### Citations

2037 |
Network Flows: Theory, Algorithms, and Applications
- Ahuja, Magnanti, et al.
- 1993
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Citation Context ...e with no capacity limits problem (3) has a trivial optimal solution equal to (d1, . . . , dT ). In the case with capacity limits, (3) can be formulated as the minimum cost 5 flow problem (see, e.g., =-=[37]-=-): min T∑ t=1 (cIt It + c B t Bt) s.t. Bt − It = ∑t j=1(dj − xj), t = 1, . . . , T, lt ≤ xt ≤ ut, t = 1, . . . , T, Bt, It ≥ 0, t = 1, . . . , T. (4) Problem (4) can efficiently solved, for instance, ... |

522 |
Possibility theory: an approach to computerized processing of uncertainty
- Dubois, Prade
- 1988
(Show Context)
Citation Context ...he first family, a defuzzification is first performed and then deterministic optimization methods are used [20, 21]. In the second one, the objective is expressed in the setting of possibility theory =-=[24]-=- and credibility theory [25]. We can distinguish: the possibilistic programming (a fuzzy mathematical programming) in which a solution optimizing a criterion based on the possibility measure is built ... |

520 |
Information Distortion in a Supply Chain: The Bullwhip Effect
- Lee, Padmanabhan, et al.
- 1997
(Show Context)
Citation Context ...ot compete as independent entities but as a part of collaborative supply chains. Uncertainty in demands creates a risk in a supply chain as backordering, obsolete inventory due to the bullwhip effect =-=[1]-=-. To reduce this risk two different approaches exist that are considered here. The first approach consists in a collaboration between the customer and the supplier and the second one consists in an in... |

275 |
Robust discrete optimization and its applications
- Kouvelis, Yu
- 1997
(Show Context)
Citation Context ...ct of uncertainty on costs, since the approaches proposed in the literature are not able to do this. 2 Popular setting of problems for hedging against uncertainty of parameters is robust optimization =-=[27]-=-. In the robust optimization setting the uncertainty is modeled by specifying a set of all possible realizations of the parameters called scenarios. No probability distribution in the scenario set is ... |

225 | Generalized benders decomposition. - Geoffrion - 1972 |

219 |
Dynamic version of the economic lot size model
- Wagner, Whitin
- 1958
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Citation Context ... but it is more penalized that inventory. This problem is equivalent to the problem of production planning with backordering, more precisely to a certain version of the lot sizing problem (see, e.g., =-=[28, 29]-=-), where: the procured quantities are production quantities, a production plan; delivering constraints are production constraints, capacity limits on production plans; and the gross requirements are d... |

120 |
A Procedure for Ordering Fuzzy Subsets of the Unit Interval
- Yager
- 1981
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Citation Context ...qual 1 and the costs of backordering one unit from period t + 1 to period t, cBt , for every t = 1, . . . , 5 equal 5. The knowledge about demands in each period is represented by the intervals: D1 = =-=[30, 45]-=-, D2 = [5, 15], D3 = [10, 30], D4 = [20, 40] and D5 = [20, 40]. The scenario set Γ (states of the world) is Γ = [30, 45] × [5, 15] × [10, 30] × [20, 40] × [20, 40] (see Figure 2). The execution of Alg... |

64 |
Uncertainty theory: An Introduction to its Axiomatic foundation
- Liu
- 2004
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Citation Context ...cation is first performed and then deterministic optimization methods are used [20, 21]. In the second one, the objective is expressed in the setting of possibility theory [24] and credibility theory =-=[25]-=-. We can distinguish: the possibilistic programming (a fuzzy mathematical programming) in which a solution optimizing a criterion based on the possibility measure is built [16, 17], the credibility me... |

47 |
Decision-making in a fuzzy environment. Manag Sci 17:141–161 Beraldi P, Ruszczyński A (2005) Beam Search heuristic to solve stochastic integer problems under probabilistic constraints. Eur J Oper Res 167(1):35–47 Bertsekas DP
- Bellman, LA
- 1970
(Show Context)
Citation Context ... which gives N(fxY ∈ G̃) < N(fxopt ∈ G̃). Let us examine a possibilistic programming (a mathematical programming with fuzzy parameters), where solution concepts are based on the BellmanZadeh approach =-=[46]-=- - see, e.g., [16, 17]. In this way, the assertion of the form “fx ∈ G̃”, where fx is a cost of production plan x, is treated as a fuzzy constraint and values of the membership function µ G̃ stand for... |

43 |
The capacitated lot sizing problem: a review of models and algorithms
- Karimi, Ghomi, et al.
(Show Context)
Citation Context ...pacity limits and minimizes the total cost of storage and backordering subject to the conditions of satisfying each demand. It is efficiently solvable when the demands are precisely known (see, e.g., =-=[30, 31, 32]-=-). However, the demands are seldom precisely known in advance and the uncertainty must be taken into account. In this paper, we consider the above problem with uncertain demands modeled by fuzzy inter... |

43 |
When upper probabilities are possibility measures. Fuzzy Sets and Systems,
- Dubois, Prade
- 1992
(Show Context)
Citation Context ...is understood as a possibility distribution, pia = µÃ, which describes the set of more or less plausible, mutually exclusive values of the variable a. It can encode a family of probability functions =-=[34]-=-. In particular, a degree of possibility can be viewed as the upper bound of a degree of probability [34]. The value of pia(v) represents the possibility degree of the assignment a = v, i.e. Π(a = v) ... |

39 | Possibility theory and data fusion in poorly informed environments.
- Dubois, Prade
- 1994
(Show Context)
Citation Context ... a λ-cut Ã[λ] with confidence (or degree of necessity) 1 − λ. A detailed interpretation of the possibility distribution and some methods of obtaining it from the possessed knowledge are described in =-=[24, 35]-=-. Let G̃ be a fuzzy interval. Then “a ∈ G̃” is a fuzzy event. The possibility of 4 “a ∈ G̃”, denoted by Π(a ∈ G̃), is as follows [36]: Π(a ∈ G̃) = sup v∈R min{pia(v), µG̃(v)}. (1) Π(a ∈ G̃) evaluates ... |

31 |
Supply chain modelling using fuzzy sets,”
- Petrovic, Roy, et al.
- 1999
(Show Context)
Citation Context ... of fuzzy demands: economic order quantity [11, 12], multi-period planning [8, 9, 10, 13, 14, 15, 16, 17], and the problem of supply chain planning (production distribution, centralized supply chain) =-=[18, 19, 20, 21, 22, 23]-=-. In the literature, there are two popular families of approaches for coping with fuzzy parameters. In the first family, a defuzzification is first performed and then deterministic optimization method... |

30 |
Fuzzy scheduling: Modelling flexible constraints vs. coping with incomplete knowledge.
- Dubois, Fargier, et al.
- 2003
(Show Context)
Citation Context ... of obtaining it from the possessed knowledge are described in [24, 35]. Let G̃ be a fuzzy interval. Then “a ∈ G̃” is a fuzzy event. The possibility of 4 “a ∈ G̃”, denoted by Π(a ∈ G̃), is as follows =-=[36]-=-: Π(a ∈ G̃) = sup v∈R min{pia(v), µG̃(v)}. (1) Π(a ∈ G̃) evaluates the extent to which “a ∈ G̃” is possibly true. The necessity of event “a ∈ G̃”, denoted by N(a ∈ G̃), is as follows: N(a ∈ G̃) = 1−Π(... |

26 |
Fuzzy-genetic approach to aggregate production-distribution planning in supply chain management,”
- Aliev, Fazlollahi, et al.
- 2007
(Show Context)
Citation Context ... of fuzzy demands: economic order quantity [11, 12], multi-period planning [8, 9, 10, 13, 14, 15, 16, 17], and the problem of supply chain planning (production distribution, centralized supply chain) =-=[18, 19, 20, 21, 22, 23]-=-. In the literature, there are two popular families of approaches for coping with fuzzy parameters. In the first family, a defuzzification is first performed and then deterministic optimization method... |

25 |
Minimax regret solution to linear programming problems with an interval objective function.
- Inuiguchi, Sakawa
- 1995
(Show Context)
Citation Context ...em ROB based on on iterative relaxation scheme for min-max problems proposed in [40]. Similar methods were developed for min-max regret linear programming problems with an interval objective function =-=[41, 42]-=-. Let us consider the problem (RX-ROB) being a relaxation of problem ROB that consists in replacing a given scenario set Γ with a discrete scenario set Γdis = {S1, . . . , SK}, Γdis ⊆ Γ: RX-ROB: a∗ = ... |

23 |
Lot sizing and scheduling – Survey and extensions
- Drexl, Kimms
- 1997
(Show Context)
Citation Context ...pacity limits and minimizes the total cost of storage and backordering subject to the conditions of satisfying each demand. It is efficiently solvable when the demands are precisely known (see, e.g., =-=[30, 31, 32]-=-). However, the demands are seldom precisely known in advance and the uncertainty must be taken into account. In this paper, we consider the above problem with uncertain demands modeled by fuzzy inter... |

23 |
Necessary conditions for Min-Max problems and algorithms by a relaxation procedure
- Shimizu, Aiyoshy
- 1980
(Show Context)
Citation Context ...nded closed set it follows that A(x) attains its minimum on X. We now construct an iterative algorithm for solving problem ROB based on on iterative relaxation scheme for min-max problems proposed in =-=[40]-=-. Similar methods were developed for min-max regret linear programming problems with an interval objective function [41, 42]. Let us consider the problem (RX-ROB) being a relaxation of problem ROB tha... |

20 |
On latest starting times and float in activity networks with ill-known durations.
- Dubois, Fargier, et al.
- 2003
(Show Context)
Citation Context ...umed that the demands are unrelated one to each other. Hence, the possibility distributions associated with the demands induce the following possibility distribution over all scenarios in S ∈ RT (see =-=[44]-=-): pi(S) = Π((d1 = s1) ∧ · · · ∧ (dT = sT )) = min t=1,...,T Π(dt = st) = min t=1,...,T µ D̃t (st). (15) The value of pi(S) stands for the possibility of the event that scenario S ∈ RT will occur. We ... |

17 | A heuristic to minimax absolute regret for linear programs with interval objective function coefficients.
- Mausser, Laguna
- 1999
(Show Context)
Citation Context ...em ROB based on on iterative relaxation scheme for min-max problems proposed in [40]. Similar methods were developed for min-max regret linear programming problems with an interval objective function =-=[41, 42]-=-. Let us consider the problem (RX-ROB) being a relaxation of problem ROB that consists in replacing a given scenario set Γ with a discrete scenario set Γdis = {S1, . . . , SK}, Γdis ⊆ Γ: RX-ROB: a∗ = ... |

16 |
Fuzzy optimization for supply chain planning under supply, demand and process uncertainties,” Fuzzy Sets and Systems,
- Peidro, Mula, et al.
- 2009
(Show Context)
Citation Context ... of fuzzy demands: economic order quantity [11, 12], multi-period planning [8, 9, 10, 13, 14, 15, 16, 17], and the problem of supply chain planning (production distribution, centralized supply chain) =-=[18, 19, 20, 21, 22, 23]-=-. In the literature, there are two popular families of approaches for coping with fuzzy parameters. In the first family, a defuzzification is first performed and then deterministic optimization method... |

14 | A single-period inventory model with fuzzy demand, - Kao, Hsu - 2002 |

13 |
Quantitative models for supply chain planning under uncertainty: a review
- Peidro, Mula, et al.
- 2009
(Show Context)
Citation Context ...out constraints. Another way to reduce a risk in a supply chain is to integrate the uncertainty in a planning process. In the literature, three different sources of uncertainty are distinguished (see =-=[6]-=- for a review): demand, process and supply. These uncertainties are due to difficulties to access to available historical data allowing to determine a probability distribution. In this paper, we focus... |

12 |
Material requirement planning with fuzzy constraints and fuzzy coefficients,”
- Mula, Poler, et al.
- 2007
(Show Context)
Citation Context ...a procurement contract) with ill-known gross requirements. Several production planning problems have been adapted to the case of fuzzy demands: economic order quantity [11, 12], multi-period planning =-=[8, 9, 10, 13, 14, 15, 16, 17]-=-, and the problem of supply chain planning (production distribution, centralized supply chain) [18, 19, 20, 21, 22, 23]. In the literature, there are two popular families of approaches for coping with... |

12 |
Fuzzy decision modeling for supply chain management.
- Wang, Shu
- 2005
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12 | The Validity of a Family of Optimization Methods - Meyer - 1970 |

11 |
Supply Chain Collaboration: How to Implement CPFR and Other Best Collaborative Practices
- Ireland, Crum
(Show Context)
Citation Context ...X iv :1 21 0. 53 86 v1s[ cs .O H]s1 9 O cts20 12 for implementing a cooperation between retailers and manufactures. This process is called Collaborative Planning, Forecasting and Replenishment (CPFR) =-=[4]-=-. More precisely, the collaborative processes are usually characterized by a set of point-to-point (customer/supplier) relationships with a partial information sharing [2, 5]. In the collaborative sup... |

10 |
Impact of information sharing and lead time on bullwhip effect and on-hand inventory
- Agrawal, Sengupta, et al.
(Show Context)
Citation Context ...ing and Replenishment (CPFR) [4]. More precisely, the collaborative processes are usually characterized by a set of point-to-point (customer/supplier) relationships with a partial information sharing =-=[2, 5]-=-. In the collaborative supply chain, a procurement plan is built and propagated through a supply chain. Namely, the procurement plan is composed of three horizons: freezing, flexible and free ones [2]... |

10 |
Modeling fuzzy multiperiod production planning and sourcing problem with credibility service levels,”
- Lan, Liu, et al.
- 2009
(Show Context)
Citation Context ...a procurement contract) with ill-known gross requirements. Several production planning problems have been adapted to the case of fuzzy demands: economic order quantity [11, 12], multi-period planning =-=[8, 9, 10, 13, 14, 15, 16, 17]-=-, and the problem of supply chain planning (production distribution, centralized supply chain) [18, 19, 20, 21, 22, 23]. In the literature, there are two popular families of approaches for coping with... |

10 |
Application of fuzzy sets to manufacturing/distribution planning decisions in supply chains,”
- Liang
- 2011
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7 |
A fuzzy linear programming based approach for tactical supply chain planning in an uncertainty environment.
- Peidro, Mula, et al.
- 2010
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6 |
Collaborative Planning in Supply Chains: A Negotiation-Based Approach
- Dudek
- 2009
(Show Context)
Citation Context ...in (the most common way to coordinate within companies). The horizontal one refers to the collaborative planning, in which a supply chain can be seen as a chain, where actors are independent entities =-=[3]-=-. The industrial collaborative planning has been standardized ∗The second author of the paper was partially supported by Polish Committee for Scientific Research, grant N N206 492938. †Corresponding a... |

6 |
A single period inventory model with imperfect production and stochastic demand under chance and imprecise constraints
- Panda, Kar, et al.
(Show Context)
Citation Context ...upplier capacity sharing due to a procurement contract) with ill-known gross requirements. Several production planning problems have been adapted to the case of fuzzy demands: economic order quantity =-=[11, 12]-=-, multi-period planning [8, 9, 10, 13, 14, 15, 16, 17], and the problem of supply chain planning (production distribution, centralized supply chain) [18, 19, 20, 21, 22, 23]. In the literature, there ... |

5 | 2009. Design of cooperative processes in a customer-supplier relationship: An approach based on simulation and decision theory. Engineering - Galasso, Thierry |

5 |
a). “Modelling of ill-known requirements and integration in production planning”, Production Planning & Control, (Juillet): doi
- Guillaume, Thierry, et al.
- 2010
(Show Context)
Citation Context ...cision on quantities of demands (MPS) [8], the imprecision on quantities of demands and uncertain orders [9] (MRP) and the imprecision on quantities and on dates of demands with uncertain order dates =-=[10]-=- (MRP). In this paper, we wish to investigate the part of the MRPII process. Namely, the procurement process in the tactical level in the collaborative context. Our purpose is to help the decision mak... |

5 |
The effectiveness of a fuzzy mathematical programming approach for supply chain production planning with fuzzy demand,”
- Mula, Peidro, et al.
- 2010
(Show Context)
Citation Context ...a procurement contract) with ill-known gross requirements. Several production planning problems have been adapted to the case of fuzzy demands: economic order quantity [11, 12], multi-period planning =-=[8, 9, 10, 13, 14, 15, 16, 17]-=-, and the problem of supply chain planning (production distribution, centralized supply chain) [18, 19, 20, 21, 22, 23]. In the literature, there are two popular families of approaches for coping with... |

5 |
Nonlinear Programming, Theory and Methods. Akadémiai Kiado
- Martos
- 1976
(Show Context)
Citation Context ...reme one. Proof. Function F (x∗, S) attains its maximum in Γ. Since F (x∗, S) is convex (Proposition 1) and Γ is the hyper-rectangle, an optimal scenario for problem (6) is an extreme one (see, e.g., =-=[38]-=-). Applying Proposition 2, we can rewrite problem (6) as: f+x∗ = A(x ∗) = F (x∗, Sw) = max S∈Γext F (x∗, S). (10) We are now ready to give a dynamic programming based algorithm for solving problem (10... |

4 |
Integration of uncertain and imprecise orders in
- Grabot, Geneste, et al.
- 2005
(Show Context)
Citation Context ...duling and a shop floor control). MRPII have been also extended to take into account: the imprecision on quantities of demands (MPS) [8], the imprecision on quantities of demands and uncertain orders =-=[9]-=- (MRP) and the imprecision on quantities and on dates of demands with uncertain order dates [10] (MRP). In this paper, we wish to investigate the part of the MRPII process. Namely, the procurement pro... |

4 |
A fuzzy aggregate production planning model for make-to-stock environments
- Tavakkoli-Moghaddam, Rabbani, et al.
- 2007
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3 |
The Use of Possibilistic Decision Theory in Manufacturing Planning and Control
- Thierry, Fargier
- 2000
(Show Context)
Citation Context ...uirement Planning (MRP)) and the operational level (a detailed scheduling and a shop floor control). MRPII have been also extended to take into account: the imprecision on quantities of demands (MPS) =-=[8]-=-, the imprecision on quantities of demands and uncertain orders [9] (MRP) and the imprecision on quantities and on dates of demands with uncertain order dates [10] (MRP). In this paper, we wish to inv... |

2 |
Fuzzy Minimum-Risk Material Procurement Planning Problem
- Sun, Liu
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2 |
Choosing robust solutions in discrete optimization problems with fuzzy costs. Fuzzy Sets and Systems
- Kasperski, Kule
(Show Context)
Citation Context ...erion is weaker than the first one and consists in choosing a plan with the maximum degree of necessity that costs of the plan fall within a given fuzzy goal. A similar criterion has been proposed in =-=[33]-=- for discrete optimization problems with fuzzy costs. We provide some methods for finding a robust production plan with respect to the proposed criteria as well as for evaluating a given production pl... |

1 |
Solving Linear Cost Dynamic Lot Sizing
- Ahuja, Hochbaum
- 2008
(Show Context)
Citation Context ...pacity limits and minimizes the total cost of storage and backordering subject to the conditions of satisfying each demand. It is efficiently solvable when the demands are precisely known (see, e.g., =-=[30, 31, 32]-=-). However, the demands are seldom precisely known in advance and the uncertainty must be taken into account. In this paper, we consider the above problem with uncertain demands modeled by fuzzy inter... |