Generalized production planning problem under interval uncertainty

Abass, Samir A.; Gomaa, Mohamed Ali; Elsharawy, Gaber A.; Elsaid, Marwa Sh.

doi:10.1016/j.eij.2010.06.004

Cited by 6 publications

(4 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We first introduce some denotations. In [5], a deterministic optimization model is presented to formulate the production planning problem:…”

Section: Model Of Generalized Production Planning Problemmentioning

confidence: 99%

“…Actually, in the fields of applied mathematics, operation research, and logistics management sciences, there are many relevant achievements on the problem of production planning. For the recent advancement, for example, see [1][2][3][4][5][6][7][8][9][10][11] and the references therein. It is noted that in the constructed models of production planning, some uncertain factors in the real-world production process, such as the price of product, the customer demand, and the production capacity, are taken into consideration (see [2,3,[5][6][7][8][9][10][11]).…”

Section: Introductionmentioning

confidence: 99%

“…It is noted that in the constructed models of production planning, some uncertain factors in the real-world production process, such as the price of product, the customer demand, and the production capacity, are taken into consideration (see [2,3,[5][6][7][8][9][10][11]). For example, in [5], the production capacities and the customer demands are represented by interval numbers, respectively. In [2,3], the customer demands, the prices of products, and the production capacities are described as fuzzy subsets.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Polymorphic Uncertain Linear Programming for Generalized Production Planning Problems

Zhang¹,

Zhang²,

Chen³

et al. 2014

Journal of Optimization

View full text Add to dashboard Cite

A polymorphic uncertain linear programming (PULP) model is constructed to formulate a class of generalized production planning problems. In accordance with the practical environment, some factors such as the consumption of raw material, the limitation of resource and the demand of product are incorporated into the model as parameters of interval and fuzzy subsets, respectively. Based on the theory of fuzzy interval program and the modified possibility degree for the order of interval numbers, a deterministic equivalent formulation for this model is derived such that a robust solution for the uncertain optimization problem is obtained. Case study indicates that the constructed model and the proposed solution are useful to search for an optimal production plan for the polymorphic uncertain generalized production planning problems.

show abstract

“…We first introduce some denotations. In [5], a deterministic optimization model is presented to formulate the production planning problem:…”

Section: Model Of Generalized Production Planning Problemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Polymorphic Uncertain Linear Programming for Generalized Production Planning Problems

Zhang¹,

Zhang²,

Chen³

et al. 2014

Journal of Optimization

View full text Add to dashboard Cite

show abstract

“…Furthermore, the comparison of interval numbers was investigated by Chanas and Zieliński (1999), and Sengupta and Pal (2000). The multi-attribute decision making with interval numbers was researched by Liu (2011), Yue (2011), and Zhou et al (2007, and the optimization problem with interval numbers was studied by Abass et al (2010), Jiang et al (2008), Liu (2006), and Wang et al (2005).…”

Section: Introductionmentioning

confidence: 99%

Cooperative fuzzy games with interval characteristic functions

2015

View full text Add to dashboard Cite

In this paper, a generalized form of fuzzy games with interval characteristic functions is proposed, which can be seen as an extension of games with crisp characteristic functions. Based on the extended Hukuhara difference, the interval Shapley function for interval fuzzy games is studied. Then, the concept of interval population monotonic allocation function (IPMAF) is defined. When interval fuzzy games are convex, we prove that the interval Shapley function is an IPMAF. Furthermore, two special types of interval fuzzy games are researched, and the associated interval Shapley function is studied.

show abstract