Development of Mathematical Models for a Class of Component Remanufacturing Problems With Break-even Analysis

Abstract

The aim of the research is to propose and address a class of Component Remanufacturing (CR) problems. This class of CR problems arise for any Original Equipment Manufacturer (OEM) who produces durable products and, acquires returns for remanufacturing components. The final products’ demand can be satisfied by the same product and/or by Backordering (BO) and/or by Product Substitution (PS). Each of the products are manufactured by assembling a set of components, which are manufactured by OEM and/or purchased and/or remanufactured from the returns. The returns are of three categories: Commercial Returns, End-of-Use Returns and End-of-Life Returns. The components remanufactured from any return-category are equivalent in all aspects as compared to the manufactured and/or purchased components. The final products assembled using components from any of the three sources are also equivalent in all aspects and satisfy the same demand. Moreover, remanufacturing of components from the return is done by installing required capacities for both dismantling the returns and remanufacturing the various components (called together as Reverse Flow Capacities (RFC)). Considering the problem complexities for the CR problem of an OEM, considered in this research, the main research problem is: “Determination of reverse flow capacities (RFC) to set-up and the Breakeven Period (BEP) for reclaiming the capital invested for installing the RFC, when CR is incorporated, along with the corresponding optimal inventory and production plans, for each period in a planning horizon, when single/multiple durable product(s), is/are demanded, backordered and/or substituted, which is/are assembled using components that could be obtained from manufacturing and/or purchasing and/or remanufacturing sources”. The main research problem considered in this research is decomposed into 5 stand-alone research problems. The first decomposed research problem is the Single Product–Component Remanufacturing problem (SP-CR problem). The second research problem is “SP-CR with RFC&BEP problem”, where RFC & BEP are additionally determined. In the third research problem, Multi Products (MP) are considered, and is referred as “MP-CR with RFC&BEP problem”. These three research problems are modelled as Integer Linear Programs. The concept of demand management by BO, along with the real-life procurement restrictions, is incorporated in the fourth research problem and is termed as “MP-CR with BO problem”. The model proposed for this problem is an Integer Non-Linear Programming (INLP) model. Finally, PS mechanism is incorporated to the MP-CR with BO problem in the fifth research problem and called as “MP-CR with BO&PS problem”. For the fifth problem, the INLP model proposed for MP-CR with BO problem is extended appropriately (and called as “E-INLP model”). The objective for the first three research problems are “minimizing total cost”. However, for research problems four and five, the objective is “profit maximization”. This is because, in these research problems the concept of backordering is incorporated, which skews results if a cost minimization objective is considered. LINGO set codes that can generate each of the proposed mathematical models for any given data are developed. A suitable numerical example is developed, based on the data collected and/or observed from a real-life industry of an Indian Automobile OEM, for representing each of the five research problems. Validation of each of the five proposed mathematical models is carried out using the numerical example developed to represent each of the five research problems, and with the help of a developed LINGO set code in a LINGO 11.0 Solver. In addition, the computational intractability of the proposed INLP model for MR-CR with BO problem is studied by proposing an experimental design, which is used to generate test instances. From the optimal solution obtained for the numerical example representing each of the five research problems, it is observed that, for the Indian Automobile OEM: (a) incorporation of CR by setting up the RMC is profitable, (b) remanufacturing replaces manufacturing as the primary source for components, (c) Backordering (BO) and the imposition of purchase restrictions indicated how the availability of the inventories for the components and raw materials can be exploited to maximize profit, and (d) proposed Product Substitution (PS), along with BO, indeed gives a boost to sales by preventing backordering to the maximum possible extent.