An economic production model with imperfect quality components and probabilistic lead times

Abstract

PurposeThis study investigates a production process that requires N kinds of components for the production of a finished product. The producer orders the various kinds of components from different suppliers and receives the orders in lots at the beginning of each production cycle. Similar to situations often encountered in real life, the lead times are random variables with known probability distributions so that a production cycle starts whenever all N kinds of components become available. Each of the lots received at the start of a production run contains both perfect and imperfect quality components. Once all N kinds of components become available, the producer initiates a screening process to detect the imperfect components. The production of the finished product uses only perfect quality components. The imperfect components are removed from inventory whenever the screening process is completed. The percentage of components of perfect quality present in each lot is a random variable with a known probability distribution.Design/methodology/approachThis production process is described and modeled mathematically and the optimal production/ordering policy is derived based on the mathematical model.FindingsThe formulated mathematical model resulted in the determination of the optimal policy consisting of the optimal number of finished items ordered to be produce during each production run, the number of components ordered from each supplier, and the reorder point. The derived closed form expression for the optimal lot size depends on the minimum of the number of perfect quality components in a lot, whereas the reorder point is determined based on the maximum lead time.Practical implicationsThe modeling approach and results of this study provide practical implications that may be beneficial to both production and supply chain managers as well as researchers.Originality/valueThis modeling approach that incorporates decision-making related to the logistics of acquiring the components and accounts for the probabilistic nature of the lead times and quality of components addresses a gap in the logistics/production literature.

Inventory planning under supplier uncertainty in a two-level supply chain

“…The proposed model extends, generalizes, modifies or aligns with many recent studies in the area of production/inventory models in supply chains. This study extends the classical economic production quantity (EPQ) model in a manner similar to recent studies by accounting for the cost of components/raw material items used in the production process (Yassine and Singh, 2020; El-Kassar et al. , 2020; Salameh and Jaber, 2000; Salemeh and El-Kassar, 2007).…”

“…Drawing upon the contingency theoretical framework, research questions that guide this study were posed and addressed mathematically by formulating a proposed model and applying optimization techniques to arrive at the optimal solution. The proposed model adds to the literature related to supplier selection (Yassine, 2021; Yassine and Singh, 2020; Girri, 2011) and unreliable raw material/components (El-Kassar et al. , 2020; Yassine, 2020; Salameh and Jaber, 2000).…”

“…This study is conducted using a mathematical methodology adapted by most similar previous studies in the area of supply chain production/inventory models (El-Kassar et al. , 2020; Islam et al.…”

“…This study is conducted using a mathematical methodology adapted by most similar previous studies in the area of supply chain production/inventory models (El-Kassar et al, 2020;Islam et al, 2020;Malik and Sarkar, 2020;Yassine and Singh, 2020;Tripathi, 2018). The first step of the mathematical methodology is to provide a list for the notation of the parameters and decision variables related to the problem at hand.…”

“…Malik and Sarkar (2020) show how cost allocation model under bargaining can result in the coordination between members of centralized or decentralized supply chain models. El-Kassar et al (2020) developed an economic production model with imperfect quality components and probabilistic lead times. Lamba et al (2019) proposed proper operational decisions such as supplier selection and lot-sizing can decrease carbon emissions costs.…”