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## The stochastic economic lot scheduling problem: heavy traffic analysis of dynamic cyclic policies (2000)

Citations: | 13 - 2 self |

### Citations

463 |
Brownian Motion and Stochastic Flow Systems
- Harrison
- 1985
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Citation Context ...dent) lot-sizing policy. In the second step, we nd the aggregate base stock level w0 that minimizes the long run average cost ∫ w0 −∞ c(w) 2 2 (w0−w)= e−2 dw; (4) 2 where we have used the fact (e.g., =-=Harrison 1985-=-) that RBM (− ; 2 )on[0; ∞) has an exponential stationary distribution with parameter 2| |= 2 . In §1.5, we calculate the average cost incurred by a generic dynamic cyclic policy when the total worklo... |

425 | Numerical methods for stochastic control problems in continuous time - Kushner, Dupuis - 1992 |

63 |
Some solvable stochastic control problems
- Shepp, Witsenhausen
- 1980
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Citation Context ...roblem (19): First, we assume that a solution to (20)–(21) yields a solution to (19); we also assume that V ∈ C2 and dene P(w)=V ′(w); this assumption is known as the heuristic principle of smooth t (=-=Benes et al. 1980-=-) and is often imposed when solving di usion control problems. Using the workload cuto levels w1 and w2 to distinguish among regions I, II, and III (w1 and w2 are unknown at this point and are not giv... |

55 |
Analytical treatment of one-dimensional Markov processes. Die Grundlehren der mathematischen Wissenschaften, Band 151 Academia Publishing House of the Czechoslovak Academy of Sciences
- Mandl
- 1968
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Citation Context ...mality Conditions Problem (19) involves a drift control (w) and a singular control via the re ecting barrier w0. Although the drift is unbounded as (w) → 0, we proceed as if standard arguments apply (=-=Mandl 1968-=-, p. 159) and state the Hamilton–Jacobi–144 / WEIN, MARKOWITZ, AND REIMAN Bellman optimality conditons: { ( c( (w);w) − g + − min (w)¿0 and + s ) V (w) ′ (w) 2 2 V ′′ } (w) = 0 for w6w0; (20) V ′ (w)... |

47 |
Dynamic scheduling of a multiclass make-to-stock queue
- Wein
- 1992
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Citation Context ...become unbounded as W (t) →∞, the only reasonable form of the optimal busy=idle policy is for the server to stay busy if W (t)¡w0 and to idle if W (t)¿w0, for the unspeci ed control parameter w0 (see =-=Wein 1992-=- for a proof of optimality for a related, but simpler, cost structure). The quantity w0 will often be referred to as the idling threshold, and can be viewed as an aggregate base stock level. Our HTAP ... |

40 |
The economic lot scheduling problem (ELSP): Review and extensions
- Elmaghraby
- 1978
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Citation Context ...c version of the classic economic lot scheduling problem ELSP, which is NP-hard (Hsu 1983) and has not been solved in general. Despite the vast literature devoted to the ELSP (see the survey paper by =-=Elmaghraby 1978-=- and Zipkin 1991 for a list of more recent references), its deterministic viewpoint has probably prevented its widespread industrial use: The solution to a deterministic problem in a make-to-stock set... |

40 |
Queues, Inventories, and Maintenance
- Morse
- 1958
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Citation Context ...e server should do while working. We begin by characterizing the busy=idle policy. Our HTAP assumption and the well-known relationship between queueing systems and production=inventory systems (e.g., =-=Morse 1958-=-) imply that the system state of the heavy tra c control problem is the one-dimensional total workload process W = ∑N i=1 Wi, which measures the total machine time embodied in the current nished goods... |

36 | On the optimal control of two queues with server set-up times and its analysis - Hofri, Ross |

36 | Dynamic scheduling of a two class queue with setups - Reiman, Wein - 1998 |

23 |
The Economic Lot-Scheduling problem: Achieving Feasibility Using Time-Varying Lot Sizes
- Dobson
- 1987
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Citation Context ...s constant in regions I and III, and gradually shifts between these two points in the intermediate area of region II. It is worth pointing out that in nearly all of the deterministic ELSP literature (=-=Dobson 1987-=- is a notable exception), the analysis is restricted to policies with constant lot sizes. Relationship to the EOQ Model. As in the economic order quantity (EOQ) model, the lot size in (12) is proporti... |

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 |

17 | Determining production schedules under base-stock policies in single facility multi-item production systems - Federgruen, Katalan - 1998 |

13 | Managing stochastic multi-product systems: model measures, and analysis - Anupindi, Tayur - 1998 |

13 | Scheduling the production of several items with random demands in a single facility - Gallego - 1990 |

10 | The strategic use of capacity slack in the economic lot scheduling problem with random demand - Bourland, Yano - 1994 |

9 | The Multi-Product Production Cycling Problem - Graves - 1980 |

8 | A heuristic scheduling policy for multi-item single-machine production systems with time-varying, stochastic demands, Management Science - Leachman, Gascon - 1988 |

8 | Multiproduct Production/Inventory Control under Random Demands - Qiu, Loulou - 1995 |

7 | Optimization-Based Planning for the Stochastic Lot Scheduling Problem - x, Muckstadt - 1995 |

4 |
Economic lot scheduling problem with raw material considerations
- Gallego, Joneja
- 1994
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Citation Context ...dle. Although our restriction to this class of policies is motivated by analytical tractability, the regularity induced by these policies eases the task of raw material procurement (e.g., Gallego and =-=Joneja 1994-=-). Each product has its own costs per unit time for holding and backordering a unit in inventory. The objective in the setup time problem is to minimize the long-run expected average inventory costs (... |

3 | Hierarchical Production and Setup Scheduling in Stochastic Manufacturing Systems - Sethi, Zhang - 1995 |

2 | Polling systems with zero switchover times: a heavy-tra c averaging principle - man, G, et al. - 1995 |

2 | Multiple channel queues in heavy tra c - Iglehart, Whitt - 1970 |

2 | Heavy tra c analysis of dynamic cyclic policies: a uni ed approach to single machine scheduling - Wein - 1996 |

1 |
A uni ed approach to single machine scheduling: heavy tra c analysis of dynamic cyclic policies
- Markowitz
- 1996
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Citation Context ...f the state space collapse inherent in the HTAP, which leaves us with a one-dimensional di usion process, and our optimization of the cycle center in (11). In our implementation of the algorithm (see =-=Markowitz 1996-=- for a detailed description of the algorithm), we introduce a slight modi cation to the heavy tra c analysis to account for the fact that setup times do not vanish in the original problem. The cycle l... |

1 |
Open queueing networks in heavy tra c
- Reiman
- 1984
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Citation Context ...newal process, where the mean and coe cient of variation of the interdemand times are given by −1 i and cdi, respectively. (Our results easily generalize to correlated compound renewal procesess; see =-=Reiman 1984-=- for details.) Hence, the tra c intensity, or long run average server utilization, is = ∑N i=1 ( i= i) and i = i= i is the utilization for product i. De ne the inventory process Ii(t) ˜ to be the numb... |

1 |
Dynamic setup scheduling and ow control in manufacturing systems. Discrete Event Dynamic Systems: Theory and Appl
- Sharifnia, Caramanis, et al.
- 1991
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Citation Context ...arising Figures 2, 4, and 6, it would appear that the corridor policy would never be very close to optimal for an asymmetric problem. In fact, Figure 6 suggests that a hyperplane corridor policy (see =-=Sharifnia et al. 1991-=-, Figure 7) might perform reasonably well in the asymmetric setup time problem; in the two-product case, the two lines forming the corridor in Figure 2 would not be parallel in the hyperplane corridor... |