**1. Introduction**

Owing to the escalating awareness of resource depletion, climate change, and increasing population, firms in the agriculture domain need to redesign their current supply chain models by taking economic and environmental impacts into account [1]. The life cycle of products held in inventory and processing produce a major concern of perishability among agri-products throughout the supply chain. Therefore, replenishment strategies, product supply, and processing indicators are crucial to consider in the research models. The global market for perishable goods, such as refrigerated products and prepared meals, is growing due to changing lifestyles and overall decreasing tariffs. Owing to their common fragility and limited lifetime, handling those goods is far more complex and includes much higher risks compared to non-perishable products [2]. However, this work deals with the sugar processing from sugarcane as a raw material in local industry with outsourcing operation as a non-perishable product because of the long life of raw sugarcane. Also, the supply chain considers a small portion of the whole network, i.e., a single sugar processing firm with a single outsourcing vendor.

It is evident that the incidence of the uncertain factors is unforeseeable, which may induce a number of decision-making mistakes through the application of a traditional supply chain, thus incurring a high cost and unclean production environment [3]. Moreover, variable demand alters the former assumptions in which demand follows a discrete known distribution for di fferent agri-products [4]. To cover up the deficit caused by the positive and negative surges in agri-product demand, an intelligent variable production model should be integrated within the supply chain. Moreover, controllable production will result in cleaner production as it will optimize the resources without losses and wastes. Because it is estimated that, by 2050, the overall production of food should increase by approx. 70% in order to feed the increasing global population [5]. Hence, the best utilization of resources in a supply chain is a key factor for cleaner agri-production.

Production technology has played a vital role in the upgradation agriculture supply chain and has been a limelight for governments and agri-business sectors. In the basic production model, the assumption of constant production rate was observed predominantly. Later on, the variable machine production rate was also included by considering optimal production costs in manufacturing systems. Although variable production rate remained the point of interest for researchers many years ago through its e ffects on machine tool cost with increasing production rate [6,7]. However, Moutaz Khouja (1995) [8] was among the pioneers to extend the basic production model and consider production rate as a decision variable for the volume flexibility of production. The model suggested the volume-flexibility of manufacturing systems for larger sized lots with a lesser production rate. Moreover, an increased production rate decreases the repeatability [9] of a robot and a ffects the quality, as discussed by [10].

This research contributes to transforming the idea of an intelligent, green supply chain production into a mathematical model. The aim of the model is to represent tangible analysis of human-machine interaction and imperfect production system in order to optimize use of resources and minimize wastes. The inclusion of carbon emission cost as an eco-e fficient attribute along with the variable production rate, satisfying agribusiness firms' demand, is also a limelight of this work, which is hardly observed in previous literature. Further, the impact of this work is extended to quantify production loss due to improper human-machine correspondence. The investigation provides a plan of action for agri-product manufacturing managers to invest in favor of optimized production with e ffective resource utilization, which ultimately leads to less rejection in a production environment.

The article is structured in a well possible way i.e., background and challenges to the agricultural supply chain managemen<sup>t</sup> (agri-SCM) are discussed in this section. In Section 2, the literature is well represented from author contributions, which are presented in consideration of the research gap. Section 3 covers the detailed mathematical formulation of controllable production rate, labor-machine interaction, inventory management, and eco-friendly agri-SCM. The solution method, i.e., algebraic approach application, is also given in Section 3. Afterwards, Section 4 deals with the numerical experiment, which consists of the required data for performing the experiment using the proposed SCM model. The numerical results are also explained and illustrated significantly in Section 4 along the sensitivity analysis of the SCM model to mathematically check the significant cost parameters with respect to the total cost are also performed. In Section 5, conclusion of the research study is discussed.

#### **2. Research Reviews**

In a cleaner production environment, prime attention is given to the reduction of production and associated costs. Fluctuation in agri-products' raw materials, fuel prices and falling sale rates drive the agribusiness firms to incorporate technologies and processes which controls expenses. In order to fulfill the requirements of the future generations, the agri-product supply chain should eliminate existing wastefulness and lay emphasis over green defective free production. Such resource waste elimination requires decision assisted tools that covers intrinsic characteristics of an agri-based product. Furthermore, a green agri-product supply chain needs more than only economic validation objective (profit), thus, it should be also able to handle eco-efficient objective. Hence, the decision assisted tool requires the evaluation of both the economic and environmental aspects simultaneously. For this purpose, mathematical optimization is fairly viable to discover best values from the domain and set a better trade-off for managerial insights [11], and for establishing eco-efficient results-based system [12]. The detailed author contributions are given in Table 1.

In the agricultural supply chain, most of the work is found in the logistic of food supply [13], food safety [14], and imperfect information system. As there is a desirable need to encounter the requirements of lean manufacturing, supervision of scraps and reworks due to the significant concerns for production systems [15–17]. In this aspect, Agri-SCM should be integrated with imperfect and green production. From the perspective of solution methodology, Minjung Kwak (2015) [18] recommended a mixed-integer linear-programming (MILP) model that optimizes the re-manufacturing plan in order to validate both the environmental and economic benefits of products. Some researchers have taken carbon footprint into account for development of cleaner production SCM models. For instance, Xiao et al. (2016) [19] optimized SCM cost via minimizing carbon footprint of both the retailers and manufacturers. In this domain, Chia-Chin Wu and Ni-Bin Chang (2004) [20] presented a grey theory model for uncertain conditions which reflects environmental impact by taking the production planning tax into account. Wang et al. (2011) [21] established a bi-objective model that evaluates the associated costs with environmental plans along a green SCM. Additionally, [22] suggested an electricity monitoring-system that considers a multi-objective linear-programming model taking carbon footprint into account by electricity usage as a supply of energy. As referred earlier, (Banasik (2019) [1]) that work included model development of an uncertain eco-efficient supply chain, however, their model lacks integration of imperfect production.

The effect of the workers' cost on production and inventory is a significant aspect to cleaner production and can be analyzed in numerous models. Most of the researchers, i.e., [23–25] studied an imperfect production environment to assist the managers in dealing with poor quality products. Though, very few studies have analyzed the cause to reduce an imperfect production in the setup. A number of factors that affect the production flow and cause imperfection include reworks, rejections, and scraps etc. The managemen<sup>t</sup> and planning of imperfect production in the model provide a cleaner production int the system and wastes are managed with modeling of the imperfect production [26]. In another study, Sarkar et al. (2018) [27] developed a global sustainable supply chain model with constant production rate having short-term production period in which synchronize mechanism is used to set the cycle time for each production stage. Tiwari et al. (2018) [28] presented a green production quantity model with random imperfect quality products, service level constraints, and failure in reworking. These are depending on the combined efficiency of the machines and workers. Further, the role of controllable production is effective in dealing with imperfect production.

Moutaz Khouja and AbrahamMehrez (1994) [29] proved the deterioration in quality of product with increase in production rates in an economic production inventory model. He reassessed Rosenblatt [30] work with an assumption of quality function. In another study, Khouja et al. [31] further extended his earlier model by assuming that the production rate had a probability to shift production system from in control to the out-of-control state. Later on, Somkiat Eiamkanchanalai and Avijit Banerjee (1999) [32] advanced the work and established model that determines both the optimal production cycle length and variable production rate for a single item. Giri et al. (2005) [33] introduced a flexible production rate EPQ model that addressed the issue of higher stress level of the human-machine interaction with the increase of production rate. In this EPQ model, the unit production cost was stated as a function of the production rate, under general failure and overhaul time. Moreover, [34] presented an EPQ model where the production cycle consisted of multiple runs at various production rates. The author revealed that the production rates should take values between demand rate and production rate that reduces the production cost. Later on, Shib Sankar Sana (2010) [35] studied unit production cost as a function of product reliability and variable production rate in imperfect production system. Giri et al.'s (2005) [33] model was later extended with stochastic demand by [36], sampling in inspection by [37], and stochastic repair time by [38]. Also, Zanoni (2014) [39] examined the case of energy consumption in two stage production system where production depends on the variable production rate.


**Table 1.** Author Contribution.

Production inventory outsourcing policy was studied by [45] for a firm with Markovian in-house production capacity that faced independent stochastic demand operating with outsourcing operation. Also, Pablo Biswas and Bhaba R Sarker (2008) [15] proposed a manufacturing process whereby finished goods are produced along with a proportion of undesirable defective products and scrap. As the system is not always perfect, some scrap is produced during the manufacturing and/or rework processes. According to Wang et al. (2013) [46], when the outsourcing quantity and wholesale price are decision variables, the competitive contract manufacturer sets a wholesale price sufficiently low to allow both parties to coexist in the market, and the original equipment manufacturer outsources its entire production to contract manufacturer. Bettayeb et al. (2014) [47] presented a risk-based approach for quality control of complex discrete manufacturing processes to prevent massive scraps. The advancement targeted from this work is the proposal of a model, aiming at the quality control allocation of the products and an understandable algorithm to prevent the production of excessive amount of scrap.

This research deals with the agri-product supply chain managemen<sup>t</sup> (Agri-SCM). Abundant work on variable production models on realistic case scenarios exists. Particularly, most of the research on eco-efficient (reducing carbon emission) supply chain assumes deterministic demands and constant production rate, and hardly flexible productivity is taken into account. Further, technology development urges for intelligent models in which man-machine interactions are optimized in order to attain minimal wastes. Such intelligent models can hardly be seen in the literature. Additionally, to assert an efficient green production through the supply chain, imperfect production plays a vital role to cut down the cost and reduce the consumption of extra resources. Moving forward, it is worth mentioning that no traces related to agri-products supply chain with intelligent eco-efficient model is found. This work contributes to the latest literature by: (1) providing a centralized, two-echelon supply chain model with variable production rates, (2) presenting an intelligent model in which human–machine interactions are optimized, (3) carbon emission cost and imperfect production are integrated with the proposed model to assure a cleaner production environment, and (4) Agri-SCM with deteriorated products is introduced.

#### **3. Method and Materials**

#### *3.1. Research Modeling*

This human–machine interface is more significant in the supply chain managemen<sup>t</sup> of agricultural products. The research contributes to transform the theoretical idea into a mathematical model with an aim to represent the tangible analysis of the imperfect production system in supply chain management. The model is based on Agri-SCM for deteriorated agri-product by considering controllable production rate from the interaction of the human and workers. The flow diagram of the Agri-SCM is illustrated in Figure 1. This research deals with the two-echelon Agri-SCM and covers the agri-food processing firm, where the vendor is involved into few operations because of capacity limitation. The first stage includes the basic food operations, second stage is dedicated to the vendor operations, and the third stage is the finishing stage. The raw material in manufacturing firms is first processed through the basic cleaning operations. Then, the semi-finished parts are outsourced to the vendor firm. The inspection operations are carried out by the vendor, where the parts are sorted as good and defective. In order to compensate for the rejection to meet the required demand, the same quantity of rejections is ordered to manufacture from the first stage of the processing firm. The good agri-products are further delivered to the final stage for further processing and packaging.

**Figure 1.** The inventory diagram of the agricultural supply chain managemen<sup>t</sup> (Agri-SCM).
