Integrated production-distribution planning in a reverse supply chain via multi-objective mathematical modeling; case study in a high-tech industry

This article presents an integrated production-distribution plan in a reverse supply chain via multi objective mathematical modeling in a high-tech environment. The objectives of the proposed model include 1) minimizing total costs including production, maintenance, inventory and manpower costs, 2) maximizing customer and supplier satisfaction, and 3) maximizing the quality of manufactured products. The supply chain consists of several suppliers, a producer, customers, a repair center to repair the customer's goods and a repair and maintenance center for repairing or disposing products that have passed their warranty period. Among the contributions of this research, we can consider such issues as considering the quality of products manufactured, returned or supplied from suppliers in order to realize the win-win relationship with suppliers, using the maximum capacity of suppliers and supply of parts by each reconstruction center. In order to validate the model, it is solved for some examples using Lingo software and LP metric method.  In reverse supply chain, what is addressed is recycling and reconstructing the products which are spending final stage of their life cycle. In this regard, after gathering and inspecting the returned products, they are partitioned in to recyclable and non-recyclable (scrap) products (Mirzapour et. al, 2013). Aggregate production planning is a process that determines the optimal level of production and stock inventory to meet the demands for the product in a long term period which considering the capacity limitation of the means and resources (Gholamian et al, 2015).
In this research, investigation is regarding designing and solving a mathematics model for aggregate production planning in reverse supply chain in a high-tech industry. High-tech products are usually made up of chemical, mechanical, and electronic components. Inspection of the products in the supply chain of latter industry is of demolition type, that is, in case where the quality of the products is not confirmed by the customer, they are in masse retuned to the supplier. The returned products are either demolished in the re-construction units or delivered to the producer after re-construction. Also, in case of the non-usage of the products by the customer after technical warranty expiration, they are dispatched to the repair and maintenance unit and after undergoing correctional measures, they are re-dispatched to the customer or producer.
The aim of the present research is to conduct an investigation into the performance manner of the producer in making decision regarding producing the afore-mentioned products. In order to achieve objectives, the producer can manufacture the required products on his/her own plant. Accordingly, he/she should decide on considering the capacity of available means and facilities, production expenditures, and the quality of the produced commodity, what measure of products to produce at regular working hours, and what amount to produce at non-regular (over-time) working hours. In his/her aggregate production planning, he/she might also decide on out-sourcing the production of a portion of his/her required products to outside suppliers. Such planning becomes of utmost importance since he/she should decide- while considering such requisite indices and criteria as expenditure, quality level, and priority- what percentage of the products to delegate to what supplier. Along this line in the proposed model, a win-win relation with the suppliers is deemed essential. Thus, in the model offered here, the optimization of the customer’s satisfaction is taken into account so that- by considering customer’s prioritization- the shortage rate of the unmet demands on the part of the supplier is kept at minimum. The supply chain of the proposed model contains three levels of suppliers, producer, consumers and a center for reconstruction, repair and maintenance. In this chain, a producer starts out by sending several merchandise to customers. The process is carried out in a way that part of customers’ needs are produced by the producer himself/herself at regular and overtime workhouse. Another portion of the producer’s needs are met by different suppliers, which are shipped to the producer who sends them to the customers. Eventually the goods delivered to the customers, in case they are defective, are returned by customers to the reconstruction center, where, after undergoing correctional actions, are sent again to the producer, so in later cycles, they are re-sent to the customers. Additionally, when the expiry data of the product’s warranty arrives, it is shipped to the reconstruction center by the customers, and if possible, after receiving necessary repairs and corrections, are re-sent to the customers; otherwise, the product is de-assembled and returned to the producer.
Hence, in the design of the applied-extended model proposed in this research study, such cases as determining the contribution of the suppliers, reconstruction centers, repair and maintenance, production at regular hours, and overtime manufacture of each of the products as well as the amount of dispatched products to each of the customers are among decisions considered in the latter model. Moreover, such objectives as minimizing producer’s cost including production expenditures, cost of retaining and inventory deficit, costs related to supplying products through outsourcing, maximizing the quality of the manufactured products at regular time, overtime, and production by suppliers or procuring products from repair, maintenance and reconstruction centers, where each one has a distinct quality are among parameters considered in the propounded model. Also, special attention is paid to the assessment of suppliers and customers so that optimum satisfaction of the latter two groups is provided.
Thus, the proposed model contains 4 objective functions and about 20 constraints. The objective functions are minimizing total costs including production, maintenance, inventory and manpower costs, maximizing customer and supplier satisfaction and maximizing the quality of manufactured products. The constraints are such as inventory balance, capacity for holding, firing and hiring of force work, over time and regular time limit and so on. Finally the proposed model has been solved for the case study and one numerical example using Lingo software and LP metric method.  The developed model has been solved by L-P metric method for case study and numerical example from the literature (Mirzapour et al, 2011). In each case, by changing P and weight of objectives (wi), the Pareto optimal solutions (POS) have been delivered. In the case study for two values of P, some Pareto optimal solutions (Zi) have been shown in Table 1. In the article, for more value of P and wi the model has been solved and more POSs have been delivered. For each POS, the optimum value of decision variables from can be determined as the outputs of the model. In this article, a multi objective model for aggregate planning in a reverse supply chain for a high-tech industry has been developed. The proposed model contains four objective functions and 20 constraints. The model has been solved by L-P metric method via LINGO software for the case study and a numerical example from the literature. For future research, uncertainty conditions can be considered in the model.