A multi-objective optimization of closed-loop supply chain problem with vehicle routing

Product recovery has become significant business strategies to increase a competitive edge in business and also in the society. Parts from discarded products due to rapid advancement and post-consumer products before & after end-oflife (EOL) are recovered to reduce landfill waste and to have become a part of circular economy. Product recovery is made possible with the help of Closed-loop supply chain (CLSC). This paper concentrates on multi-period, multiproduct, and multi-echelon Closed Loop Green Supply Chain (CLGSC) network. A bi-objective (cost and emission) Mixed Integer Linear Programming (MILP) model has been formulated for the network and has been optimized using Goal Programming approach and Genetic Algorithm. Results are discussed for providing some managerial insights of the model.


Introduction
Product recovery is made possible with the help of CLSC. Researchers and practitioners are keen on solving CLSC, Green Supply Chain (GSC), Remanufacturing, CO2 saving rate and Travelling Salesman Problem (TSP) models as Green has become more popular. Recapturing value from End-of-Use (EOU) and EOL product and related information from the customer to the manufacturer is known as Reverse Logistics (RL) (Rogers and Tibben -Lembke, 1998). Due to legislative, environmental and economic reasons, the importance of RL has amplified considerably in the last two decades (Ritichie et al., 2000). Value recovering as much as possible is the use of RL (EISaadany et al., 2013) and reduce the extraction of virgin materials and solid waste dumps. (Bonney and Jaber, 2011;Matar et al., 2014). Dell has developed an RL by which the products are refurbished or purchase fresh parts easily (Kumar and Craig, 2007). CLSC has two parts, Forward Logistics (FL) and Reverse Logistics. RL has become a fundamental part of Green Supply Chain Management. It exists in different industries including electronics, basic materials, and others. Increased customer's awareness and concern for the environment, the products that are not environmentally friendly are given less importance and it is used to fill warranty pools of sold products by refurbishing, and the remaining are sold in secondary markets (Krikke et al., 2004). Remanufacturing is a popular research topic among researchers and practitioners in developing countries due to resource scarcity (Rashid et al., 2013). Remanufactured products will result in less greenhouse emission over virgin manufacturing practices with less consumption of energy and cost (Sutherland et al., 2008). The researchers also interested in building the low-carbon supply chain. CO2 emission in the supply chain beyond single organization is reduced and visualized. Many studies proposed by extending the classical Vehicle Routing  (Seitz, 2007) for EOL vehicles with strategies like repair,  reconditioning or reuse with warranties equivalent to a new product with better quality, new appearance, upgraded  parts and original specifications (Ijomah, 2002 andIjomah et al, 2007). Remanufacturing has become popular in other sectors especially in electronic industries where the EOL and a premature product is more. But in developing countries, remanufacturing is still in the initial stages and still struggling with remanufacturing implementation (Kannan et al., 2016).
The contributions of this paper are as follows. (1) developing a multi-objective, multi-period, and multi-part & product MILP model to optimize the integrated location-allocation-emission reduction planning for a CLGSC network with TSP between distribution hubs and retailers; (2) Purchasing and reprocessing costs are considered to manage the realistic trade-off problem; (3) results from the computational experiments used to analyze various performance components and some managerial insight for the proposed model through a sample problem instance.
The outline of this report is as follows. Problem definition is presented in section 2. Section 3, the mathematical model is presented. The data description, solution methodology is presented in section 4, and results are presented in section 5. Computation Experiment in section 6. Section 7 presents the conclusions and future scope.

Problem definition
From the literature, the major objective framed was to design and optimize a multi-objective, multi-product, multiperiod CLGSC network. A real life CLGSC network is presented in this section and it composed of suppliers, processing units, assembling units, distribution hubs, retailers, Sorting and dismantling units, and reprocessing units as shown in Figure 1. Vehicle routing is done between distribution hubs and retailers. Two products are used to flow in the CLGSC network (Santhosh Srinivasan and Shahul Hamid Khan, 2016a).   TZ  QZ  TW  QW   TY  QY  TR  QR  QN  TN  TNR  TSR  TA

Objective Functions
The objectives are to minimize total cost (TC) and total emission (TE) in the supply chain. The total cost objective has five components. Total transportation cost (TrC) of CLGSC network is represented is the first component

Solution methodology
In this section, a new Genetic Algorithms is proposed to solve the model. Before solving the problem, the multiple objectives were converted into a single objective to find an efficient solution. A pre-emptive method can be used when the model has several objectives with different priorities. Combined Objective Function COF = w1 * Z1 + w2* Z2 The new proposed Genetic Algorithms is as follows: Step 1: Generate an initial population which must satisfy all constraints. Population size is 50.
Step 2: Calculate the objective values of chromosomes in the population Step 3: Evaluate fitness: For this minimization problem, the fitness function is an equivalent maximization problem chosen, such that optimum point remains unchanged.
Step 4: Selection: The roulette wheel selection is used. The probability of selecting the ith string was explained in Wang et al 2010.
Step 5: Crossover: The Random cut two point crossover is used, here the two cutting point is randomly fixed in each generation. The Probability of crossover is 0.8.
Step 6: Inverse Mutation: here the bits are entirely reversed with respect to parent bits. Probability of mutation is 0.1 Step 7: Elite strategy: The elite strategy keeps the fit chromosomes from the previous generation into the next generation. The elite size is 4.
Step 8: Replacement: The new population generated in accordance with the above-mentioned steps updates the old population.
Step 9: Stopping rule. If the number of generations equals 500 then stop, otherwise go to Step 1.

Computational experiments
In this section, the result of a realistic proposed CLGSC network problem for random instances are illustrated. Computational properties and complexities of solving the problem are studied. Some insights are provided for the model based on different scenarios. The network constitutes a sample problem of 5 suppliers, 3 processing units, 2 assembling units, 2 distribution hubs, 4 retailers, 2 SD units, 1 reprocessing unit, and 1 disposal unit. Five kinds of ram material that have different utilization rate are supplied by suppliers, which in turn, are converted into four parts in processing units (Santhosh Srinivasan and Shahul Hamid Khan, 2018).   Table 2 it is clear that purchasing cost and Logistics cost dominates the Total cost. Setup cost and reprocessing cost does not contribute more. Whenever the percentage of return product increases then Purchasing cost decreases and Reprocessing cost is increased. Table 3 shows the optimal and feasible solution for different problem size.

Conclusion
In this paper, an MILP model was framed for a multi-objective CLGSC. The model is optimized using Goal programming and NGA. The relative importance of performance components is studied in detail. Logistics cost and purchase cost dominates the total cost and fixed cost and reprocessing cost does not contribute more. Similarly emission in the facilities contributes more in the total cost. The performance of NGA is better for complex problem it is clearly visible from the results obtained.

Disclosure of conflict of interest
All authors declare that they no conflict of interest.