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## The Stochastic Economic Lot Scheduling Problem: A Survey (2005)

### Citations

232 |
Inventory management and production planning and scheduling
- Silver, Pyke, et al.
- 1998
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Citation Context ... set-up times. The present paper does not comprise the other subproblems shown in Figure 1. Suggested books for readers who would like to pursue their knowledge of these subproblems are Silver et al. =-=[37]-=- and Zipkin [47]. Nevertheless, in Section 2 of the present paper we describe the relationship between the SELSP and subproblem 4, which is usually called the (deterministic) 3seconomic lot scheduling... |

77 |
A review of scheduling research involving setup considerations
- Allahverdi, Gupta, et al.
- 1999
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Citation Context .... Consequently, this effect will hinder the timely fulfillment of demand. The trade-off between these contrasting effects forms a challenging issue from a theoretical point of view. Allahverdi et al. =-=[2]-=- recently wrote a survey on deterministic scheduling problems involving set-ups, in which they indicate stochastic scheduling problems with set-ups as an avenue of future research. The SELSP is a comm... |

40 |
The economic lot scheduling problem (ELSP): Review and extensions
- Elmaghraby
- 1978
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Citation Context ...n with the deterministic ELSP The deterministic counterpart of the SELSP, the so-called ELSP, has received lots of attention in the literature over the past decades (for surveys see, e.g., Elmaghraby =-=[11]-=- and Salomon [36]). In the literature two approaches can be distinguished for the ELSP (see again, e.g., Elmaghraby [11]), which has been proven to be NP-hard (see Hsu [26]): analytical approaches wit... |

37 |
Lot-sizes, lead times and in-process inventories
- Karmarkar
- 1987
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Citation Context ...ct or whether to idle the machine. The primary goal of such a production plan is minimization of the total costs, that is, the sum of holding, backlogging and set-up costs. As emphasized by Karmarkar =-=[27]-=-, set-up costs should not be used as surrogate for set-up times in the modeling of scheduling problems. Costs do not completely capture the problematic nature associated with set-up times, i.e., the l... |

29 |
The stochastic Economic Lot Scheduling Problem: cyclical base-stock policies with idle times
- Federgruen, Katalan
- 1996
(Show Context)
Citation Context ...nce of the total demand during a cycle and, thus, larger safety stock levels are needed compared to the uncorrelated demand case. The next strategy we describe is introduced by Federgruen and Katalan =-=[14, 15, 16]-=-. Besides the basic assumptions for the SELSP as described in Section 2.1, the following additional assumptions are made in their model: unfullfiled demand is backlogged, the demand for a product foll... |

23 | Deterministic Lotsizing Models for Production Planning - Salomon - 1991 |

20 |
Combining make to order and make to stock
- Adan, Wal
- 1998
(Show Context)
Citation Context ...e, this diagram only provides a global classification of multiproduct single-machine scheduling problems. One can easily think of examples of so-called hybrid systems (see, e.g., Adan and Van der Wal =-=[1]-=- and Federgruen and Katalan [17] for the combination of make-to-order and make-to-stock). The present paper considers the production of multiple standardized products on a single machine with limited ... |

19 | On the General Feasibility Test of scheduling Lot Size for several Products on One Machine; Management science 29; 93-105. www.SID.ir Ar chi ve - Hsu - 1983 |

19 |
Heavy traffic analysis of dynamic cyclic policies: a unified treatment of the single machine scheduling problem
- Markowitz, Wein
(Show Context)
Citation Context ...on of the policies proposed by Markowitz et al. [33]. products in stock minus the sum of production times for products backlogged, i.e., the actual stock position of the system. In Markowitz and Wein =-=[34]-=- the same kind of heavy traffic analysis is applied to all kinds of related stochastic multi-product single-machine scheduling problems. Bourland and Yano [9] use a two-level hierarchical policy for t... |

19 |
Models for Design and Control of Stochastic Multi-Item Batch Production Systems
- Zipkin
- 1986
(Show Context)
Citation Context ...ing to standard single product inventory control strategies such as (s, Q) or (s, S) policies, whereas the sequencing decisions are dynamically resolved by using priority rules. In particular, Zipkin =-=[46]-=- studies a continuous-time model under the assumption of backlogging, Poisson demand processes and generally distributed set-up and production times. The individual lot sizing policies are of the (s, ... |

18 | Combined make-to-order and make-to-stock in a food production system
- Soman, Donk, et al.
(Show Context)
Citation Context ... should be bounded. For a literature overview of combined make-to-order and maketo-stock production situations for food processing companies, in which products are highly perishable, see Soman et al. =-=[39]-=-. In conclusion, we believe that both extensions, limited stock space and perishable goods, are worth studying. Local lot sizing strategy incorporating global information. In the present paper we have... |

17 |
Determining production schedules under base-stock policies in single facility multi-item production systems
- Federgruen, Katalan
- 1998
(Show Context)
Citation Context ...of the system whether to continue production of the current product, whether to switch to another product or whether to idle the machine, as described by Bourland and Yano [9]. Federgruen and Katalan =-=[16]-=- correctly argue that a policy making the aforementioned decisions at each point in time in a dynamic fashion based on a complete state description of the system will lead to the optimal costs. Howeve... |

17 |
Foundations of Inventory Management. McGraw-Hill/Irwin, 2000. CHAPTER 7 APPENDICES −5
- Zipkin
(Show Context)
Citation Context ...he present paper does not comprise the other subproblems shown in Figure 1. Suggested books for readers who would like to pursue their knowledge of these subproblems are Silver et al. [37] and Zipkin =-=[47]-=-. Nevertheless, in Section 2 of the present paper we describe the relationship between the SELSP and subproblem 4, which is usually called the (deterministic) 3seconomic lot scheduling problem (ELSP).... |

14 |
A decomposition method for multi-product kanban systems with setup times and lost sales
- Krieg, Kuhn
(Show Context)
Citation Context ...ed by Grasman et al. [24], 20s3 K A K A % 3 K A K A & 3 K A K A $ 5 A H L A H 3 K A K A 3 K A K A # 3 K A K A 3 K A K A " Figure 5: Dual polling model for 8 products. one introduced by Krieg and Kuhn =-=[29, 30]-=- and one proposed by Winands et al. [45]. Grasman et al. [24] extend the exhaustive base-stock model of Federgruen and Katalan by adding random yields for the cases of backlogging, lost sales and expe... |

13 | Managing stochastic multi-product systems: model measures, and analysis
- Anupindi, Tayur
- 1998
(Show Context)
Citation Context ..., but also in bulk production of consumer products such as detergents and beers. Some specific applications described in the open literature are a laminate manufacturing plant (see Anupindi and Tayur =-=[7]-=-), a glass-containers manufacturing company (see Fransoo et al. [19]), a large consumer products manufacturer (see Gascon et al. [22]), a producer of plastic bumpers for cars (see Grasman et al. [24])... |

13 |
Scheduling the production of several items with random demands in a single facility
- Gallego
- 1990
(Show Context)
Citation Context ...u and Loulou [35] Zipkin [46] Sox and Muckstadt [40] Fixed + Bourland and Yano [8], [9] Anupindi and Tayur [7] dynamic cycle length Fransoo et al. [19] Federgruen and Katalan [14], [15], [16] Gallego =-=[20]-=-, [21] Grasman et al. [24] Gascon et al. [22], [31], [32] Krieg and Kuhn [29], [30] Markowitz et al. [33], [34] Smits et al. [38], [44] Vaughan [42] Winands et al. [45] Fixed + Giezenaar [23] Erkip et... |

13 | The stochastic economic lot scheduling problem: heavy traffic analysis of dynamic cyclic policies
- Markowitz, Reiman, et al.
(Show Context)
Citation Context ...using a global lot sizing policy or a local one. These two types of strategies are discussed in more detail in the remainder of the present subsection. 4.2.1 Global lot sizing policy Markowitz et al. =-=[33]-=- propose a model, in which the demands are allowed to follow general renewal processes. At each point in time, the production manager has the following options: produce the product currently set-up, i... |

12 |
A review of the stochastic lot scheduling problem
- Sox, Jackson, et al.
- 1999
(Show Context)
Citation Context ...as a challenging problem; the finite production capacity has to be dynamically distributed among the products in order to be reactive to the stochastic demands, productions and setups (see Sox et al. =-=[41]-=-). The presence of set-up times in combination with the stochastic environment are the key complicating factors of the problem. On the one hand, one seeks for short cycle lengths, and thus frequent pr... |

10 |
The strategic use of capacity slack in the economic lot scheduling problem with random demand
- Bourland, Yano
- 1994
(Show Context)
Citation Context ...ibe for each possible state of the system whether to continue production of the current product, whether to switch to another product or whether to idle the machine, as described by Bourland and Yano =-=[9]-=-. Federgruen and Katalan [16] correctly argue that a policy making the aforementioned decisions at each point in time in a dynamic fashion based on a complete state description of the system will lead... |

9 |
The Multi-Product Production Cycling Problem
- Graves
- 1980
(Show Context)
Citation Context ...stem is quite common in industry and demand is inevitably stochastic. The first papers that recognized the need for analytical models for the SELSP were published by Vergin and Lee [43] and by Graves =-=[25]-=-. Although both papers make the assumption, in contrast to the SELSP, that the set-up times equal zero, these papers can be seen as the beginning of the research on the SELSP. More particular, in the ... |

8 |
Multiproduct Production/Inventory Control under Random Demands
- Qiu, Loulou
- 1995
(Show Context)
Citation Context ... product is incurred even if the same product was produced in the preceding period. They argue that this assumption can easily be relaxed at the expense of increased computation times. Qiu and Loulou =-=[35]-=- present a multi-product model with limited stock space for each product under the assumption of backlogging, Poisson demand and deterministic production and setup times. They model the problem as a c... |

7 |
Approximating queue size and waiting time distributions in general polling systems (Queueing Systems
- Federgruen, Katalan
- 1994
(Show Context)
Citation Context ...is defined by identifying each product with a queue and the demand process of a product with the arrival process at the corresponding queue (see Figure 5). In an earlier paper (Federgruen and Katalan =-=[13]-=-), an efficient algorithm is developed to compute the complete steady-state queue size distributions of this dual polling problem for a given total idle time. The optimal total idle time can be obtain... |

7 |
Demand management and production control in process industries
- Fransoo
- 1993
(Show Context)
Citation Context ...he added value and utilizes the most expensive installation, the so-called bottleneck. Production on the bottleneck often has to be done under very tight capacity constraints, as described by Fransoo =-=[18, 19]-=-. Bourland [8] indicates that in practice the bottleneck is often one of the stages that produce products used in the assembly of finished goods. The scheduling decisions of the plant are in general d... |

7 |
Optimization-Based Planning for the Stochastic Lot Scheduling Problem
- x, Muckstadt
- 1995
(Show Context)
Citation Context ...al. [19]), a large consumer products manufacturer (see Gascon et al. [22]), a producer of plastic bumpers for cars (see Grasman et al. [24]) and an aerospace component supplier (see Sox and Muckstadt =-=[40]-=-). The aim of the present paper is twofold. First of all, it gives an overview of the research on the SELSP along with a comprehensive list of references. Secondly, several areas for future 4sresearch... |

7 |
A local search algorithm for the optimization of the stochastic economic lot scheduling problem
- Wagner, Smits
- 2004
(Show Context)
Citation Context ...al application. From these results, it clearly emerges that the popular product-focussed performance measures based on costs cannot be used as substitute for order-focussed measures. Wagner and Smits =-=[44]-=- suggest a two-level continuous time model, where at the upper level an optimal fixed cycle schedule with respect to the expected set-up and holding costs is derived. At the lower level a periodic bas... |

6 | The Impact of Adding a Make-to-order Item to a Make-to-Stock Production System - Federgruen, Katalan - 1999 |

6 |
Analysis of multi-product kanban systems with state-dependent setups and lost sales
- Krieg, Kuhn
(Show Context)
Citation Context ...ed by Grasman et al. [24], 20s3 K A K A % 3 K A K A & 3 K A K A $ 5 A H L A H 3 K A K A 3 K A K A # 3 K A K A 3 K A K A " Figure 5: Dual polling model for 8 products. one introduced by Krieg and Kuhn =-=[29, 30]-=- and one proposed by Winands et al. [45]. Grasman et al. [24] extend the exhaustive base-stock model of Federgruen and Katalan by adding random yields for the cases of backlogging, lost sales and expe... |

5 |
Single-stage, multi-product production/inventory systems with lost sales
- Altiok, Shiue
- 1995
(Show Context)
Citation Context ...ional assumption that the production time of a batch is (nearly) independent of the size of this batch. He derives optimal batch sizes and reorder points with respect to total costs. Altiok and Shiue =-=[3, 4, 5]-=- study a model for the SELSP, in which an (s, S) policy is implemented. The sequencing decision is made based on either one of the following two priority 14srules. The first one is a standard priority... |

5 |
Production To Order: Models and Rules for Production Planning
- Dellaert
- 1989
(Show Context)
Citation Context ...ch to the next product in the sequence and thus the machine is idled. Their strategy is modeled as a quasi-birth-death process, which can be solved numerically by the matrix-analytic method. Dellaert =-=[10]-=- mentions some drawbacks of such a fixed cycle strategy. The most important one is that no pooling effect is obtained by the fixed pre-allocation of production capacities to products. For a more detai... |

4 |
On the stability of timed token rings, Performance Evaluation 26
- Altman, Liu
- 1996
(Show Context)
Citation Context ...ting (partial) information of the rest of the system. This strategy originates from the fiber distributed data interface (FDDI) protocol used in optical local area networks (see, e.g., Altman and Liu =-=[6]-=-). We assume that a base-stock policy is implemented. Furthermore, each individual product possesses its own timer. When production of a tagged product ends, the corresponding timer is started. At the... |

4 |
A quasi-birth-and-death model to evaluate fixed cycle time policies for stochastic multi-item production/inventory problem
- Erkip, Güllü, et al.
- 2000
(Show Context)
Citation Context ...he stages is improved, the estimates of total lead time may get better and, therefore, the company may be able to set more realistic due dates, as described by Anupindi and Tayur [7] and Erkip et al. =-=[12]-=-. In order to simplify the coordination with downstream and upstream stages, these stages may impose all kinds of restrictions on the production plan of the bottleneck. In general, these restrictions ... |

4 |
A hierarchical approach for capacity coordination in multiple products single-machine production systems with stationary stochastic demands
- Fransoo, Sridharan, et al.
- 1995
(Show Context)
Citation Context ...he added value and utilizes the most expensive installation, the so-called bottleneck. Production on the bottleneck often has to be done under very tight capacity constraints, as described by Fransoo =-=[18, 19]-=-. Bourland [8] indicates that in practice the bottleneck is often one of the stages that produce products used in the assembly of finished goods. The scheduling decisions of the plant are in general d... |

4 |
Scheduling Rules for the Multiple Product Single Machine System with Stochastic Demand
- Vergin, Lee
- 1978
(Show Context)
Citation Context ...was not caused by an absence of practical interest, but by the intrinsic analytical complexity of the problem. To illustrate this feeling we cite here the following conclusion drawn by Vergin and Lee =-=[43]-=- in 1978 concerning the state of the research on the SELSP at that time: The literature is almost completely void of not only the development of analytical models, but even of discussion of the proble... |

3 |
When is a base stock policy optimal in recovering disrupted cyclic schedules? Naval Res
- Gallego
- 1994
(Show Context)
Citation Context ...sting the production quantities without altering the production sequence. The size of these adjustments for a product depends in general on the stock levels of all the individual products. In Gallego =-=[21]-=- sufficient conditions are given for a base-stock recovery policy to be optimal. In case of a base-stock policy one only needs to monitor the stock level of the product currently set-up. Several autho... |

3 |
Multi-item, single-machine scheduling problem with stochastic demands: a comparison of heuristics
- Gascon, Leachman, et al.
- 1994
(Show Context)
Citation Context ...terature are a laminate manufacturing plant (see Anupindi and Tayur [7]), a glass-containers manufacturing company (see Fransoo et al. [19]), a large consumer products manufacturer (see Gascon et al. =-=[22]-=-), a producer of plastic bumpers for cars (see Grasman et al. [24]) and an aerospace component supplier (see Sox and Muckstadt [40]). The aim of the present paper is twofold. First of all, it gives an... |

3 | Setting basestock levels in multi-product systems with setups and random yield
- Grasman, Olsen, et al.
(Show Context)
Citation Context ...r [7]), a glass-containers manufacturing company (see Fransoo et al. [19]), a large consumer products manufacturer (see Gascon et al. [22]), a producer of plastic bumpers for cars (see Grasman et al. =-=[24]-=-) and an aerospace component supplier (see Sox and Muckstadt [40]). The aim of the present paper is twofold. First of all, it gives an overview of the research on the SELSP along with a comprehensive ... |

3 |
The Dynamic Cycle Lengths Heuristic for Scheduling Muti-Item
- Leachman, Gascon
- 1985
(Show Context)
Citation Context ...ll products in a cycle, while maintaining the fixed production sequence. The last step is the possible insertion of an idle period in a cycle, when all products have sufficient stock. Leachman et al. =-=[32]-=- improve the heuristics by increasing the lengths of the operational cycles, i.e., the operational cycles closer to the target cycles, which result in lower costs and improved customer service. Furthe... |

3 |
Determination of an order-up-to policy in the stochastic economic lot scheduling model
- Smits, Wagner, et al.
- 2004
(Show Context)
Citation Context ...d (R, S)-policy, is used. The review periods are fixed and determined by the solution at the planning level, while the optimal base-stock levels are obtained by an algorithm developed by Smits et al. =-=[38]-=-. The planning and control levels are then instantaneously optimized by an integrative approach, which uses a Local Search optimization technique. Vaughan [42] studies a model for the SELSP under the ... |

2 |
Pull-type manufacturing systems with multiple product types
- Altiok, Shiue
- 2000
(Show Context)
Citation Context ...ional assumption that the production time of a batch is (nearly) independent of the size of this batch. He derives optimal batch sizes and reorder points with respect to total costs. Altiok and Shiue =-=[3, 4, 5]-=- study a model for the SELSP, in which an (s, S) policy is implemented. The sequencing decision is made based on either one of the following two priority 14srules. The first one is a standard priority... |

2 | Customer waiting-time distributions under base-stock policies in single-facility multi-item production systems - Federgruen, Katalan - 1996 |

2 |
Ontwerp voor een productie- en voorraadstrategie voor de productieplant Laurox bij AKZO Nobel Chemicals te Deventer
- Giezenaar
- 1997
(Show Context)
Citation Context ...ength. That is, production plans using a global lot sizing policy on the one hand and local lot sizing strategies on the other hand. 4.3.1 Global lot sizing policy In the Master’s thesis of Giezenaar =-=[23]-=-, a case study of a chemical plant in the Netherlands is presented, for which a fixed production sequence strategy in combination with a fixed cycle length has been developed under the assumption of d... |

2 |
A heuristic policy for multi-item, single-machine production systems with time-varying stochastic demands
- Leachman, Gascon
- 1988
(Show Context)
Citation Context ...e third level, Gallego [20] adds safety stocks in order to efficiently use the control policy, that was shown to be optimal after a single disruption, in a stochastic environment. Leachman and Gascon =-=[31]-=- develop a so-called dynamic cycle lengths heuristic in a discretetime model under the assumption of non-stationary demand and deterministic production and set-up times. The first step in their heuris... |

2 |
The effect of correlated demand on the cyclical scheduling system
- VAUGHAN
- 2003
(Show Context)
Citation Context ...y an algorithm developed by Smits et al. [38]. The planning and control levels are then instantaneously optimized by an integrative approach, which uses a Local Search optimization technique. Vaughan =-=[42]-=- studies a model for the SELSP under the assumption of correlated demand, backlogging, deterministic production and set-up times. His policy is characterized by an exhaustive base-stock policy and a t... |

1 |
Production planning and control links and the stochastic economic lot scheduling problem (Working paper no. 299, The Amos Tuck School of Business Administration
- Bourland
- 1994
(Show Context)
Citation Context ... Bourland and Yano [9], Federgruen and Katalan [16] or Sox et al. [41]). Therefore, one should take stochasticity into account when constructing the sequence and cycle length as indicated by Bourland =-=[8]-=- and not straightforwardly implement deterministic solutions. The importance of the cycle length follows from the fact that this length determines not only to a large extent the levels of both the cyc... |

1 |
Stochastic dynamic product cycling problem (European
- unknown authors
- 1994
(Show Context)
Citation Context ...they state that preliminary results indicate that this aggregation of products is promising, no results have appeared in the open literature yet. Finally, we want to mention work of Karmarkar and Yoo =-=[28]-=-, in which the SELSP is also studied under the assumption of backlogging, deterministic production and set-up times. They present a formulation of a discrete-time dynamic stochastic programming proble... |

1 |
A quantity-limited basestock policy in a stochastic two-item single-capacity production system (Working paper, Beta Research School for Operations Management and Logistics
- Winands, Adan, et al.
- 2004
(Show Context)
Citation Context ...K A K A & 3 K A K A $ 5 A H L A H 3 K A K A 3 K A K A # 3 K A K A 3 K A K A " Figure 5: Dual polling model for 8 products. one introduced by Krieg and Kuhn [29, 30] and one proposed by Winands et al. =-=[45]-=-. Grasman et al. [24] extend the exhaustive base-stock model of Federgruen and Katalan by adding random yields for the cases of backlogging, lost sales and expediting. In case of backlogging they deri... |