Multi-objective Programming Models

A multi-objective evaluation is needed to represent various aspects of supply chain performance and customers requirements satisfaction, as well as to balance the performance of individual supply chain units. Two main technical approaches to representing multi-objective simations are (1) assigning weights to each objective, characterizing relative importance and (2) preemptive optimization starting with 

The generic formulation can be extended to multi-objective setting in various ways. Objectives associated with environmental issues, responsiveness, and reliability including customer service are considered most frequently. The generic supply chain configuration optimization model is extended to incorporate these additional objectives and the objective function (8.1) is reformulated as 

The responsiveness is evaluated as a time spent during transportation of materials and products along the supply chain links 

The supply chain reliability is evaluated by the fill rate 

Other multi-objective supply chain configuration models have been developed by Li and O Brien (1999), Sabri and Beamon (2000), Talluri and Baker (2002), Brandenburg (2015) and Das and Rao Posinasetti (2015) (see Chap. 3). 

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Given the heterogeneous nature of supply chains, optimization often cannot be performed with respect to a single objective. Multi-objective programming models seek an optimal solution with regard to multiple objectives. These models rely on judgmental assessment of the relative importance of each objective. 

The problem is formulated as a multie-objective optimisation model and is solved using Goal Programming technique. The optimal solution includes one oil boiler (B3), one... 

Sabri and Beamon (2000) consider a four-stage (suppliers, plants, DCs, and customer zones) problem with both strategic (plant and DC locations) and tactical decisions. Demands for products are deterministic and have to be satisfied. There are fixed costs associated with DCs and transportation links between DCs and customer zones. Production cost is assumed to be linear. Two objectives are considered (a) Total cost, (b) Volume flexibility (difference between plant capacity and its utilization, and difference between DC capacity and its utilization). The strategic sub-model of the problem is formulated as a multi-objective MIR Two operational sub-models (suppliers, production) are formulated and solved as a non-linear programming problem. An overall iterative procedure is proposed which combines the strategic sub-model with the operational sub-models. 

Xia and Wu (2007) AHP with multi-objective mathematical programming Formulated a multi-criteria supplier selection problem with supplier price breaks. Incorporates AHP to calculate criteria weights to be used in the model... 

Bilsel, R. U. and A. Ravindran. 2011. A Multi-objective chance constrained programming model for supplier selection. Transportation Research Part B. 45(8) 1284-1300. 

Multi-objective, stochastic, and nonlinear mathematical programming models are other models that find application in supply chain configuration. 

Bozotgi-Amiri A, Jabalameli MS, Mirzapour AI-e-Hashem SMJ (2013) A multi-objective robust stochastic programming model for disaster relief logistics under uncertainty. OR Spectmm. doi 10.1007/s00291-011-0268-x... 

The economic objective, Fi, is measured by the total CLSC cost, including total material purchasing cost (PC), total installation cost (BC), total production cost (MC), total capacity expansion cost (CEC), total transportation cost (TC), and total disposal cost (DC). The environmental objective, F2, is measured by the total carbon (CO2) emission, including total production carbon emission (PCOE), total installation carbon emission (BCOE), and total transportation carbon emission (TCOE) in all the CLSC. For a MCSCD problem, we also need to consider material supply constraints, flow conservation constraints, capacity expansion and limitation constraints, and transportation constraints. Consequently, the MCSCD problem may be formulated as a multi-objective mixed integer programming model. 

Pishvaee, M. S., and Razmi, J. Environmental supply chain network design using multi-objective fuzzy mathematical programming. Applied Mathematical Modelling 36, no. 8 (2012) 3433-3446. 

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