Research Article

Multiple Objective Fuzzy Sourcing Problem with Multiple Items in Discount Environments

Table 2

Fuzzy multiobjective supplier selection studies and their properties (updated version of Table in [2]).

Author, year, reference The current studyArikan (2014) [2]Nazari-Shirkouhi et al. (2013) [57]Kang and Lee (2010) [58]Razmi and Maghool (2010) [59] Amid et al. (2009) [46]Torabi and Hassini (2009) [16]Torabi and Hassini (2008) [60]

Discount scheme(s)All units (incremental, volume)All unitsAll units All units All units, incremental, volume All units Lead time-dependent Lead time-dependent

PeriodSingleSingleSingleMultipleMultipleSingleMultipleMultiple

ItemMultipleSingleMultipleSingleMultipleSingleMultipleMultiple

Sources of fuzzinessAspiration levels of objectives and demand level Aspiration levels of objectives and demand levelAspiration levels of objectives Aspiration levels of objectives and fuzzy triangular numbers in FAHPFuzzy capacity and demand levels Aspiration levels of objectives and demand level Aspiration levels of objectives and capacities and demand levelsAspiration levels of objectives demand, capacity, quality, and service levels

ObjectivesTo minimize
(1) the total production and ordering costs,
(2) the total number of rejected units,
(3) the total number of late delivered units
To minimize
(1) the total monetary cost, (2) the total number of rejected units,
(3) the total number of late deliveries
To minimize
(1) the total purchasing and ordering costs,
(2) the total number of defective units,
(3) the total number of late delivered units
(1) To minimize the total cost
(2) To maximize the yield rate
(3) To fix the replenishment to a desired rate
(1) To minimize the total purchasing cost
(2) To maximize the total value of purchasing
To minimize
(1) the total purchasing cost,
(2) the number of rejected items,
(3) the number of late delivered units
To minimize
(1) the total cost of logistics,
(2) the total value of purchasing,
(3) the number of defective items,
(4) the late deliveries of purchased items
To minimize
(1) the total cost of logistics,
(2) the total value of purchasing

Solution approachInteractive approach which utilizes
Tiwari et al.’s [17] additive fuzzy model; Lai and Hwang’s [18, 19] augmented max-min model; Chen and Tsai’s [20] fuzzy model
Two phased additive approach [39] which utilizes
Tiwari et al.’s [17] additive fuzzy model; Chen and Tsai’s [20] fuzzy model
Interactive approach including fuzzy goal programming representation with piecewise linear membership functions, max-min operator, and fuzzy add operatorTwo models constructed:
(1) Zimmermann max-min approach [41]
(2) Tiwari et al.’s [17] weighted additive fuzzy model
Fuzzy constraints were converted to crisp constraints and the augmented ε-constraint method is performed in which objectives are considered lexicographicallyTiwari et al.’s [17] weighted additive fuzzy modelInteractive approach including
fuzzy goal programming, the weighted average method for defuzzification, and fuzzy model defined by Werners’ [61] fuzzy or operator
Interactive approach including
the weighted average method for defuzzification, Lai and Hwang’s augmented max-min model [18, 19], and fuzzy model defined by Werners (1988) fuzzy or operator

SoftwareGAMSGAMSGAMSLINGOGAMSLINDO/LINGOGAMSGAMS