Improved Lower Bounds for the Proportional Lot Sizing and Scheduling Problem

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

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by A. Kimms , Alf Kimms

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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 ...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...
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 ...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...
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 ...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...
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 ...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	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...