1. 2016 International Conference on Grey Systems and Uncertainty Analysis
A negotiation model on price and due date in an assembly system under uncertainty
Liangyan Tao
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2. Outline
Introduction
The Negotiation Framework for Assembly System under Uncertainty
The Negotiation Model
Nash Bargaining between Manufacture and Customer
The schedule Relation between the Suppliers and the Manufacture
The negotiation model between the manufacture and the suppliers
Illustrated Example
Conclusions
Further Study
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3. 1. Introduction
Many industrial manufacturers outsource some or all their part and component production to independent suppliers and undertaking the final assembly work internally, e.g. aerospace, automotor, computer, and electronics industries(Fang 2014)
Most research focus on quantity and price decision (Jiang L,2010; Gerchak 2004)
Many existing literature: non-cooperation game
The duration is deterministic ; no rework
For assembly system where the supplier and the assembler are cooperative, e.g. Boeing and its strategic suppliers in Japan, and the duration is stochastic, it is desirable to develop a new method to address the issue.
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4. 2.The negotiation framework
a manufacture needs to negotiate the price and the due date with some suppliers
the relationship between the manufacture’s schedule and the suppliers’ schedule is random, which can be described by GERT
Nash Bargaining between the Manufacture and the Customer
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5. 2.The negotiation framework
In the first stage, Nash bargaining game is employed to analyze the price and due date negotiation between the manufacture and the customer, with the goal to maximize their respective utility function.
In the second stage, we assume that the manufacture and the suppliers are vertical integrated strategic alliance. The remaining question is how to allocate the total profit. Then we establish optimization model to derive the Nash solution of the allocation problem.
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6. 3.The negotiation model
3.1 Nash Bargaining between Manufacture and Customer
Utility function
As the price and the due date are interactional in practical, we utilized the utility function to handle the trade-off between due date and price. The utility functions for the manufacture and the customer are described as following respectively(Pan 2013).
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7. 3.The negotiation model
3.1 Nash Bargaining between Manufacture and Customer
The trade-off between the due date and the price
The maximum price for the customer’s early due date(CEDD) is CPEDD, and the maximum price for the customer’s late due date(CLDD) is CPLDD
The shaded area the possible agreement area.
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8. 3.The negotiation model
3.1 Nash Bargaining between Manufacture and Customer
Nash bargaining model
we model the negotiation process as a Nash bargaining model as given in the following equation .
is the adjusted Nash Bargaining Product, is the bargaining power, let be the manufacturer’s and customer’s threat points, respectively.
We can get the agreed price and the due date .
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9. 3.The negotiation model
3.2 Schedule Relation between Suppliers and the Manufacture
There sometimes exist rework and complex logic relation among the assembly activities in the assembly process.
We can use GERT to describe the relation due to its capability to counter probability branches and loops simultaneously.
Employ Mason formula to derive the relation among the manufacture’s completion time and the suppliers’ due date.
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10. 3.The negotiation model
3.3 The negotiation model between the manufacture and the suppliers
The profit of the vertical integrated strategic alliance is defined as
the manufacture’s expected completion time should meet the agreed due date with the customer derived from Nash Bargaining game
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11. the due date of activity (3,3)
4. Illustrated Example
Suppose a manufacture needs to assemble a product for a unique customer, the GERT network of the assembly process is shown in Fig.3
TABLE I. the parameters of the GERT network
Activity p
w function
Unknown parameters
(1,2) 1
e6s --
(2,3)
the due date of the supplier
(3,3)
0.2
0.2 ecs
the due date of activity (3,3)
(3,4)
0.8
0.8 e7s
(4,5)
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12. 4. Illustrated Example 4.1 The Nash Bargaining model
the adjusted Nash bargaining product is
the agreed completion time is 25 months and the price is 85 units.
The remaining task is to bargain due date and price with the supplier to ensure that the expected completion time is 25 months.
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13. 4. Illustrated Example
4.2 The relation between the manufacture’s expected time and the supplier’s due date
According to the analytical algorithm of GERT, we get the equivalent w function:
The expected completion time is affected by the unknown parameters which are the bargaining parameters in the next steps.
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14. 4. Illustrated Example
4.3 The Nash equilibrium of Cooperation game between manufacturer and supplier
The production cost associated with supplier is determined by the early due date and the late due date, with the equation shown as following: .
We use Lingo software to solve this model, and then get the results: the price of the supplier is 35.9 units when the early due date is 5.08 months, and the late due date is 7.11 months.
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15. 5. Conclusions
This paper focuses on the stochastic precedence, and establishes a synthetic framework consisting of the negotiation among the manufacture, the customer and the suppliers.
We use Nash bargaining game to analyze the negotiation between the manufacture and the customer with the utility function maximized considering the trade-off of the due date and the price.
GERT is employed to describe the complex and stochastic precedence of the assembly process.
The optimization model is proposed to allocate the total profit, when the manufacture and the suppliers adopt vertical integrated strategy
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16. 6. Further study
The first one is to conduct sensitive analysis to explore the different impact of the model parameters
The second is to incorporate delivery service level reputation in the model
A third one is to handle the stochastic property of the manufacture’s completion time. Chance constrained programming(CCP) may be used to extend the proposed model.
Utilize Grey number and fuzzy number to represent the uncertainty
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17. Reference
[1]Fang X, Ru J, Wang Y. Optimal procurement design of an assembly supply chain with information asymmetry[J]. Production and Operations Management, 2014, 23(12):
[2] Jiang L, Wang Y. Supplier competition in decentralized assembly systems with price-sensitive and uncertain demand[J]. Manufacturing & Service Operations Management, 2010, 12(1):
[3]Gerchak Y, Wang Y. Revenue‐Sharing vs. Wholesale‐Price Contracts in Assembly Systems with Random Demand[J]. Production and operations Management, 2004, 13(1):
[4]Laperrire L, Reinhart G. CIRP Encyclopedia of Production Engineering [M]. Springer Publishing Company, Incorporated, 2014.
[5] Lotter B, Wiendahl H P. Changeable and reconfigurable assembly systems[M]//Changeable and Reconfigurable Manufacturing Systems. Springer London, 2009,pp
[6]Benjaafar S, ElHafsi M, Lee C Y, et al. Technical note-optimal control of an assembly system with multiple stages and multiple demand classes. Operations Research, 2011, vol.59, no.2, pp
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18. Thank You !
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