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## A Brownian approximation of a production-inventory system with a manufacturer that subcontracts

Venue: | Operations Research |

Citations: | 10 - 0 self |

### Citations

867 | A second course in stochastic processes - Karlin, Taylor - 1981 |

61 | Investment Strategies for Flexible Resources
- Mieghem
- 1998
(Show Context)
Citation Context ...t closed-form optimal policies are available only under restrictive conditions. We construct a Brownian approximation of the two-source inventory problem in Section 3 in the spirit of Reiman and Wein =-=[1998]-=-. We demonstrate the tractability of this model in Section 4, where we compute a closed-form exact optimal solution for one base stock and an analytical expression for the other optimal base stock, wh... |

47 |
Dynamic scheduling of a multiclass make-to-stock queue
- Wein
- 1992
(Show Context)
Citation Context ... approximation parameters. Rather than prove a heavy-traffic limit theorem, we assume the existence of a large integer n such that √ n |1− P | is of moderate size, as do Reiman and Wein [1998], Wein =-=[1992]-=- and others, by which we scale (6): Y nP (t) = YP (nt)√ n : (7) (Note that the process YP (t) by itself need not be stable given our assumptions, but the expression in (7) is motivated because the con... |

43 |
Optimal Policies for the Inventory Problem with Negotiable Leadtime
- Fukuda
- 1964
(Show Context)
Citation Context ...ng inventory when a manufacturer subcontracts some production fits within the context of a two-source inventory problem, variants of which have been analyzed by Barankin [1961], Daniel [1963], Fukuda =-=[1964]-=-, Whittemore and Saunders [1977], and Bradley [1999]. Optimal policy structures for these periodic models have been found under certain conditions, but closed-form optimal policies are available only ... |

36 | Dynamic scheduling of a two class queue with setups
- Reiman, Wein
- 1998
(Show Context)
Citation Context ...t closed-form optimal policies are available only under restrictive conditions. We construct a Brownian approximation of the two-source inventory problem in Section 3 in the spirit of Reiman and Wein =-=[1998]-=-. We demonstrate the tractability of this model in Section 4, where we compute a closed-form exact optimal solution for one base stock and an analytical expression for the other optimal base stock, wh... |

30 |
Mieghem. Multi-resource investment strategies: Operational hedging under demand uncertainty
- Harrison, Van
(Show Context)
Citation Context ...mple, the aggregate revenue of contract manufacturers in the electronics industry is growing at approximately 20% annually while the overall revenue in that industry is growing at only 6.6% (Gordon 1 =-=[1999]-=-). Subcontracting is also prevalent in the pharmaceutical, food, and beverage industries (Tully [1994]). Even Toyota, which is known for its manufacturing competence, outsources vehicle assembly (Anon... |

29 |
Optimal inventory under stochastic demand with two supply options
- Whittemore, Saunders
- 1977
(Show Context)
Citation Context ... subcontracts some production fits within the context of a two-source inventory problem, variants of which have been analyzed by Barankin [1961], Daniel [1963], Fukuda [1964], Whittemore and Saunders =-=[1977]-=-, and Bradley [1999]. Optimal policy structures for these periodic models have been found under certain conditions, but closed-form optimal policies are available only under restrictive conditions. We... |

28 |
Computing the optimal policy for capacitated inventory models. Stochastic Models 9
- Tayur
- 1993
(Show Context)
Citation Context ...itten rO (¯; °;∆∗s; s ∗ P (¯; °;∆ ∗ s)) = hs ∗ P (¯; °;∆ ∗ s) + cP¸: The optimal inventory cost is equal to hs∗P (·) in many cases when goods are provided by only one source (e.g., Wein [1992], Tayur =-=[1993]-=-, Robinson [1993], Bradley and Glynn [2002], and Bradley [2003]). Corollary 1 shows that this succinct expression, hs∗P (·), summarizes inventory cost plus the premium cost of contingent sourcing for ... |

25 |
A Delivery-Lag Inventory Model with Emergency Provision (The Single Period
- BARANKIN
- 1961
(Show Context)
Citation Context ...ost, and capacity cost. Managing inventory when a manufacturer subcontracts some production fits within the context of a two-source inventory problem, variants of which have been analyzed by Barankin =-=[1961]-=-, Daniel [1963], Fukuda [1964], Whittemore and Saunders [1977], and Bradley [1999]. Optimal policy structures for these periodic models have been found under certain conditions, but closed-form optima... |

24 |
A Delivery-Lag Inventory Model with Emergency. Chapter 2
- DANIEL
- 1963
(Show Context)
Citation Context ...ty cost. Managing inventory when a manufacturer subcontracts some production fits within the context of a two-source inventory problem, variants of which have been analyzed by Barankin [1961], Daniel =-=[1963]-=-, Fukuda [1964], Whittemore and Saunders [1977], and Bradley [1999]. Optimal policy structures for these periodic models have been found under certain conditions, but closed-form optimal policies are ... |

24 | Sell the plant? The impact of contract manufacturing on innovation, capacity and profitability
- Plambeck, Taylor
- 2005
(Show Context)
Citation Context ...1998]. Among the operations management literature on subcontracting most relevant to our work is Kamien and Li [1990], Gaimon [1994], Van Mieghem [1999], Brown and Lee [1998], and Plambeck and Taylor =-=[2001]-=-. Kamien and Li investigate how a bi-directional subcontracting relationship between two manufacturers reduces inventory and production variability. Our work differs from Kamien and Li’s because each ... |

15 | Optimal sizing and timing of capacity expansions with implications for modular semiconductor wafer fabs. Research Paper No.1479. Graduate - Angelus, Porteus, et al. - 1997 |

6 | Optimal control of a dual service rate M/M/1 production-inventory
- Bradley
(Show Context)
Citation Context ...supply, and capacity policies as joint decision variables. Only rarely are inventory and capacity variables treated jointly; Harrison [1985], Van Mieghem [1999], Bradley and Glynn [2002], and Bradley =-=[2003]-=- are examples of this. Our model also realistically represents both primary and contingent capacity as finite. Assuming otherwise, that a subcontractor can deliver goods at an infinite rate, as is som... |

6 |
A Diffusion Model Approximation for the GI/G/1 Queue in Heavy Traffic
- HEYMAN
- 1975
(Show Context)
Citation Context ...ce, respectively, are nP = √ n µ ¸− ¯ w ¶ (8) 2P = ¸º 2 D + ¯ w º2P : (9) The infinitesimal variance in (9) is obtained by computing the time-average variance as in Bradley and Glynn [2002]. Heyman =-=[1975]-=- obtains this result by another approach. Wein [1992] uses a different infinitesimal variance, to which (9) simplifies as ¯=w approaches ¸. We report results using (9), which we found to be superior t... |

4 |
Make-to-order policies for a stochastic lot-sizing problem using overtime
- Dellaert, Melo
- 1998
(Show Context)
Citation Context ...t closed-form optimal policies are available only under restrictive conditions. We construct a Brownian approximation of the two-source inventory problem in Section 3 in the spirit of Reiman and Wein =-=[1998]-=-. We demonstrate the tractability of this model in Section 4, where we compute a closed-form exact optimal solution for one base stock and an analytical expression for the other optimal base stock, wh... |

3 |
Subcontracting versus Capacity Expansion and the Impact on Pricing of Services
- Gaimon
- 1994
(Show Context)
Citation Context ...imately 20% annually while the overall revenue in that industry is growing at only 6.6% (Gordon 1 [1999]). Subcontracting is also prevalent in the pharmaceutical, food, and beverage industries (Tully =-=[1994]-=-). Even Toyota, which is known for its manufacturing competence, outsources vehicle assembly (Anonymous [2002]). Van Mieghem [1999] reports that cost efficiency motivates outsourcing of maintenance an... |

3 |
Brownian motion and stochastic systems
- Harrison
- 1985
(Show Context)
Citation Context ...ent sourcing policies, our model does treat inventory, contingent supply, and capacity policies as joint decision variables. Only rarely are inventory and capacity variables treated jointly; Harrison =-=[1985]-=-, Van Mieghem [1999], Bradley and Glynn [2002], and Bradley [2003] are examples of this. Our model also realistically represents both primary and contingent capacity as finite. Assuming otherwise, tha... |

3 |
You'll Never Guess Who Really Makes
- Tully
- 1994
(Show Context)
Citation Context ...imately 20% annually while the overall revenue in that industry is growing at only 6.6% (Gordon 1 [1999]). Subcontracting is also prevalent in the pharmaceutical, food, and beverage industries (Tully =-=[1994]-=-). Even Toyota, which is known for its manufacturing competence, outsources vehicle assembly (Anonymous [2002]). Van Mieghem [1999] reports that cost efficiency motivates outsourcing of maintenance an... |

2 |
The Win-Win Nature of Options-Based Capacity Reservation Arrangements. Working Paper, Xilinx Incorporated
- BROWN, LEE
- 1998
(Show Context)
Citation Context |

2 |
Contract Manufacturing from a Global Perspective
- GORDON
- 1999
(Show Context)
Citation Context ...ports that cost efficiency motivates outsourcing of maintenance and information systems. Cost efficiency is also the predominant criterion for outsourcing in the electronics industry (Gordon [1995a], =-=[1995b]-=-, [1997], [1999]). The prevalence of subcontracting motivates our study of productioninventory systems when goods are procured from a subcontractor, and the focus of real-world managers on cost effici... |

2 |
The Cost of Following the Optimal Inventory Policy
- ROBINSON
- 1993
(Show Context)
Citation Context ...itten rO (¯; °;∆∗s; s ∗ P (¯; °;∆ ∗ s)) = hs ∗ P (¯; °;∆ ∗ s) + cP¸: The optimal inventory cost is equal to hs∗P (·) in many cases when goods are provided by only one source (e.g., Wein [1992], Tayur =-=[1993]-=-, Robinson [1993], Bradley and Glynn [2002], and Bradley [2003]). Corollary 1 shows that this succinct expression, hs∗P (·), summarizes inventory cost plus the premium cost of contingent sourcing for ... |

1 |
to Outsource Production. Automotive News
- Toyota
(Show Context)
Citation Context ...contracting is also prevalent in the pharmaceutical, food, and beverage industries (Tully [1994]). Even Toyota, which is known for its manufacturing competence, outsources vehicle assembly (Anonymous =-=[2002]-=-). Van Mieghem [1999] reports that cost efficiency motivates outsourcing of maintenance and information systems. Cost efficiency is also the predominant criterion for outsourcing in the electronics in... |

1 |
A Discrete-Time Subcontracting Model. Working Paper. Johnson Graduate
- BRADLEY
- 1999
(Show Context)
Citation Context ...mple, the aggregate revenue of contract manufacturers in the electronics industry is growing at approximately 20% annually while the overall revenue in that industry is growing at only 6.6% (Gordon 1 =-=[1999]-=-). Subcontracting is also prevalent in the pharmaceutical, food, and beverage industries (Tully [1994]). Even Toyota, which is known for its manufacturing competence, outsources vehicle assembly (Anon... |

1 | Managing Capacity and Inventory Effectively in Manufacturing Systems - BRADLEY, GLYNN - 2002 |

1 |
Diffusion Approximations. From Handbooks
- GLYNN
- 1990
(Show Context)
Citation Context ...is related the large literature on this topic including, for example, Dallaert and Melo [1998]. Among the operations management literature on subcontracting most relevant to our work is Kamien and Li =-=[1990]-=-, Gaimon [1994], Van Mieghem [1999], Brown and Lee [1998], and Plambeck and Taylor [2001]. Kamien and Li investigate how a bi-directional subcontracting relationship between two manufacturers reduces ... |

1 |
Outsourcing Strategies: Case
- GORDON
- 1995
(Show Context)
Citation Context ...[1999] reports that cost efficiency motivates outsourcing of maintenance and information systems. Cost efficiency is also the predominant criterion for outsourcing in the electronics industry (Gordon =-=[1995a]-=-, [1995b], [1997], [1999]). The prevalence of subcontracting motivates our study of productioninventory systems when goods are procured from a subcontractor, and the focus of real-world managers on co... |

1 |
Coordinating Investment
- MIEGHEM
- 1999
(Show Context)
Citation Context ...mple, the aggregate revenue of contract manufacturers in the electronics industry is growing at approximately 20% annually while the overall revenue in that industry is growing at only 6.6% (Gordon 1 =-=[1999]-=-). Subcontracting is also prevalent in the pharmaceutical, food, and beverage industries (Tully [1994]). Even Toyota, which is known for its manufacturing competence, outsources vehicle assembly (Anon... |