Li green supplier selection model for the

Li and Zabinsky (Li and Zabinsky, 2011) proposed a two-stage stochastic programming (SP) and a chance-constrained programming (CCP) model for the problem of supplier selection under uncertainty. In their research, they aim to determine a minimal set of suppliers along with optimal order quantities. To do so, they used business volume discount.

Dobos and Vörösmarty (Dobos and Vörösmarty, 2014) employed the method of composite indicators (CI) to study the extension of traditional supplier selection methods with consideration of environmental factors. In this method, they divide the criteria into two categories: the traditional (managerial) and environmental (green) factors. They aimed to determine environmental factors as crucial decision factors for their weighting system, since such weight set can affect the result of the selection procedure.

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Mahdiloo and et.al  (Mahdiloo et al., 2015) considered a problem of modeling undesirable outputs in DEA as a linear goal programming. They decompose the efficiency factor of suppliers into technical, environmental and eco-efficiency measurements. They also present a real-world application of their findings by means of a case of the Hyundai Steel Company in South Korea.

Based on a Bayesian framework and Monte Carlo Markov Chain (MCMC) simulation, Sarkis and Dhavale (Sarkis and Dhavale, 2015) presented a methodological approach in order to rank and select suppliers. Results obtained from the MCMC simulation provide much information about supplier performance, which form the basis for additional statistical analyses.

Hashemi and at.al (Hashemi et al., 2015) used a combination of environmental and economic criteria and proposed a green supplier selection model for the automotive industry. They used an analytic network process (ANP) and modified the traditional Grey relational analysis (GRA) and applied the ANP and an improved GRA to weight the criteria and rank the suppliers.

Scott and et.al (Scott et al., 2015) proposed an integrated method in the bioenergy industry in order to select best suppliers and allocates orders optimally with using a combined Analytic Hierarchy Process– Quality Function Deployment (AHP–QFD) and chance constrained optimization algorithm approach.

Chai and Ngai (Chai and Ngai, 2015) analyzed the strategic supplier selection problem in decision environments under uncertainty. They proposed a soft decision model involving multiple stakeholders and multiple perspectives. To perform theoretical decision modeling, they used interval and hesitant fuzzy methodology.

Recently, Firouz and et.al (Firouz et al., 2017) considered the multi-sourcing, supplier selection and inventory problem. In their research, they considered lateral transshipments of a firm offering a single product, by means of several warehouses. To solve the problem, they developed a decomposition based heuristic algorithm. They also show that contractual costs, capacity, and disruption characteristics of suppliers, and the interactions of these factors are the most significant factors while selecting suppliers.

Using multiple criteria decision-making techniques, Awasthi and et.al (Awasthi et al., 2018) presented an integrated fuzzy AHP-VIKOR approach-based framework for sustainable global supplier selection. They solve the problem in two steps. In the first step, they applied fuzzy AHP to generate weights for criteria for sustainable global supplier selection, and in the second part, they used fuzzy VIKOR to rate supplier performances against the evaluation criteria.

Order acceptance

The problem of order selection, acceptance and scheduling deals with joint decisions on which orders to accept and how to schedule them. Similar to supplier selection, this problem has been widely studied with different assumptions and various problem settings.

Rom and Slotnick (Rom and Slotnick, 2009) used a genetic algorithm to solve an order acceptance problem in which orders are selected with the objective of maximizing profit, under limited capacity and tardiness penalty. They compared the results obtained from a myopic heuristic and the employed genetic algorithm to demonstrate the outperformance of the GA.

Oguz and et.al (Og?uz et al., 2010) examined simultaneous order acceptance and scheduling decisions where the orders are defined by their release dates, due dates, and processing times. They solved the problem in a single-machine setting with sequence dependent setup times. The objective is to maximize the total revenue. They assumed that a revenue gained from an order is a function of its deadline and tardiness.

Cesaret and et.al (Cesaret et al., 2012) considerd a make-to-order production system with a single machine and sequence-dependent setup times, where limited production capacity and order delivery requirements dictates selective acceptance of the orders. They present a tabu search algorithm to solve this problem. The results show that the tabu-search algorithm gives near-optimal solutions with higher performance than that of two heuristic algorithms.

Altendorfer and Minner (Altendorfer and Minner, 2015) discussed the influence of the application of queue state-dependent order acceptance policies. In their research, decisions are either with a customer to make, or with the manufacturer. They developed three policies accepting orders where both the customer and the manufacturer have a certain service level threshold. Their findings show that that all order acceptance policies might lead to cost reduction compared to when all orders are accepted.

Lei and Guo (Lei and Guo, 2015) modeled the problem of order acceptance and scheduling as a mixed integer linear programming model in a flow shop environment. In order to solve the problem, used an effective parallel neighborhood search algorithm with the objective of minimizing the makespan and maximizing the total net revenue.

Wang and et.al (Wang et al., 2015) studied the integrated order acceptance and scheduling problem in the two-machine flow shop environment. They formulate the problem as mixed-integer linear programming models and developed branch and bound algorithms to solve the problem. Their results and findings demonstrates the efficiency of their algorithm in problem with large size.

Most recently, Ou and Zhong (Ou and Zhong, 2017) studied two bi-criteria order acceptance and scheduling problems. They considered a filling rate and their problem setting consists of a parallel-machine environment. They provide approximation algorithm to solve the problem. In their model, the number of orders being rejected has an upper bound. Moreover, the total processing time of the rejected orders, cannot be greater than a specific value. By imposing these assumptions, they aim to satisfy a fill rate constraint.