each period is also limited. The goal is to satisfy all demands in the planning horizon at minimal total cost. We show that this problem can be solved in O(T^4logT) time where T is the number of periods in the planning horizon.