Capacitated lot sizing with linked lots for general product structures in job shops

This paper proposes two new mixed integer programming models for capacitated multi-level lot-sizing problems with backlogging, whose linear programming relaxations provide good lower bounds on the optimal solution value. We show that both of these strong formulations yield the same lower bounds. In addition to these theoretical results, we propose a new, effective optimization framework that achieves high quality solutions in reasonable computational time. Computational results show that the proposed optimization framework is superior to other well-known approaches on several important performance dimensions.

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“…See Oztürk and Ornek (2010) for the lot-sizing problem with setup carryover as well as with external demands for component items.…”

Section: Problem Formulationsmentioning

confidence: 99%

An optimization framework for solving capacitated multi-level lot-sizing problems with backlogging

Shi

Geunes

et al. 2011

European Journal of Operational Research

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“…Therefore, the length of the shortest path from node i to node j in the network constructed by Algorithm 1 is Hence, we generate arcs (0, 1), (1, 2), (1, 3), (2,3) and (3,4) with production volumes 100 units, 60 units, 120 units, 60 units and 120 units respectively. In this network, period 1, 2, 3 and 4 are production points.…”

Section: Algorithm 1 a Network Algorithm To Deal With The (I+1 J)-pmentioning

confidence: 99%

“…Lot sizing problems are categorized as single item problems [5]- [8] and multi-item problems [1]- [4] , or uncapacitated problems and capacitated problems. Reference [5] studied an uncapacitated single item lot sizing problem with dynamic demand and finite time horizon.…”

Section: Introductionmentioning

confidence: 99%

A solution to the capacitated lot sizing problem

Zhang

Wei-ping

et al. 2011

2011 IEEE International Conference on Industrial Engineering and Engineering Management

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We study a capacitated dynamic lot sizing problem with special cost structure involving fixed setup cost, freight cost, production cost and inventory holding cost. The freight cost is proportional to the number of containers used. We investigate the problem in which the maximal production capacity in one period is integral multiple of the capacity of a container and reveal the special structure of the optimal solution. We transfer the lot sizing problem into a shortest path problem and propose a network algorithm to deal with it. The T-period problem is solved in O(T 4 ) effort by the network algorithm.

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“…Only few researchers have addressed capacitated lot sizing problems with back-ordering Daniel Quadt, Heinrich Kuhn [11], also the complexity of the modeling setup carry over in CLSP problems result in the not much attention in the literatures [18]. So in this paper we consider a lot sizing and scheduling in flow shop with sequence-dependent setups, setups carry over and backlogging.…”

Section: Mathematical Modelmentioning

confidence: 99%

“…The sequence of items scheduled between the first and last does not affect the total required setup time unless the items are sequence dependent, where setups can be done in any order. The complexity of modeling setup carry over in CLSP problems is why it has not received much attention in the literature [18]. Diwakar Gupta and Thorkell Magnusson [1], have presented the single machine capacitated lot-sizing and scheduling problem (CLSP) with sequence-dependent setup costs and non-zero setup times, with the additional feature that setups may be carried over from one period to the next, and that setups are preserved over idle periods.…”

Section: Introductionmentioning

confidence: 99%

Lot Sizing and Scheduling in Flow Shop with SequenceDependent Setups and Backlogging

Babaei¹,

Mohammadi²,

Ghomi³

2011

IJCA

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Lot sizing and scheduling in flow shop has been considered in this paper. Our study includes a multi-level and multi-period capacitated lot sizing and scheduling problem (CLSP) with sequence-dependent setups, setups carry over in flow shop. In manufacturing environments backlogging is unavoidable. If the production capacity is infinite, any demand can be satisfied on time. But in the real world, production capacity is not infinite so some demand may not be satisfied on time. In this condition backlogging arises naturally. CLSP problems with considering backlogging has been studied fewer by researchers. Also, the sequence-dependent setups and setups carry over are two important events that occur occasionally in factories. In this study an exact mixed integer problem (MIP) in a flow shop CLSP problem with considering sequence-dependent setups, setups carry over and backlogging has been formulated. Our formulation is presented to optimize objective function (including, inventory costs, product costs and setup cost). Since the CLSP problems are extremely NP-hard a lower bound is developed and compared against the optimal solution. General TermsLot sizing and Scheduling.

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Capacitated lot sizing with linked lots for general product structures in job shops

Cited by 21 publications

References 11 publications

An optimization framework for solving capacitated multi-level lot-sizing problems with backlogging

An optimization framework for solving capacitated multi-level lot-sizing problems with backlogging

A solution to the capacitated lot sizing problem

Lot Sizing and Scheduling in Flow Shop with SequenceDependent Setups and Backlogging

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