The effects of green technologies and human error on the vendor buyer supply chain system

Abstract

The emergence of numerous green solutions to be considered in the supply chain system is responsible for ecological problems and the increasing pressure from the government. The effects of green technologies and human error on the vendor buyer supply chain system by considering two carbon emissions strategies, including the carbon taxation and limited total carbon emissions, have been addressed in this paper. It entails inspection of every shipped lot by the buyer to identify the defective products that could have resulted from the vendor’s production process. The inspection process becomes challenging for the buyer due to the classification of defective and non-defective products. A mathematical model is derived in two different scenarios to minimize total integrated cost. This involves designing an algorithm to achieve optimal conditions that are shown numerically. The effects of varying the central parameter values on the optimal solution are performed by sensitivity analysis.

Introduction

The common practice in the international market is the integrated inventory management system, and it provides economic benefits both to the seller and the buyer. Most integrated inventory management systems have targeted the integration of the seller and buyer in recent years. To maximize profit and minimize cost, the trading parties form a strategic alliance and share information to attain improved benefits. Several authors have discussed the integrated supply chain system in different environments. Product quality has been rapidly becoming a vital competitive matter. Inspection is often carried out by buying companies to ensure the incoming raw materials and products are of high quality. New technologies are being developed, which could contribute to quality inspection automation, but most businesses rely on human inspectors. Human fault is one of the key factors influencing logistics efficiency and inventory system. The shipped or produced batches may be sorted into either perfect quality products or defective items by the operator.

Khan et al. [7] documented an economic order quantity for those items found with imperfect quality and inspection. Synergic economic order quantity model having trade credit, shortages, and imperfect quality and verification errors have also been studied by Zhou et al. [8]. A study by Priyan & Uthayakumar [9] has shown the mathematical modeling and algorithm for solving multi-echelon multi constraint inventory problems that have faults in quality inspection. Alfares & Attia [10] suggested a more complicated model that synchronizes inventories with multiple buyers and a single supplier. Khan et al. [11] discussed the error in inspection and the defective items in supplier-buyer Supply Chain by assuming that there is an option for the buyer to repair the faulty items through a local manufacturer replace them by buying new things from a local seller. Taheri-Tolgari et al. [12] developed an inventory model for faulty items, preventive maintenance, inspection errors, and partial backlogging in uncertain environments. Tiwari et al. [13] addressed the effect of the human errors on an integrated stochastic supply chain model having a backorder price discount and setup cost.

Another problem with inventory communication between buyer and seller is the Lead time. The lead time reduction and backorder price discounts become significant when the supply chain results from an uncertain demand. Liao and Shyu did one of the earliest researches that investigated variable lead time. They suggested an inventory model by the assumption that the lead time can be broken down into various linear components with differing piecewise linear continuous crashing costs whereby crashing costs component may reduce by consideration of a normally distributed lead time demand. Another study done by Pan and Yang based their assumption on the vendor reducing the lead time when requested by the buyer. Hoque and Goyal [16] and Hoque [17] examined the effects of batch sizes and shortened lead time on renewing stock decisions of the supplier-buyer relationship. Modak and Kelle have indicated a dual-channel supply chain where the customer can buy from online or the stores derived via DFA. Priyan & Mala [19] suggested a health care supply chain model considering varying quality characteristics for both raw materials and finished products, varying lead time and service level constraint. They used the game theory payoff matrix approach to attain the targeted service level of the hospital, which is an optimal inventory strategy.

Emissions from carbon trap heat in the atmosphere, making the planet warmer. The increase in greenhouse gases within the atmosphere in the last 150 years has resulted from human activities. Burning of fossil fuels from for generating electricity, heat and transportation is the major source of carbon emissions. The primary source of carbon emissions from industries is from burning fossil fuels to generate energy and the greenhouse gases emitted from chemical reactions that produce goods from raw materials. The emission rise and fall from year to year depending on the fuel prices, changes in the economy, and other factors. Climate change resulting from carbon pollution has led to high costs that are already being felt globally. There is a need for developing policies that will shift the carbon pollution costs facing the polluters. This will reduce carbon emissions across all sectors, such as the industry, energy, and transportation. The best option will be setting a price for carbon that will shift the cost to the polluters, which will reduce greenhouse gas emissions. Carbon pricing can be done in two ways: a cap-and-trade program or emission trading program, and a carbon tax. This paper addresses the competitive and cooperative matters for detective products, the production distribution model with a collaborative investment in reducing carbon emissions technology under the policies for carbon taxation, and limited carbon emissions.

The literature on emissions of carbon in inventory management has increased significantly over the past few years. Benjaafar et al. [20] did one of the leading studies in this field. Hammami et al. [21] designed two multi-echelon supply chain models having lead time constraints found in the regulation for carbon emission tax and cap. Li et al. [22] reported development for two optimized models for supply chain system and incorporation of emissions of carbon in a production and transportation operation problem found in the cap and trade rules and regulation for joint carbon cap and trade and tax. Tang et al. [23] developed the reduction of emission in the transport industry and inventory management found in (R, Q) inventory policy. The effect of synchronization and regulation of carbon on carbon emission, inventory cost, and objective role of the government by game theory approach has been studied by Halat et al. Qingguo et al. [25] addressed the carbon emission reduction effects on supply chain coordination with merchant managed deteriorating product. Huang et al. [26] have recently investigated the effects policies of carbon and green technologies on the integrated supply chain by considering carbon emission during product production, transportation, and storage. Yang et al. [27] developed the mathematical models for quantifying optimal green technology and product pricing and comparing the effects of two allocation regulations on the operational decisions and total emission.

This paper involves combining our research streams, which are controllable lead-time, integrated two-echelon supply chain model, green investment in different carbon emission policies, and human error in inspection in one research frame. Therefore, this study entails the integrated production-inventory, considering the human errors and emissions of carbon. The assumption is that the carbon emission results from production, transportation, and storage. We attempt to answer the following questions from the assumption and the model setting

1. If demand is stochastic in differing carbon emissions policies during replenishment, lead time, what would be the optimum ordering strategy for an industry?
2. To reduce carbon emissions, what would be the exact green investment?
3. What impacts misclassification errors have during decision making?

The rest of the paper is structured as follows: notations and assumptions are indicated in section 2. The mathematical formulations of the problem and procedure for solution are indicated in section 3. Part 4 contains the discussion for numerical and sensitivity analysis. The summary of the study is discussed in section 5.

Assumption.

1. The lead time demand X follows a normal probability distribution function having mean DL and standard deviation. The reorder point, r = anticipated demand during lead time plus safety stocks (s) and s= k x (standard deviation of lead- time demand), i.e., wherein k is the safety factor.
2. The inventory level is checked continuously, and when it reaches the reorder point r, the buyer can place an order of size Q to be shipped in n number of equal size shipments.
3. The percentage of faulty items is found in each lot, and thus each lot is immediately screened at a fixed rate higher than the demand rate D.
4. The lead time L comprises of m mutually independent components whereby the component has a crashing cost per unit time normal duration, and minimum duration. For convenience is rearranged such that. The lead time components are crashed at one time, beginning with the first component since it has the minimum unit crashing cost, then the second component follows.
5. Let be the length of lead time components crashed to their minimum duration, then can be expressed as, and the lead time is crashing cost per cycle is.
6. Carbon emissions occur in the processing, transportation, and storage processes. Carbon emissions from other sources are not considered.
7. To reduce the emissions, investment of green technology can be done, and the function for carbon reduction for the green technology is given by, where is the carbon reduction efficiency factor and is the offsetting carbon reduction factor (Huang et al. [26]).

3. Model development

The vendor delivers the products to the buyer who places an order of units and with n number of shipments. Every lot delivers by the seller has y percent of items that are defective. Therefore, the buyer has to inspect each received lot upon arrival of each shipment at a given constant screening rate to remove faulty items. However, during the buyer verification process, two forms of error (Type I & Type II) can occur. The type I happens when non-defective products are classified as defective products while type II error occurs when imperfect products are classified as non-defective products. Hence the fraction of defective items identified by inspectors is given as where and and are the percentages for Type II and Type I inspection errors, respectively.

The inspection process and the defective rate are naturally random, and therefore, it is assumed that y, and are random variables that are independent of each other. The expected value of reported defective products is given by is Hereafter is simply used as or just simply.Therefore the ordering cycle length of the purchaser is.

3.1.1 Buyers total cost

Whenever the non-defective inventory falls to the reorder point r, an order of size Q is placed by the buyer. Shortages happen when . Therefore the buyers expected demand shortages at the end of the cycle are given by where and are the standard normal p.d.f and cumulative distribution function (c.d.f), respectively. Hence, the back order quantity is expected is.

The loss of sale per ordering cycle is, and the stock-out cost per ordering cycle is expected. Therefore, over the given cycle the average inventory of non-defective items is. Thus, the cost of non-defective and defective items per unit time for the buyer’s total holding is.

Some miscalculation costs are incurred by the buyer because of errors in inspection, and these are the costs for the falsely accepted defective items and non-defective items that are falsely rejected. The cost for miscalculation for type I error that is the cost of false rejected non-defective items is whereas the miscalculation cost for type II error, which is the cost of false accepted defective items, is. Thus the total miscalculation cost per unit time is given by. In addition, the defective items correctly identified are. Hence, scraping cost for the buyer per unit time is. Thus, the total cost expected for the buyer is the sum of misclassification cost, holding cost, screening cost, ordering cost, and backorder cost.

3.2.1 Carbon taxation

For this section, the carbon tax is denoted as Ct from unit carbon emissions. The cost of paying carbon tax is minimized, as both sellers and buyers will invest in green technology for carbon pollution reduction. Thus, in this scenario the joint expected total cost for the integrated inventory supply chain model is the sum of vendor’s production set up cost, vendor’s and buyers’ holding costs, buyer’s order processing cost, product transportation cost, Carbon tax of holding inventory for both parties, Carbon tax of production process, misclassification cost, Carbon tax of production setup, screening cost, scrapping cost, buyer’s back order cost and subtracting the effectiveness for reduction of carbon emissions from the green cost.

3.2.2. Limited Carbon Emission

The business operations have to be corrected by both the vendor and the buyer to fulfill the limited carbon emissions U. Both parties can invest in renewable technologies for the reduction of carbon emissions in case of excessive releases of carbon. For this, the overall cost is the aggregate of the purchaser ‘s purchasing cost, vendor’s setup cost, commodity delivery cost, purchaser’s backorder cost, lead time crashing cost, purchaser, and vendor keeping cost, misclassification cost and the amount spent on investing in green technology. The total amount of carbon emissions is the sum of emissions of carbon from the production process, transportation of the product, and holding inventories for the buyer and the vendor then subtracting effectiveness of reduction of carbon emissions from the green cost which should be equal to carbon emissions upper limit due to of green investment maximization.

4.3. Managerial implications

The summary of the main managerial implications based on the results from the numerical and sensitivity analyses is outlined by the following:

1. The effects of carbon regulation evaluated by this study are based on carbon emission, the objective function of the supply chain system, and inventory cost.
2. Comparison of the cost of the system among various scenarios, which are the limited carbon emission and carbon taxation, can be done from the results. The results indicate that the limited carbon emission is less than the carbon taxation for the inventory cost system.
3. The purchasing power allowances can be reduced by the investment in decreasing carbon outflows even for a lesser limit for carbon emissions.
4. Table 7 indicates that an increase in vendor’s limited carbon emission quantity (U) an increase in is recorded. The high limited carbon emissions allowed by the government may lead to the vendor producing more products. Nonetheless, increasing carbon emissions (U) limits is not always a positive option for reducing carbon emissions. Defining appropriate carbon emission strategies that align economic development with environmental protection is important for the government.
5. Companies should continue to work under low carbon emissions and low carbon tax policy. Industries can also choose to work under restricted carbon emission policy conditions, with a high carbon emission cap and high carbon tax.
6. The managers can only invest in renewable technologies to reduce carbon emissions and meet the requirements for lower pollution levels, resulting in a high total inventory cost. The total inventory cost then decreases as the carbon emissions cap slowly increases. The total inventory cost is retained at a given cost when the carbon emission limit rises above a threshold, which makes the supply chain limited by the carbon emission limit.
7. Table 6 and 7 indicates that all scenarios slightly increase by increasing the system cost and the order quantity Q.
8. L is moderately sensitive, whereas n less sensitive. The managers should understand the impact of misclassification errors on decision making, as shown in the results of this model.
9. Imperfect products can be identified by inspection. The performance of the product under warranty and the rest of its life affect customer satisfaction. The warranty costs can be reduced, and customer satisfaction increased by a precise inspection strategy.

5. Conclusion

There is a growing pressure in many nations to reduce carbon emissions with few objectives to lessen emission or the minimal preparations being effected to lower emissions to prevent climatic change. Moreover, the expectations at the quality level of the set by the customer should be met by the production system because of the human error impact on issues such as productivity, customer service quality, and decision making. Therefore, all industrial sectors need to undertake to evade human error and minimize emissions.

The impact of human errors and renewable methods on the integrated two-echelon supply chain system by considering emissions of carbon during product production transportation and storage has been addressed in this study. The limited total carbon emissions and carbon taxes are the carbon emission strategies considered in this paper. To minimize the system cost in various carbon emission strategies, the model can be applied by industries in developing operating optimum conditions and amounts to spend on green investment. This study also has outlined the need for the government to adopt relevant policies to protect thae environment.

In the future, when finding a solution to this problem, multiproduct will be considered in the model. Also, the setup/or ordering cost, which was constant in this in this study, should be considered as a decision variable and find out the effects of reducing setup or ordering costs. This research can be done studied by considering buyers getting products from multiple vendors. Periodic review policy and service level constraint in the inventory model is another way to extend this study.