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## Improved Lower Bounds for the Proportional Lot Sizing and Scheduling Problem (1996)

### Citations

343 |
The Lagrangian relaxation method for solving integer programming problems”, Management Science 27
- Fisher
- 1981
(Show Context)
Citation Context ...aints are violated. Such an approach which additionally guarantees to give lower bounds for the original problem is known as Lagrangean relaxation. A nice introduction to it is given in [7] (see also =-=[9, 6]-=-). Subsequently, we will describe how to apply a Lagrangean relaxation to the PLSP--MM in order to get a lower bound. Again, the capacity constraints are considered as the complicating constraints. We... |

46 |
B.Carter, “Hewlett-Packard gains control of inventory and service through design for localization
- Lee, Billington
- 1993
(Show Context)
Citation Context ...ve function value of a PLSP--MM--instance, or lower bound for short. It also provides a solution for the uncapacitated problem which may appear in distribution networks and supply chains for instance =-=[26, 27, 32]-=-. On the basis of this, Section 5 introduces a method to solve a Lagrangean relaxation of the capacity constraints. Finally, Section 6 summarizes the lower bounds obtained. 2 Multi--Level PLSP with Mu... |

40 |
The discrete lot–sizing and scheduling problem
- Fleischmann
- 1990
(Show Context)
Citation Context ...y choosing the length of each time period appropriately small, the PLSP is a good approximation to a continuous time axis. It refines the well--known discrete lot sizing and scheduling problem (DLSP) =-=[3, 8, 17, 25, 31]-=- as well as the continuous setup lot sizing problem (CSLP) [1, 18, 19]. Both assume that at most one item may be produced per period. All three models could be classified as small bucket models since ... |

36 |
Solving multi-item capacitated lot-sizing problems using variable redefinition
- Eppen, Martin
- 1987
(Show Context)
Citation Context ...od. All three models could be classified as small bucket models since only a few (one or two) items are produced per period. In contrast to this, the well--known capacitated lot sizing problem (CLSP) =-=[2, 5, 10, 16, 24, 28, 29] represent-=-s a large bucket model since many items can be produced per period. Remember, the CLSP does not include sequence decisions and is thus a much "easier" problem. An extension of the single--le... |

34 |
A Lagrangean-based heuristic for dynamic multilevel multiitem constrained lotsizig with setup times
- Tempelmeier, Derstroff
- 1996
(Show Context)
Citation Context ...ctive assumptions such as linear or assembly gozinto-- structures. If scarce capacities are considered, the work is mostly confined to single--machine cases. The most general methods are described in =-=[35, 36]-=- where the multi--level CLSP is attacked. The text is organized as follows: Section 2 gives a MIP--model formulation of the PLSP--MM. Solving the LP--relaxation of a PLSP--MM--model optimally is a str... |

23 |
The Deterministic Dynamic Product Cycling Problem
- Karmarkar, Schrage
- 1985
(Show Context)
Citation Context ...good approximation to a continuous time axis. It refines the well--known discrete lot sizing and scheduling problem (DLSP) [3, 8, 17, 25, 31] as well as the continuous setup lot sizing problem (CSLP) =-=[1, 18, 19]-=-. Both assume that at most one item may be produced per period. All three models could be classified as small bucket models since only a few (one or two) items are produced per period. In contrast to ... |

21 |
Multi-Item Single-Level Capacitated Dynamic Lot33 Heuristics: A General Review
- Maes, Wassenhove
- 1988
(Show Context)
Citation Context ...od. All three models could be classified as small bucket models since only a few (one or two) items are produced per period. In contrast to this, the well--known capacitated lot sizing problem (CLSP) =-=[2, 5, 10, 16, 24, 28, 29] represent-=-s a large bucket model since many items can be produced per period. Remember, the CLSP does not include sequence decisions and is thus a much "easier" problem. An extension of the single--le... |

18 | Capacitated lot-sizing with sequence dependent setup costs - Haase - 1996 |

17 |
A heuristic for dynamic multi-item multi-level capacitated 36 for general product structures
- Tempelmeier, Helber
- 1994
(Show Context)
Citation Context ...ctive assumptions such as linear or assembly gozinto-- structures. If scarce capacities are considered, the work is mostly confined to single--machine cases. The most general methods are described in =-=[35, 36]-=- where the multi--level CLSP is attacked. The text is organized as follows: Section 2 gives a MIP--model formulation of the PLSP--MM. Solving the LP--relaxation of a PLSP--MM--model optimally is a str... |

16 |
Proportional Lotsizing and Scheduling
- Drexl, Haase
(Show Context)
Citation Context ...wo items sharing a common resource for which a setup state exists may be produced per period. Due to this assumption, the problem is known as the proportional lot sizing and scheduling problem (PLSP) =-=[4, 12, 23]-=-. By choosing the length of each time period appropriately small, the PLSP is a good approximation to a continuous time axis. It refines the well--known discrete lot sizing and scheduling problem (DLS... |

15 |
A Lagrangean relaxation approach for very-large-scale capacitated lot-sizing
- Diaby, Bahl, et al.
- 1992
(Show Context)
Citation Context ...od. All three models could be classified as small bucket models since only a few (one or two) items are produced per period. In contrast to this, the well--known capacitated lot sizing problem (CLSP) =-=[2, 5, 10, 16, 24, 28, 29] represent-=-s a large bucket model since many items can be produced per period. Remember, the CLSP does not include sequence decisions and is thus a much "easier" problem. An extension of the single--le... |

12 |
Lotsizing and scheduling for production planning
- Haase
- 1994
(Show Context)
Citation Context ...wo items sharing a common resource for which a setup state exists may be produced per period. Due to this assumption, the problem is known as the proportional lot sizing and scheduling problem (PLSP) =-=[4, 12, 23]-=-. By choosing the length of each time period appropriately small, the PLSP is a good approximation to a continuous time axis. It refines the well--known discrete lot sizing and scheduling problem (DLS... |

12 |
Competitive methods for multi-level lot sizing and scheduling: tabu search and randomized regrets
- Kimms
- 1996
(Show Context)
Citation Context ... that there is an unambiguous mapping from items to machines. Of course, some items may share a common machine. Special cases are the single--machine problem for which models and methods are given in =-=[21, 22]-=-, and the problem with dedicated machines where items do not share a commonmachine. For the latter optimal solutions can be easily computed with a lot--for--lot policy [20]. Heuristics for the PLSP--M... |

12 | A New Heuristic Approach for the Multi-Item Dynamic Lot Sizing Problem - Kirca, Kökten - 1994 |

10 |
Solving the CLSP by a tabu search heuristic
- Hindi
- 1996
(Show Context)
Citation Context |

10 |
The Dynamic Lotsizing Problem with Startup and Reservation
- Karmarkar, Kekre, et al.
- 1987
(Show Context)
Citation Context ...good approximation to a continuous time axis. It refines the well--known discrete lot sizing and scheduling problem (DLSP) [3, 8, 17, 25, 31] as well as the continuous setup lot sizing problem (CSLP) =-=[1, 18, 19]-=-. Both assume that at most one item may be produced per period. All three models could be classified as small bucket models since only a few (one or two) items are produced per period. In contrast to ... |

9 |
Mixed integer programming model formulations for dynamic multi-item multi-level capacitated lotsizing
- Stadtler
- 1996
(Show Context)
Citation Context ...ere the LP--relaxation of an instance has an optimum objective function value that is greater than the optimum objective function value of the LP--relaxations of the straightforward model formulation =-=[5, 30, 33, 34]-=-. 3.1 A Simple Plant Location Representation For the multi--level CLSP, a computational study in [33] reveals that a simple plant location representation adapted from [30] gives the same lower bounds ... |

8 |
Approximation Formulations for the SingleProduct Capacitated Lot Size Problem
- Bitran, Matsuo
(Show Context)
Citation Context ...good approximation to a continuous time axis. It refines the well--known discrete lot sizing and scheduling problem (DLSP) [3, 8, 17, 25, 31] as well as the continuous setup lot sizing problem (CSLP) =-=[1, 18, 19]-=-. Both assume that at most one item may be produced per period. All three models could be classified as small bucket models since only a few (one or two) items are produced per period. In contrast to ... |

8 |
single-machine lot sizing and scheduling (with initial inventory)", Manuskripte aus den Instituten f}ur Betriebswirtschaftslehre der universitat
- Kimms
- 1993
(Show Context)
Citation Context ... that there is an unambiguous mapping from items to machines. Of course, some items may share a common machine. Special cases are the single--machine problem for which models and methods are given in =-=[21, 22]-=-, and the problem with dedicated machines where items do not share a commonmachine. For the latter optimal solutions can be easily computed with a lot--for--lot policy [20]. Heuristics for the PLSP--M... |

6 | sizing and scheduling with sequence dependent setup costs and times and efficient rescheduling opportunities, Working Paper No
- Haase, Kimms
- 1996
(Show Context)
Citation Context ...per period. Remember, the CLSP does not include sequence decisions and is thus a much "easier" problem. An extension of the single--level CLSP with partial sequence decisions can be found in=-= [11]. In [14]-=- a large bucket single--level lot sizing and scheduling model is discussed. A comprehensive review of the multi--level lot sizing literature is given in [23] where it is shown that most authors do not... |

6 |
A Linear Description of the Discrete Lot-Sizing and Scheduling Problem
- Hoesel, Kolen
- 1994
(Show Context)
Citation Context ...y choosing the length of each time period appropriately small, the PLSP is a good approximation to a continuous time axis. It refines the well--known discrete lot sizing and scheduling problem (DLSP) =-=[3, 8, 17, 25, 31]-=- as well as the continuous setup lot sizing problem (CSLP) [1, 18, 19]. Both assume that at most one item may be produced per period. All three models could be classified as small bucket models since ... |

6 |
Reformulations of the shortest route model for dynamic multi-item multilevel capacitated lotsizing
- Stadtler
- 1997
(Show Context)
Citation Context ...ere the LP--relaxation of an instance has an optimum objective function value that is greater than the optimum objective function value of the LP--relaxations of the straightforward model formulation =-=[5, 30, 33, 34]-=-. 3.1 A Simple Plant Location Representation For the multi--level CLSP, a computational study in [33] reveals that a simple plant location representation adapted from [30] gives the same lower bounds ... |

5 |
Lagrangian Relaxation and its Uses
- Geoffrion
- 1974
(Show Context)
Citation Context ...aints are violated. Such an approach which additionally guarantees to give lower bounds for the original problem is known as Lagrangean relaxation. A nice introduction to it is given in [7] (see also =-=[9, 6]-=-). Subsequently, we will describe how to apply a Lagrangean relaxation to the PLSP--MM in order to get a lower bound. Again, the capacity constraints are considered as the complicating constraints. We... |

5 |
Multi--Level Lot Sizing and Scheduling --- Methods for Capacitated, Dynamic, and Deterministic Models
- Kimms
- 1996
(Show Context)
Citation Context ...wo items sharing a common resource for which a setup state exists may be produced per period. Due to this assumption, the problem is known as the proportional lot sizing and scheduling problem (PLSP) =-=[4, 12, 23]-=-. By choosing the length of each time period appropriately small, the PLSP is a good approximation to a continuous time axis. It refines the well--known discrete lot sizing and scheduling problem (DLS... |

4 | Capacitated lot-sizing with linked production quantities of adjacent periods
- Haase
- 1998
(Show Context)
Citation Context ...produced per period. Remember, the CLSP does not include sequence decisions and is thus a much "easier" problem. An extension of the single--level CLSP with partial sequence decisions can be=-= found in [11]-=-. In [14] a large bucket single--level lot sizing and scheduling model is discussed. A comprehensive review of the multi--level lot sizing literature is given in [23] where it is shown that most autho... |

3 |
An Optimal Algorithm for the Multi-- Item Capacitated Production Planning Problem
- Lotfi, Chen
- 1991
(Show Context)
Citation Context |

2 |
Zum Problem der Produktionsplanung
- Dinkelbach
- 1964
(Show Context)
Citation Context ...y choosing the length of each time period appropriately small, the PLSP is a good approximation to a continuous time axis. It refines the well--known discrete lot sizing and scheduling problem (DLSP) =-=[3, 8, 17, 25, 31]-=- as well as the continuous setup lot sizing problem (CSLP) [1, 18, 19]. Both assume that at most one item may be produced per period. All three models could be classified as small bucket models since ... |

2 |
An Applications Oriented Guide to Lagrangian
- FISHER
- 1985
(Show Context)
Citation Context ...removed constraints are violated. Such an approach which additionally guarantees to give lower bounds for the original problem is known as Lagrangean relaxation. A nice introduction to it is given in =-=[7]-=- (see also [9, 6]). Subsequently, we will describe how to apply a Lagrangean relaxation to the PLSP--MM in order to get a lower bound. Again, the capacity constraints are considered as the complicatin... |

2 |
Planning Lot Sizes and Capacity Requirements in a Single--Stage Production System
- unther, O
- 1987
(Show Context)
Citation Context |

2 |
Optimal Multi--Level Lot Sizing and Scheduling with Dedicated Machines, Working Paper No
- Kimms
- 1994
(Show Context)
Citation Context ...nd methods are given in [21, 22], and the problem with dedicated machines where items do not share a commonmachine. For the latter optimal solutions can be easily computed with a lot--for--lot policy =-=[20]-=-. Heuristics for the PLSP--MM are described in [23]. Let us first introduce some notation. In Table 1 the decision variables are defined. Likewise, the parameters are explained in Table 2. From these ... |

2 |
An Efficient Algorithm for Multi
- Lasdon, Terjung
- 1971
(Show Context)
Citation Context |

2 |
Optimal lot-sizing for dynamic assembly systems
- Rosling
- 1985
(Show Context)
Citation Context ...ere the LP--relaxation of an instance has an optimum objective function value that is greater than the optimum objective function value of the LP--relaxations of the straightforward model formulation =-=[5, 30, 33, 34]-=-. 3.1 A Simple Plant Location Representation For the multi--level CLSP, a computational study in [33] reveals that a simple plant location representation adapted from [30] gives the same lower bounds ... |

1 |
Multiple Stage Production Planning Research: History and Opportunities
- Simpson, Erenguc
- 1994
(Show Context)
Citation Context ...ve function value of a PLSP--MM--instance, or lower bound for short. It also provides a solution for the uncapacitated problem which may appear in distribution networks and supply chains for instance =-=[26, 27, 32]-=-. On the basis of this, Section 5 introduces a method to solve a Lagrangean relaxation of the capacity constraints. Finally, Section 6 summarizes the lower bounds obtained. 2 Multi--Level PLSP with Mu... |