
Based on the Environmental Kuznets's Curve theory, this study seeks to investigate the asymmetric relationship between the financial globalization uncertainty and the environmental quality alongside the test of Kuznets's hypothesis. The research covers the data set of nine Sub Saharan African countries from 1980-2019. The Kuznets's hypothesis of the relationship between economic growth and the environment quality has been validated, identifying the pivotal point of the relationship's transition. The results further reveal that the positive shock of FGU is inversely related to CO2 emissions, implying that as the foreign capital flow increases, the accompanying CO2 emissions decreases. Whereas, the negative decomposed component of the financial globalization uncertainty indicates a negative and significance coefficient. While, renewable energy reduces the deterioration of the environmental quality. In the last part of the study, policy implications are recommended accordingly.
Citation: Ibrahim Sambo Farouq, Nuraddeen Umar Sambo, Ali Umar Ahmad, Aminu Hassan Jakada, Isma'il Aliyu Danmaraya. Does financial globalization uncertainty affect CO2 emissions? Empirical evidence from some selected SSA countries[J]. Quantitative Finance and Economics, 2021, 5(2): 247-263. doi: 10.3934/QFE.2021011
[1] | Soumya Kanti Hota, Santanu Kumar Ghosh, Biswajit Sarkar . A solution to the transportation hazard problem in a supply chain with an unreliable manufacturer. AIMS Environmental Science, 2022, 9(3): 354-380. doi: 10.3934/environsci.2022023 |
[2] | Bijoy Kumar Shaw, Isha Sangal, Biswajit Sarkar . Reduction of greenhouse gas emissions in an imperfect production process under breakdown consideration. AIMS Environmental Science, 2022, 9(5): 658-691. doi: 10.3934/environsci.2022038 |
[3] | Subhash Kumar, Ashok Kumar, Rekha Guchhait, Biswajit Sarkar . An environmental decision support system for manufacturer-retailer within a closed-loop supply chain management using remanufacturing. AIMS Environmental Science, 2023, 10(5): 644-676. doi: 10.3934/environsci.2023036 |
[4] | Mowmita Mishra, Santanu Kumar Ghosh, Biswajit Sarkar . Maintaining energy efficiencies and reducing carbon emissions under a sustainable supply chain management. AIMS Environmental Science, 2022, 9(5): 603-635. doi: 10.3934/environsci.2022036 |
[5] | Richi Singh, Dharmendra Yadav, S.R. Singh, Ashok Kumar, Biswajit Sarkar . Reduction of carbon emissions under sustainable supply chain management with uncertain human learning. AIMS Environmental Science, 2023, 10(4): 559-592. doi: 10.3934/environsci.2023032 |
[6] | Benjamin Hersh, Amin Mirkouei, John Sessions, Behnaz Rezaie, Yaqi You . A review and future directions on enhancing sustainability benefits across food-energy-water systems: the potential role of biochar-derived products. AIMS Environmental Science, 2019, 6(5): 379-416. doi: 10.3934/environsci.2019.5.379 |
[7] | Soumya Kanti Hota, Santanu Kumar Ghosh, Biswajit Sarkar . Involvement of smart technologies in an advanced supply chain management to solve unreliability under distribution robust approach. AIMS Environmental Science, 2022, 9(4): 461-492. doi: 10.3934/environsci.2022028 |
[8] | Anna Lymperatou, Ioannis V. Skiadas, Hariklia N. Gavala . Anaerobic co-digestion of swine manure and crude glycerol derived from animal fat—Effect of hydraulic retention time. AIMS Environmental Science, 2018, 5(2): 105-116. doi: 10.3934/environsci.2018.2.105 |
[9] | Raj Kumar Bachar, Shaktipada Bhuniya, Santanu Kumar Ghosh, Biswajit Sarkar . Sustainable green production model considering variable demand, partial outsourcing, and rework. AIMS Environmental Science, 2022, 9(3): 325-353. doi: 10.3934/environsci.2022022 |
[10] | Atinuke Chineme, Getachew Assefa, Irene M. Herremans, Barry Wylant, Marwa Shumo, Aliceanna Shoo, Mturi James, Frida Ngalesoni, Anthony Ndjovu, Steve Mbuligwe, Mike Yhedgo . Advancing circular economy principles through wild black soldier flies. AIMS Environmental Science, 2023, 10(6): 868-893. doi: 10.3934/environsci.2023047 |
Based on the Environmental Kuznets's Curve theory, this study seeks to investigate the asymmetric relationship between the financial globalization uncertainty and the environmental quality alongside the test of Kuznets's hypothesis. The research covers the data set of nine Sub Saharan African countries from 1980-2019. The Kuznets's hypothesis of the relationship between economic growth and the environment quality has been validated, identifying the pivotal point of the relationship's transition. The results further reveal that the positive shock of FGU is inversely related to CO2 emissions, implying that as the foreign capital flow increases, the accompanying CO2 emissions decreases. Whereas, the negative decomposed component of the financial globalization uncertainty indicates a negative and significance coefficient. While, renewable energy reduces the deterioration of the environmental quality. In the last part of the study, policy implications are recommended accordingly.
A production system with a similar type of multi-product is gaining attention nowadays. A traditional economic production quantity (EPQ) produces each type of product separately [1]. This process uses a machine multiple times for a similar process. Production of multi-products in a shared production system can reduce machine usage and can produce the generic structure of multi-product. Agarwal [2] introduced an easy grouping concept under a common order cycle to solve a multi-product supply chain. They introduced a computation method to find the optimal value of the common order cycle. Rosenblatt and Rothblum [3] presented a multi-item production management policy under a single resource capacity constraint. Aliyu and Andizani [4] examined a multi-item production-inventory system with shortages, deterministic demand, deterioration, and capacity and budget constraints. They used a linear quadratic concept to find the value of the optimal control policy. Balkhi and Foul [5] discussed a multi-product production model in finite time periods where shortages and backorders are allowed for every product. For every product, they derived optimal production and restarting times for each period. Rahmani et al. [6] investigated a two-stage capacity-based production system with uncertain demand and production costs. An initial robust schedule was used by them. Chiu et al. [7] proposed a production model to find the production and shipment decisions, simultaneously, with the rework process. They considered a single-stage production process without involving the common intermediate part. Their outcomes helped managers to understand and control the effects of different system parameters on the optimal production-shipment policy. Additional studies related to multi-product production-inventory systems are found in the literature [8].
The evolution of industries over the past century has been characterized by the integration of supply chains (SCs), titled a supply chain integration (SCI) [9]. The SCI activities within an organization, correspond to the suppliers, the customers and the SC levels [10]. In other words, the SCI is an organizational process to integrate the suppliers, the customers, and the internal functional units to optimize the SC's total performance of the SC [11]. Rosenzweig et al., [12] further defined the SCI as the linkages among various SC elements. Many authors discussed the SCI as a common place for SCs [13]. These integration definitions have undergone various modifications owing to research from different perspectives. The SCI aims at coordinating processes in the SCs as an important competitive advantage over competitors [14] and [15]. The experts of the supply chain management (SCM) believe that the integration leads to higher performance for SC levels [16,17,18]. Generally, the global competition and the demand for better customer services have significantly increased the needs for SCI among the companies. The most well-established frameworks for studying SC relate to lot-sizing problems [19].
Gharaei et al. [20] proposed the growth patterns for all dead and live-grown items, along with mortality and survival probabilities. Gharaei et al. [21] developed and optimized a lot-sizing policy in an integrated EPQ model with partial backorders and re-workable products. They considered linear and fixed backordering costs. Gharaei et al. [22] designed and optimized an integrated four-level SC, which contained a supplier, a producer, a wholesaler, and multiple retailers. Gharaei et al. [23] provided a new generation of inventory models, entitled economic growing quantity (EGQ), which focused on growing items of agricultural industries, such as fisheries, poultry, and livestock. Gharaei et al. [24] addressed the optimum number of stockpiles and the economic period length for inventories. Amjadian et al. [25] designed an integrated five-level SC, which contained a supplier, a producer, a wholesaler, multiple retailers, and a collector. Accordingly, a closed-loop supply chain (CLSC) with multi-stage products were designed by them with respect to the green production principles and quality control (QC) policy under backlogged and lost sale. Taleizadeh et al. [26] described optimal decisions and operational strategies in a logistics network considering two capital-constrained manufacturers. They produced products of different qualities, and sold them to a retailer with deterministic demand over a specific period. Gharaei et al. [27] proposed a multi-product, multi-buyer SC model with stochastic constraints. Moreover, the model differentiated between the holding costs for financial and non-financial components, in which the first included the investment in the market, and the second included the cost for physical storage, movement, and insurance of products.
In multi-item production system, if multiple products share a common intermediate part, vendors can be interested in evaluating a two-stage production scheme. The first-stage makes common intermediate parts and the second stage produces end products to reduce overall system costs and shorten the replenishment cycle time. Reduce costs along with shortening the refill cycle period. Gerchak et al. [28] created a model for an arbitrary number of products with a normal demand distribution. They explained the service level measure where the production of common components might be required. Garg and Tang [29] discussed that there are differences among similar types of multiple products. They created two replicas of products with a difference of more than one position. They decided on necessary conditions when one type of delayed differentiation was more beneficial than the other. They found that variations in demand and lead times have significant effects on determining which point of differentiation should be delayed. Graman [30] explained a two-product, single-term, order-up-to cost model to decide inventory levels of end products and postponement capacity. Non-linear programming was chosen to decide the optimal solutions to inventory levels and capacity that minimized the system costs. The study indicated that altering product value, holding cost, cost of postponement, packaging cost, and fill rate reduced expected total cost and increased postponement capacity. Other studies addressed various aspects of the multi-product production management system [31]. It is inevitable to produce defective items due to various uncontrolled factors in the production process. Quality assurance, quality inspections, rework, and elimination of imperfect items, are studied in several studies [32]. In contrast to a continuous review model, a period review model is important within a multi-product-based production system. Several aspects of the periodic review model and multi-shipment issues are discussed in the literature too [33].
Mukherjee et al. [34] estimated maximum product flow within a cross-dock. Mridha et al. [35] discussed a green product manufacturing system but did not discuss a multi-product system. Habib et al. [36] discussed a green product manufacturing system where raw materials were collected from multi-type waste products. Sarkar et al. [37] proposed a model that aimed to reduce waste by reworking defective products and maximizing profit. Saxena et al. [38] proposed an SC model for a single type of eco-designed product and solved the model using the Stackelberg-Nash game policy. Bachar et al. [39] described a production model where partial outsourcing of products was allowed to remove shortages from the system. Discussed studies formulated production and SC model single type of products without shared-production facility. This model expands on the earlier work of Chiu [7] for a period-review model flexible production system (Figure 1).
The proposed model describes a flexible production system integrated with shared-production techniques and remanufacturing. The flexible production system has a single machine. The vendor's annual demand is ∑Mi=1δi for M number of different products. These M customized items are made using a two-stage shared-production system. Stage 1 makes only common components, and Stage 2 produces the final product with the rest of the components within sequence M. This two-stage production system has a common cycle time. The study aims to reduce machine usage by reducing the replenishment period and optimizing production quantity. The common parts are produced at the rate of q1,0 in Stage 1. Then, M different customized products are assembled (Figure 1) at a production rate q1,i. Here, i=0,1,2,...,M and i=0 indicates the shared-production process of Stage 1.
Material and development costs of each product are added in unit production cost of product i for production and remanufacturing as Fi=(Cm1,i+CD1,iq1,i+αq1,i)+(Cm2,i+CD2,iq2,i+αq2,i). The production process at each Stage randomly produce yi portion of defective products at the rate g1,i, where g1,i = q1,iyi. Production rate q1,i of Stage 2 is greater than (δi+g1,i), i.e., (q1,i−g1,i−δi)>0, i.e., (1−yi−δiq1,i)>0. All defective products are remanufactured in each stage. The remanufacturing process begins at a rate q2,i as soon as the production process ends in both stages (Figure 2).
Common components of all products are manufactured in Stage 1 in time T1,0 and remanufactured imperfect products at time T2,0. After completion of production and remanufacturing in Stage 1, M products are ready for the Stage 2. Total inventory from shared-production facility is represented in Figure 3. Production in Stage 2 happens in succession order, from i=1 to M. In Stage 2, customized production of all products takes (T1,i) time for product i and remanufacturing of finished products requires T2,i times. Then, products are sent for delivery in N number of shipments at time T3,i (Figure 4). The supply level of finished products from the flexible production system is represented in Figure 4.
Index | |
i | Number of products i=1,2,...,M;i=0 represents shared-production of all products |
Decision | variables |
t | Production cycle length (time unit) |
N | Number of shipments of finished products in each cycle (integer) |
q1,i | Production rate of product i (units/time unit) |
q2,i | Remanufacturing rate for product i (units/time unit) |
Parameter | |
δi | Market demand of product i (units/time unit) |
Ai | Production lot size of product finished product i (units/cycle) |
Bi | Production setup cost of product i ($/setup) |
Fi | Unit production cost of product i ($/unit) |
Cm1,i | Unit material cost of product i for production ($/unit) |
Cm2,i | Unit material cost of product i for remanufacturing ($/unit) |
CD1,i | Unit development cost of product i for production ($/unit) |
CD2,i | Unit development cost of product i for remanufacturing ($/unit) |
H1,i | Unit holding cost of new produced product i ($/unit/unit time) |
H2,i | Unit holding cost per remanufactured item i ($/unit/unit time) |
H3,i | Unit holding cost for storing finished product i ($/unit/unit time) |
H4,i | Unit holding cost for safety stocks for product i ($/unit/unit time) |
FR,i | Unit remanufacturing cost for product i ($/unit) |
T1,i | Production uptime for product i (time unit) |
T2,i | Remanufacturing time for product i (time unit) |
T3,i | Delivery time of product i (time unit) |
hi | Inventory level of common components for product i (units) |
h1,i | Perfect quality item i at the end of the production up time (units) |
h2,i | Perfect quality items i at the end of remanufacturing process (units) |
g1,i | Random defective rate of product i in Stage 1 |
g2,i | Random defective rate of product i in Stage 2 |
yi | Defective percentage of product i in production |
B1,i | Fixed delivery cost per shipment for product i ($/shipment) |
FT,i | Unit delivery cost per unit product i ($/unit) |
TN,i | Fixed interval of time between each of shipment of finished item i during T3,i |
(time unit) | |
I(T)i | On-hand inventory level of perfect quality items i at any time T (units) |
Ig(T)i | On-hand inventory level of imperfect items i at any time T (units) |
Ic(T)i | On-hand inventory level of finished product i at any time T (units) |
li | Leftover finished product i in each TN,i (units) |
Gi | Number of delivered finished product i in each shipment (units) |
β | Completion rate of common component of products as compared to the finished |
product | |
α | scaling parameter of unit production cost |
TC | Total cost of the production system ($) |
E[t] | Expected production cycle length (time unit) |
E[TCU] | Expected total cost ($/cycle) |
This section describes the mathematical modeling and total cost analysis of these study.
A two-stage flexible production model produces M distinct multi-product with annual market demand δi. The production cycle is (Figure 1)
t=T1,i+T2,i+T3,i=Aiδi. | (5.1) |
Stage 1 produces common components of all products in a lot size A0. It depends on the production batch Ai of product i. Then, the following (Figure 1) equations are found:
Ai=δit;A0=M∑i=1Ai=δ0t, | (5.2) |
T1,0=A0q1,0=h1,0q1,0−g1,0, | (5.3) |
h1,0=T1,0(q1,0−g1,0);h2,0=h1,0+q2,0T2,0=M∑i=1Ai, | (5.4) |
T2,0=y0A0q2,0=g1,0T1,0q2,0=h2,0−h1,0q2,0, | (5.5) |
h1=h2,0−A1, | (5.6) |
hi=h(i−1)−Aiwhere,i=2,3,...,M | (5.7) |
hM=h(M−1)−AM=0. | (5.8) |
In Stage 2 (i=1,2,...,M), the following equations are found from Figures 2 to 4.
T1,i=Aiq1,i=h1,iq1,i−g1,i, | (5.9) |
h1,i=(q1,i−g1,i)t1,i, | (5.10) |
h2,i=h1,i+q2,iT2,i, | (5.11) |
T2,i=yiAiq2,i=g1,iT1,iq2,i=h2,i−h1,iq2,i, | (5.12) |
T3,i=NtN,i, | (5.13) |
Gi=h2,iN, | (5.14) |
li=Gi−δiTN,i, | (5.15) |
Nli=δi(T1,i+T2,i). | (5.16) |
Different costs for the two-stage flexible production system are developed as follows.
Total setup cost is the sum of the setup amount for Stage 1 and Stage 2 for item i in a production cycle. Therefore, total setup cost for the production process can be formulated as
SEC=B0+M∑i=1Bi. | (5.17) |
Unit production cost depends on metrical cost, development cost, and production rate, and remanufacturing rate of product i. Thus, the unit production cost of the product i for both Stages are given by
PRC=[Cm1,0+CD1,0q1,0+αq1,0+Cm2,0+CD2,0q2,0+αq2,0]A0+M∑i=1[Cm1,i+CD1,iq1,i+αq1,i+Cm2,i+CD2,iq2,i+αq2,i]Ai. | (5.18) |
Imperfect products are produced through the production process of both stages for the product i. Those imperfect products are remanufactured right after the production process are finished. The corresponding remanufacturing cost is
REC=FR,0y0A0+M∑i=1FR,iyiAi. | (5.19) |
To overcome the stock out situation, some safety stock is required. Imperfect products are not send to the market as new products. The manufacturer uses the remanufactured products as safety stock to avoid shortages.
SSC=H4,0(y0A0)t+M∑i=1H4,i(yiAi)t. | (5.20) |
IHC is used for holding common components, both manufactured and remanufactured product i, throughout T1,i and T2,i (Figures 1 and 2). Thus, the inventory holding cost is
IHC=H1,0[h1,0T1,02+(h2,0+h1,0)T2,02+M∑i=1hi(T1,i+T2,i)]+H1,0[(g1,0T1,0)T1,02]. | (5.21) |
In Stage 2, IHCF is used for holding the production of customized product i (Figure 3). The associative cost is written as
IHCF=M∑i=1H1,i[AiT1,i2]. | (5.22) |
IHCI is used for holding imperfect products after remanufacturing until the time T2,i. The corresponding holding cost is
IHCI=H2,0[g1,0T1,02(T2,0)]+M∑i=1[H2,i(q2,iT2,i2)(T2,i)]. | (5.23) |
Total perfect customized products after production and remanufacturing are stored until the time T2,i for product i. Besides, number of reworked items are stored until time T3,i. Total holding cost for perfect customized products is
HRR=M∑i=1H1,i[h2,i+h1,i2(T2,i)+(N−12N)h2,iT3,i]. | (5.24) |
Defective customized product i is stored in every production cycle until the production up time T1,i. HCDIis given as follows:
HCDI=M∑i=1H1,i[g1,iT1,i2(T1,i)]. | (5.25) |
Thus, the average holding cost of customized new items at the end of the production up time T1,i is HCMQ, which can be expressed as
HCMQ=M∑i=1H1,i[h1,iT1,i2]. | (5.26) |
After finishing the production in two-stages, all finished products are stored for distribution. Then, products are sent in shipments. After sending product in shipment, other products are still stored. Thus, SHC is used to hold finished product i after production (Figure 4). Associative stock holding cost is
SHC=M∑i=1H3,i[N(Gi−li)TN,i2+N(N+1)liTN,i2+Nli(T1,i+T2,i)2]. | (5.27) |
After Stage 2, finished products are sent to the market in N number of shipments. FVD is used for fixed transportation cost and IHC is used for variable transportation cost in T3,i. Corresponding transportation cost is
FVD=M∑i=1[NB1,i+FT,iAi]. | (5.28) |
The total cost (TC) of the flexible production system is TC(t,N,q1,i,q2,i), which can be written as
TC(t,N,q1,i,q2,i)=SEC+PRC+REC+SSC+IHC+IHCF+IHCI+FVD+SHC+HRR.+HCMQ+HCDI | (5.29) |
=(B0+[Cm1,0+CD1,0q1,0+Cm2,0+CD2,0q2,0+αq1,0+αq2,0]A0+FR,0y0A0+H2,0(g1,0T1,02)(T2,0)+H4,0(y0A0)t+H1,0[h1,0T1,02+h2,0+h1,02(T2,0)+g1,0T1,02(T1,0)+M∑i=1hi(T1,i+T2,i)])+M∑i=1(Bi+[Cm1,i+CD1,iq1,i+Cm2,i+CD2,iq2,i+αq1,i+αq2,i]Ai+FR,iyiAi+NB1,i+FT,iAi+H2,i(q2,iT2,i2)(T2,i)+H1,i[Ai2(T1,i)+h1,iT1,i2+h2,i+h1,i2(T2,i)+(N−12N)h2,iT3,i+g1,iT1,i2(T1,i)]+H3,i[N(Gi−Ii)TN,i2+N(N+1)2IiTN,i+NIi(T1,i+T2,i)2]+H4,i(yiAi)t). | (5.30) |
This is a period review model, i.e., inventory is checked in a certain time period. Substituting Eqs (5.1) to (5.16) in Eq (5.30), expected total cost (E[TCU]) for M number of products per cycle can be obtained as below.
E[TCU(t,N,q1,i,q2,i)]=E[TC(t,N,q1,i,q2,i)]E[t]=(B0t+δ0[Cm1,0+CD1,0q1,0+Cm2,0+CD2,0q2,0+αq1,0+αq2,0]+FR,0δ0E[y0]+w0t)+M∑i=1([Bit+δi[Cm1,i+CD1,iq1,i+Cm2,i+CD2,iq2,i+αq1,i+αq2,i]+FR,iδiE[yi]+NB1,it+FT,iδi]+H1,itδ2i2(γ2,i−γ1,iN)+H2,itδ2iE[yi]22q2,i+H3,itδ2i2[1q1,i+E[yi]q2,i+γ1,iN]+tH4,iδiE[yi]),wherew0=H1,0δ202[1q1,0+2E[y0]q2,0−E[y0]2q2,0]+H2,0δ20E[y0]22q2,0+H1,0M∑i=1((δiq1,i+δiE[yi]q2,i)[M∑i=1(δi)−i∑j=1(δj)])+H4,0δ0E[y0]γ1,i=[1δi−1q1,i−E[yi]q2,i],andγ2,i=[1δi−E[yi]2q2,i+1q1,i+E[yi]q2,i]. | (5.31) |
Eq (5.31) states the expected total cost of the proposed production system. There are four decision variables t,N,q1,i, and q2,i. The paper gives a unique solution to the problem and finds the best strategy for the flexible production system.
A classical optimization technique is used to obtain the total cost E[TCU]. Solutions of decision variables are found by using first order derivatives. The convex nature of the objective function in Eq (5.31) are proved by the Hessian matrix. First order partial derivatives of Eq (5.31) with respect to t,N,q1,i and q2,i are given below.
∂E[TCU(t,N,q1,i,q2,i)]∂t=−B0t2+w0+M∑i=1(−Bit2−NB1,it2+H1,iδ2i2(γ2,i−γ1,iN)+H2,iδ2iE[yi]22q2,i+H3,iδ2i2(1q1,i+E[yi]q2,i+γ1,iN)+H4,iδiE[yi]) | (6.1) |
∂2E[TCU(t,N,q1,i,q2,i)]∂t2=2B0t3+M∑i=1(2Bit3+2NB1,it3) | (6.2) |
∂2E[TCU(t,N,q1,i,q2,i)]∂t∂N=M∑i=1(−B1,it2+H1,iγ1,iδ2i2N2−H3,iδ2iγ1,i2N2) | (6.3) |
∂2E[TCU(t,N,q1,i,q2,i)]∂t∂q1,i=M∑i=1(−H3,iδ2i2q21,i) | (6.4) |
∂2E[TCU(t,N,q1,i,q2,i)]∂t∂q2,i=M∑i=1(−H3,iδ2iE[yi]2q2,i−H2,iδ2iE[yi]22q2,i) | (6.5) |
∂E[TCU(t,N,q1,i,q2,i)]∂N=M∑i=1(B1,it+H1,itδ2iγ1,i2N2−H3,itδ2iγ1,i2N2) | (6.6) |
∂2E[TCU(t,N,q1,i,q2,i)]∂N2=M∑i=1(−H1,itδ2iγ1,iN3+H3,itδ2iγ1,iN3) | (6.7) |
∂2E[TCU(t,N,q1,i,q2,i)]∂N∂q1,i=0 | (6.8) |
∂2E[TCU(t,N,q1,i,q2,i)]∂N∂q2,i=0 | (6.9) |
∂E[TCU(t,N,q1,i,q2,i)]∂q1,i=−H1,0M∑i=1δiq21,i(M∑i=1δi−M∑j=1δj)t+M∑i=1(−δiCD1,iq21,i+α−H3,itδ2i2q21,i−H1,itδ2i2q21,i−H1,itδ2i2Nq21,i+H3,itδ2i2Nq21,i) | (6.10) |
∂2E[TCU(t,N,q1,i,q2,i)]∂q21,i=2H1,0M∑i=1δiq31,i(M∑i=1δi−M∑j=1δj)t+M∑i=1(2δiCD1,iq31,i+H3,itδ2iq31,i+H1,itδ2iq31,i+H1,itδ2iNq31,i−H3,itδ2iNq31,i) | (6.11) |
∂2E[TCU(t,N,q1,i,q2,i)]∂q1,i∂q2,i=0 | (6.12) |
∂E[TCU(t,N,q1,i,q2,i)]∂q2,i=−H1,0M∑i=1δiE[yi]q22,i(M∑i=1δi−M∑j=1δj)t+M∑i=1(−δiCD2,iq22,i+α−H2,itδ2iE[y2i]2q22,i−H3,itδ2iE[yi]2q22,i+H3,itδ2iE[yi]Nq22,i+H1,itδ2iE[y2i]2q22,i−H1,itδ2iE[yi]2q22,i−H1,itδ2iE[yi]2Nq22,i) | (6.13) |
∂2E[TCU(t,N,q1,i,q2,i)]∂q22,i=2H1,0M∑i=1δiE[yi]q32,i(M∑i=1δi−M∑j=1δj)t+M∑i=1(2δiCD2,iq32,i+H2,itδ2iE[y2i]q32,i+H3,itδ2iE[yi]q32,i−H3,itδ2iE[yi]2Nq32,i−H1,itδ2iE[y2i]q32,i+H1,itδ2iE[yi]q32,i+H1,itδ2iE[yi]Nq32,i) | (6.14) |
First order derivatives in Eqs (6.1), (6.6), (6.10), and (6.13) give unique solutions after equating the equations to zero (necessary condition of classical optimization). Thus, unique solutions t∗,N∗,q∗1,i, and q∗2,i are
t∗=√B0+∑Mi=1(Bi+NB1,i)w0+∑Mi=1(H1,iδ2i2(γ2,i−γ1,iN)+H2,iδ2iE[yi]22q2,i+H3,iδ2i2(1q1,i+E[yi]q2,i+γ1,iN)+H4,iδiE[yi]) | (6.15) |
N∗=√(B0+∑Mi=1Bi)∑Mi=1δ2i2γ1,i(H3,i−H1,i)(∑Mi=1B1,i)(w0+∑Mi=1A1) | (6.16) |
q∗1,i=√H1,0∑Mi=12Nδi(∑Mi=1δi−∑Mi=1δj)t+∑Mi=1B12αN | (6.17) |
q∗2,i=√H1,0∑Mi=12NδiE[yi](∑Mi=1δi−∑Mi=1δj)t+∑Mi=1C12αN | (6.18) |
[See Appendix 1 for all the values]
The following proposition proves that the ETC cost of the flexible production system is a global minimum.
Proposition: Expected total cost of the production system in Eq (5.31) has a global minimum value at t∗,N∗,q∗1,i, and q∗2,i if the values principal minors of order one (H11), two (H22), three (H33), and four (H44) of the fourth order Hessian matrix are greater than zero.
Proof: The Hessian matrix of order four can be written as
H=|∂2E∂t∗2∂2E∂t∗∂N∗∂2E∂t∗∂q∗1,i∂2E∂t∂q2,i∂2E∂N∗∂t∗∂2E∂N∗2∂2E∂N∗∂q∗1,i∂2E∂N∗∂q∗2,i∂2E∂q∗1,i∂t∗∂2E∂q∗1,i∂N∗∂2E∂q∗1,i2∂2E∂q∗1,i∂q∗2,i∂2E∂q∗2,i∂t∗∂2E∂q∗2,i∂N∗∂2E∂q∗2,i∂q∗1,i∂2E∂q∗2,i2| |
The first order principal minor is
H11=∂2E∂t∗2=2B0t3+∑Mi=1(2Bit3+2NB1,it3)>0.
The first order principal minor is
H11=2B0t3+∑Mi=1(2Bit3+2NB1,it3)>0.
The second order principal minor is
H22=∂2E∂t∗2∂2E∂N∗2−(∂2E∂t∗∂N∗)2=(2B0t3+∑Mi=1(2Bit3+2NB1,it3))(∑Mi=1(−H1,itδ2iγ1,iN3+H3,itδ2iγ1,iN3))−(∑Mi=1(−B1,it2+H1,iγ1,iδ2i2N2−H3,iδ2iγ1,i2N2))2>0.
The third order principal minor is
H33=∂2E∂N∗2det(H22)−(∂2E∂t∗∂N∗)2(∂2E∂q∗1,i2)>0.
The fourth principal minor is
H44=∂2E∂q∗2,i2det(H33)−(∂2E∂t∗∂q∗2,i)2(∂2E∂N∗2)(∂2E∂q∗1,i2)>0.
Therefore, one can conclude that the unique solutions of the objective function provides a global minimum cost.
The numerical examples are provided to investigate the outcomes of the mathematical model. Five distinct products are produced with a common component manufacturing rate β=q2,iq1,i. Associative input data are taken from Chiu et al. [7]. Annual demand of five products are δ1 = 3000 units/year, δ2 = 3200 units/year, δ3 = 3400 units/year, δ4 = 3,600 units/year, and δ5 = 3800 units/year. A linear relationship 1β is assumed for these relevant manufacturing rates. The relationship between the relevant amount of the common components and the participation rate β can be linear or nonlinear. All cases are investigated in the following subsections.
The correlation between the common components production and the customized production of products is linear with the participation rate β = 0.5. Setup cost of Stage 1 (B0) = $8500/setup, remanufacturing cost of Stage 1 (FR,0) = $25/unit, holding cost (H1,0) = $5/unit/unit time, holding cost for safety stock cost for Stage 1 (H4,0) = $5/unit/unit time. Unit holding cost H1,1 = $10/unit/unit time, H1,2 = $15/unit/unit time, H1,3 = $20/unit/unit time, H1,4 = $25/unit/unit time, and H1,5 = $30/unit/unit time. Holding cost for remanufactured products for Stage 1 (H2,0) = $15/unit/unit time. Setup cost for Stage 2 are B1 = $8500/setup, B2 = $9000/setup, B3 = $9500/setup, B4 = $10,000/setup, B5 = $10,500/setup. Random defective rate in Stage 1 follows uniform distribution y0∼U[0, 0.04].
q1,i=11/q1,i−1/q1,0. Random defective rate in Stage 2 follows uniform distribution y1∼U[0, 0.01], y2∼U[0, 0.06], y3∼U[0, 0.11], y4∼U[0, 0.16], and y5∼U[0, 0.21]. Unit remanufacturing costs of Stage 2 are FR,1 = $25/unit, FR,2 = $30/unit, FR,3 = $35/unit, FR,4 = $40/unit, and FR,5 = $45/unit. q2,i=11/q2,i−1/q2,0. Unit holding cost of remanufactured product for Stage 2 are H2,1 = $30/unit/unit time, H2,2 = $35/unit/unit time, H2,3 = $40/unit/unit time, H2,4 = $45/unit/unit time, and H2,5 = $50/unit/unit time. Fixed delivery cost per shipment are B1,1 = $1800/shipment, B1,2 = $1900/shipment, B1,3 = $2000/shipment, B1,4 = $2100/shipment, and B1,5 = $2200/shipment. Unit variable delivery cost are FT,1 = $0.1/unit, FT,2 = $0.2/unit, FT,3 = $0.3/unit, FT,4 = $0.4/unit, and FT,5 = $0.5/unit. Holding cost of finished product after Stage 2 are H3,1 = $70/unit/unit time, H3,1 = $75/unit/unit time, H3,3 = $80/unit/unit time, H3,4 = $85/unit/unit time, and H3,5 = $90/unit/unit time. Holding cost of safety stock for Stage 2 are H4,1 = $10/unit/unit time, H4,2 = $15/unit/unit time, H4,3 = $20/unit/unit time, H4,4 = $25/unit/unit time, and H4,5 = $30/unit/unit time.
Annual demand for common components of products is δ0 = 17,000 units, which is obtained by applying Eqs (5.2) and (5.3). Then, by using Eqs (6.15) to (6.18), the optimum shipment number is obtained as N∗ = 4, optimum production cycle time t∗ = 0.6785 years, optimum production rate of Stage 1 q1,0=104,368unit/year, q1,1112,258 unit/year, q1,2 = 116,066 unit/year, q1,3 = 120,000 unit/year, q1,4 = 124,068 unit/year, and q1,5 = 128,276 units unit/year, optimum remanufacturing rate of of Stage 2 q2,0=85,752unit/year, q2,1 = 89,806 units/year, q2,2 = 92,852 units/year, q2,3 = 96,000 units/year, q2,4 = 99,254 units/year, and q2,5 = 102,621 units/year and the expected total cost is E[TCU] = $107,471,000/cycle. When the participation rate β rises, the total cost E[TCU] decreases 3.76% at β = 0.5 (total cost decreases from $111,511,910/cycle (β=1) to $107,471,000/cycle). These analytic results show that the expected total cost is a significantly useful investigation for manufacturers who produce multiple items through a shared-production facility. As the participation rate β=q2,iq1,i rises, the optimum cycle period t∗ reduces significantly. The optimum cycle period t∗ is decreased by 25.5% at β = 0.5 (declines from 0.8515 years (β=1) to 0.6785 years). Results indicate that the proposed two-stage multi-product flexible production system provides a reduced cycle length than with global minimum cost.
This investigation examines the nonlinear relationship between shared-production and customized production with a participation rate β=q2iq1,i. Hence it has a more production rate than a linear participation rate. Using the new relation, parametric values are FR,0 = $40/unit, B0 = $13,493/setup, H1,0 = H4,0 = $8/unit time, H2,0 = $24/unit/unit time. Other parameters remain identical as expressed in Subsection 7.1. y0∼U[0, 0.04]. Therefore, Bi = $3507/setup, $4007/setup, $4507/setup, $5007/setup, and $5507/setup. FR,i = $10/unit, $15/unit, $20/unit, $25/unit, and $30/unit, and yi follows a uniform distribution with the interval [0, 0.01], [0, 0.06], [0, 0.11], [0, 0.16], and [0, 0.21], for five products, respectively.
If β1/3 is the nonlinear relation, then F0 = β1/3F1 = $63/unit. Using Eqs (6.15) to (6.18) and (5.31), one can get the optimum numeral values of the shipment N∗ = 4, optimum production cycle time t∗ = 0.6005 (years), optimum production rate q1,0 = 101,821 unit/year, q1,1 = 105,272 unit/year, q1,2 = 109,518 unit/year, q1,3 = 113,233 unit/year, q1,4 = 117,072 unit/year, q1,5 = 125,146 unit/year, optimum remanufacturing rate q2,0 = 83,659 unit/year, q2,1 = 87,614 unit/year, q2,2 = 90,586 unit/year, q2,3 = 93,657 unit/year, q2,4 = 96,832 unit/year, q2,5 = 100,117 unit/year, and the expected total cost is E[TCU] = $104,837,961/cycle. For the non-linear relationship of β, when β increases, total cost E[TCU] decreases and it decreases by 2.45% (i.e., the total cost reduces from $107,471,000/cycle for β = 0.5, to $104,837,961/cycle) correlated to the initial linear occurrence. For the nonlinear case, optimum cycle time t∗ decreases by 13.20% than the linear relationship β = 0.5 (it reduces from 0.6785 years to 0.5889 years). Hence, it shows that the proposed two-stage multi-product flexible production system is significantly useful for manufacturers for a short replenishment cycle. The manufacturer can provide multiple products with less cycle time. The analytic outcomes reveal that the shared-production has a higher cost than the customized production system. Besides, a nonlinear participation β1/3 provides less system cost than a linear relation. But, the optimum cycle period t∗ reduces significantly for a non-linear participation rate.
The managers aim to achieve a less cost-sensitive production system such that the system cost becomes low. In a high price-sensitive system, market demand decreases with a few price increases. The risk of borrowing from the online platform increases for high-price-sensitive products. Besides, a long cycle time can increase the risk of lost sales for a cost-sensitive system. Thus, a shared-production facility along with a flexible production system solve the problem by adjusting production and remanufacturing rate within a reduced cycle time. Thus, industry managers can reduce the risk of lost sales due to a flexible production system.
A shared-production facility-based flexible production was discussed where multi-products were produced. The production system was a two-stage facility where each stage had a production and remanufacturing process. Multi-products were produced in the production process and imperfect products were remanufactured after finishing the production process. Both the production and remanufacturing processes had a single flexible machine. Thus, the shared production helped to produce common components of all products in Stage 1 and Stage 2 finished the rest. Results showed that the participation ratio of shared-production in the production process had a major impact on the system's cost and production cycle time. If the production cost of Stage 1 and Stage 2 became independent of one another, then the system cost was maximum. If the production cost of Stage 1 is linearly dependent on Stage 2, then the production cost of Stage 1 became less than Stage 2, and both the cycle time along with system cost were reduced. But, the maximum reduction in cost and cycle time happened when the relation β became non-linear. The flexible production system supported the whole process as the reduction of cycle time implies a fast production process in less amount of time. Adjustment of production and remanufacturing rate of the flexible production system helped the manager to decide on the new reduced cycle time. The present model developed a flexible production model by considering simultaneous scheduling and lot-sizing with a single machine. This study can be extended using parallel flexible machines [40]. The study can be extended for a supply chain scenario with multiple buyers. Moreover, consideration of uncertainty within the market demand will make the model more practical. Instead of linear relation [41], future research can be conducted using nonlinear control theory techniques [42,43]. Environmental issue of carbon emissions can be considered within the proposed system [44].
This research is not funded through any source.
There are no conflicts of interest.
A1=(H1,iδ2i2(γ2,i−γ1,iN)+H2,iδ2iE[yi]22q2,i+H3,iδ2i2(1q1,i+E[yi]q2,i+γ1,iN)+H4,iδiE[yi]
B1=δiCD1,i2N+H3,itδ2iN+H1,itδ2iN+H1,itδ2i−H3,itδ2iN
C1=δiCD2,i2N+H3,itδ2iNE[yi]+H1,itδ2iNE[yi]+H1,itδ2iE[yi]−H3,itδ2i2E[yi]+NH2,itδ2iE[y2i]−NH1,itδ2iE[y2i]
[1] |
Acheampong AO (2018) Economic growth, CO2 emissions and energy consumption: What causes what and where? Energy Econ 74: 677-692. doi: 10.1016/j.eneco.2018.07.022
![]() |
[2] |
Adedoyin FF, Gumede MI, Bekun FV, et al. (2020) Modelling coal rent, economic growth and CO2 emissions: does regulatory quality matter in BRICS economies? Sci Total Environ 710: 136284. doi: 10.1016/j.scitotenv.2019.136284
![]() |
[3] |
Adedoyin F, Ozturk I, Abubakar I, et al. (2020) Structural breaks in CO2 emissions: Are they caused by climate change protests or other factors? J Environ Manage 266: 110628. doi: 10.1016/j.jenvman.2020.110628
![]() |
[4] |
Ahmad M, Khan Z, Ur Rahman Z, et al. (2018) Does financial development asymmetrically affect CO2 emissions in China? An application of the nonlinear autoregressive distributed lag (NARDL) model. Carbon Manage 9: 631-644. doi: 10.1080/17583004.2018.1529998
![]() |
[5] |
Ahmad N, Du L, Lu J, et al. (2017) Modelling the CO2 emissions and economic growth in Croatia: is there any environmental Kuznets curve? Energy 123: 164-172. doi: 10.1016/j.energy.2016.12.106
![]() |
[6] |
Ali R, Bukhsh K, Yasin MA (2019) Impact of urbanization on CO2 emissions in emerging economy: Evidence from Pakistan. Sust Cities Society 48: 101553. doi: 10.1016/j.scs.2019.101553
![]() |
[7] |
Al-Mulali U, Tang CF, Ozturk I (2015) Estimating the environment Kuznets curve hypothesis: evidence from Latin America and the Caribbean countries. Renew Sust Energy Rev 50: 918-924. doi: 10.1016/j.rser.2015.05.017
![]() |
[8] |
Al-Mulali U, Saboori B, Ozturk I (2015) Investigating the environmental Kuznets curve hypothesis in Vietnam. Energy Policy 76: 123-131. doi: 10.1016/j.enpol.2014.11.019
![]() |
[9] |
Alola AA, Bekun FV, Sarkodie SA (2019) Dynamic impact of trade policy, economic growth, fertility rate, renewable and non-renewable energy consumption on ecological footprint in Europe. Sci Total Environ 685: 702-709. doi: 10.1016/j.scitotenv.2019.05.139
![]() |
[10] |
Atasoy BS (2017) Testing the environmental Kuznets curve hypothesis across the US: Evidence from panel mean group estimators. Renew Sust Energy Rev 77: 731-747. doi: 10.1016/j.rser.2017.04.050
![]() |
[11] | Ayanwale AB (2007) FDI and economic Growth: Evidence from Nigeria. African Economic Research Consortium Paper 165, Nairobi. |
[12] |
Aye GC, Edoja PE (2017) Effect of economic growth on CO2 emission in developing countries: Evidence from a dynamic panel threshold model. Cogent Econ Financ 5: 1379239. doi: 10.1080/23322039.2017.1379239
![]() |
[13] |
Baloch MA, Ozturk I, Bekun FV, et al. (2021) Modeling the dynamic linkage between financial development, energy innovation, and environmental quality: Does globalization matter? Bus Strat Environ 30: 176-184. doi: 10.1002/bse.2615
![]() |
[14] |
Begum RA, Sohag K, Abdullah SMS, et al. (2015) CO2 emissions, energy consumption, economic and population growth in Malaysia. Renew Sust Energy Rev 41: 594-601. doi: 10.1016/j.rser.2014.07.205
![]() |
[15] |
Bilgili F, Koçak E, Bulut Ü (2016) The dynamic impact of renewable energy consumption on CO2 emissions: a revisited environmental Kuznets curve approach. Renew Sust Energy Rev 54: 838-845. doi: 10.1016/j.rser.2015.10.080
![]() |
[16] |
Bölük G, Mert M (2015) The renewable energy, growth and environmental Kuznets curve in Turkey: an ARDL approach. Renew Sust Energy Rev 52: 587-595. doi: 10.1016/j.rser.2015.07.138
![]() |
[17] |
Bortz PG, Kaltenbrunner A (2018) The international dimension of financialization in developing and emerging economies. Dev Change 49: 375-393. doi: 10.1111/dech.12371
![]() |
[18] |
Boufateh T (2019) The environmental Kuznets curve by considering asymmetric oil price shocks: evidence from the top two. Environ Sci Pollut Res 26: 706-720. doi: 10.1007/s11356-018-3641-3
![]() |
[19] | BP (2019) Statistical Review of World Energy 2019. Available from: https://www.bp.com/en/global/corporate/energy-economics/statistical-review-of-world-energy.html. |
[20] | Carkovic M, Levine R (2005) Does foreign direct investment accelerate economic growth? In: T. H. Moran, E. M. Graham, and M. Blomström, Does foreign direct investment promote development? ed., Washington, DC: Institute for International Economics, 195-220. |
[21] |
Cetin M, Ecevit E, Yucel AG (2018) The impact of economic growth, energy consumption, trade openness, and financial development on carbon emissions: empirical evidence from Turkey. Environ Sci Pollut Res 25: 36589-36603. doi: 10.1007/s11356-018-3526-5
![]() |
[22] |
Charfeddine L, Mrabet Z (2017) The impact of economic development and social-political factors on ecological footprint: A panel data analysis for 15 MENA countries. Renew Sust Energy Rev 76: 138-154. doi: 10.1016/j.rser.2017.03.031
![]() |
[23] |
Chen X, Huang B, Lin CT (2019) Environmental awareness and environmental Kuznets curve. Econ Model 77: 2-11. doi: 10.1016/j.econmod.2019.02.003
![]() |
[24] | Crestanello JP (2020) The impact of renewable electricity production on carbon emissions. Available from: https://scholar.harvard.edu/. |
[25] | Dabachi UM, Mahmood S, Ahmad AU, et al. (2020) Energy consumption, energy price, energy intensity environmental degradation, and economic growth nexus in African OPEC countries: evidence from simultaneous equations models. J Environ Treat Tech 8: 403-409. |
[26] | Danish S, Zafar-ul-Hye M (2019) Co-application of ACC-deaminase producing PGPR and timber-waste biochar improves pigments formation, growth and yield of wheat under drought stress. Sci Rep 9: 1-13. |
[27] |
Danlami MR, Loganathan N, Streimikiene D, et al. (2018) The effects of financial development-trade openness nexus on nigeria's dynamic economic growth. Econ Sociol 11: 128. doi: 10.14254/2071-789X.2018/11-4/8
![]() |
[28] |
Dar JA, Asif M (2017) Is financial development good for carbon mitigation in India? A regime shift-based cointegration analysis. Carbon Manage 8: 435-443. doi: 10.1080/17583004.2017.1396841
![]() |
[29] | Dauvergne C (2008) Making people illegal: What globalization means for migration and law, Cambridge University Press. |
[30] |
Destek MA, Sinha A (2020) Renewable, non-renewable energy consumption, economic growth, trade openness and ecological footprint: Evidence from organisation for economic co-operation and development countries. J Clean Prod 242: 118537. doi: 10.1016/j.jclepro.2019.118537
![]() |
[31] |
Dogan E, Seker F (2016) The influence of real output, renewable and non-renewable energy, trade and financial development on carbon emissions in the top renewable energy countries. Renew Sust Energy Rev 60: 1074-1085. doi: 10.1016/j.rser.2016.02.006
![]() |
[32] |
Dogan E, Ozturk I (2017) The influence of renewable and non-renewable energy consumption and real income on CO2 emissions in the USA: evidence from structural break tests. Environ Sci Pollut Res 24: 10846-10854. doi: 10.1007/s11356-017-8786-y
![]() |
[33] |
Erdogan S, Adedoyin FF, Bekun FV, et al. (2020) Testing the transport-induced environmental Kuznets curve hypothesis: The role of air and railway transport. J Air Trans Manage 89: 101935. doi: 10.1016/j.jairtraman.2020.101935
![]() |
[34] |
Farhani S, Ozturk I (2015) Causal relationship between CO2 emissions, real GDP, energy consumption, financial development, trade openness, and urbanization in Tunisia. Environ Sci Pollut Res 22: 15663-15676. doi: 10.1007/s11356-015-4767-1
![]() |
[35] | Farouq IS, Sulong Z (2020) The impact of economic growth, oil price, and financial globalization uncertainty on financial development: evidence from selected leading african countries. Int J Bus 7: 274-289. |
[36] | Farouq IS, Sulong Z, Sambo NU (2020) The effects of environmental quality, trade openness, and economic growth on financial development in algeria: A diks and panchenko approach. J Crit Rev 7: 45-554. |
[37] | Farouq IS, Sulong Z (2021) The effects of foreign direct investment uncertainty on financial development in Nigeria: an asymmetric approach. Iran J Manage Stud 14: 383-399. |
[38] | Sulong Z, Farouq IS (2021) Energy-Finance Nexus: Evidence from African Oil Exporting Countries. Int Energy J 21. |
[39] |
Farouq I, Sulong Z, Ahmad U, et al. (2020) Heterogeneous Data Approach on Financial development of Selected African Leading Economies. Data in Brief 30: 105670. doi: 10.1016/j.dib.2020.105670
![]() |
[40] | Ghorashi N, Alavi Rad A (2018) Impact of financial development on CO2 emissions: panel data evidence from Iran's economic sectors. J Community Health Res 7: 127-133. |
[41] | Gowan P (1999) The global gamble: Washington's Faustian bid for world dominance, London Verso. |
[42] |
Grossman GM, Krueger AB (2017) Environmental impacts of a north American free trade agreement; national bureau group estimators. Renew Sust Energy Rev 77: 731-747. doi: 10.1016/j.rser.2017.04.050
![]() |
[43] |
Hanif I, Raza SMF, Gago-de-Santos P, et al. (2019) Fossil fuels, foreign direct investment, and economic growth have triggered CO2 emissions in emerging Asian economies: some empirical evidence. Energy 171: 493-501. doi: 10.1016/j.energy.2019.01.011
![]() |
[44] |
Hübler M, Keller A (2009) Energy Savings via FDI: Evidence from Developing Countries. Environ Dev Econ 15: 59-80. doi: 10.1017/S1355770X09990088
![]() |
[45] | IPCC (2014) Climate Change 2014. Available from: https://www.ipcc.ch/pdf/assessment-report/ar5/wg3/ WGIIIAR5_SPM_TS_Volume.pdf (accessed on 22 December 2020). |
[46] | Jakada AH, Mahmood S (2020) An asymmetric effect of economic growth, foreign direct investment and financial development on the quality of environment in Nigeria. J Manage Theory Pract 1: 5-13. |
[47] |
Jakada AH, Mahmood S, Ahmad AU, et al. (2020) Financial development and the quality of the environment in Nigeria: an application of non-linear ARLD approach. Res World Econ 11: 78-92. doi: 10.5430/rwe.v11n1p78
![]() |
[48] |
Javid M, Sharif F (2016) Environmental Kuznets curve and financial development in Pakistan. Renew Sust Energy Rev 54: 406-414. doi: 10.1016/j.rser.2015.10.019
![]() |
[49] |
Jebli MB, Youssef SB, Ozturk I (2016) Testing environmental Kuznets curve hypothesis: The role of renewable and non-renewable energy consumption and trade in OECD countries. Ecol Indic 60: 824-831. doi: 10.1016/j.ecolind.2015.08.031
![]() |
[50] |
Jiang P, Yang H, Ma X (2019) Coal production and consumption analysis, and forecasting of related carbon emission: evidence from China. Carbon Manage 10: 189-208. doi: 10.1080/17583004.2019.1577177
![]() |
[51] |
Kaika D, Zervas E (2013) The environmental Kuznets curve (EKC) theory-part A: Concept, causes and the CO2 emissions case. Energy Policy 62: 1392-1402. doi: 10.1016/j.enpol.2013.07.131
![]() |
[52] |
Katircioğlu ST, Taşpinar N (2017) Testing the moderating role of financial development in an environmental Kuznets curve: empirical evidence from Turkey. Renew Sust Energy Rev 68: 572-586. doi: 10.1016/j.rser.2016.09.127
![]() |
[53] | Kuznets S (2019) Economic growth and income inequality. Am Econ Rev 45: 25-37. |
[54] |
Lall S, Marsden JE, Glavaški S (2002) A subspace approach to balanced truncation for model reduction of nonlinear control systems. Int J Robust Nonlinear Control IFAC‐Affiliated J 12: 519-535. doi: 10.1002/rnc.657
![]() |
[55] |
Lin B, Zhu J (2019) Determinants of renewable energy technological innovation in China under CO2 emissions constraint. J Environ Manage 247: 662-671. doi: 10.1016/j.jenvman.2019.06.121
![]() |
[56] |
Liu X, Bae J (2018) Urbanization and industrialization impact of CO2 emissions in China. J Clean Prod 172: 178-186. doi: 10.1016/j.jclepro.2017.10.156
![]() |
[57] |
Nathaniel SP, Iheonu CO (2019) Carbon dioxide abatement in Africa: The role of renewable and non-renewable energy consumption. Sci Total Environ 679: 337-345. doi: 10.1016/j.scitotenv.2019.05.011
![]() |
[58] |
Omri A, Daly S, Rault C, et al. (2015) Financial development, environmental quality, trade and economic growth: What causes what in MENA countries. Energy Econ 48: 242-252. doi: 10.1016/j.eneco.2015.01.008
![]() |
[59] |
Otchere I, Senbet L, Simbanegavi W (2017) Financial sector development in Africa-an overview. Rev Dev Financ 7: 1-5. doi: 10.1016/j.rdf.2017.04.002
![]() |
[60] |
Ozcan B (2013) The nexus between carbon emissions, energy consumption and economic growth in Middle East countries: a panel data analysis. Energy Policy 62: 1138-1147. doi: 10.1016/j.enpol.2013.07.016
![]() |
[61] |
Özokcu S, Özdemir Ö (2017) Economic growth, energy, and environmental Kuznets curve. Renew Sust Energy Rev 72: 639-647. doi: 10.1016/j.rser.2017.01.059
![]() |
[62] |
Paramati SR, Alam MS, Apergis N (2018) The role of stock markets on environmental degradation: A comparative study of developed and emerging market economies across the globe. Emerg Mark Rev 35: 19-30. doi: 10.1016/j.ememar.2017.12.004
![]() |
[63] |
Pata UK (2018) Renewable energy consumption, urbanization, financial development, income and CO2 emissions in Turkey: testing EKC hypothesis with structural breaks. J Clean Prod 187: 770-779. doi: 10.1016/j.jclepro.2018.03.236
![]() |
[64] |
Pesaran MH (2006) Estimation and inference in large heterogeneous panels with a multifactor error structure. Econometrica 74: 967-1012. doi: 10.1111/j.1468-0262.2006.00692.x
![]() |
[65] |
Pesaran MH (2007) A simple panel unit root test in the presence of cross‐section dependence. Journal Appl Econometrics 22: 265-312. doi: 10.1002/jae.951
![]() |
[66] |
Qamruzzaman M, Jianguo W (2020) The asymmetric relationship between financial development, trade openness, foreign capital flows, and renewable energy consumption: Fresh evidence from panel NARDL investigation. Renew Energy 159: 827-842. doi: 10.1016/j.renene.2020.06.069
![]() |
[67] |
Raza SA, Shah N (2018) Testing environmental Kuznets curve hypothesis in G7 countries: the role of renewable energy consumption and trade. Environ Sci Pollut Res 25: 26965-26977. doi: 10.1007/s11356-018-2673-z
![]() |
[68] |
Rafindadi AA, Ozturk I (2017) Impacts of renewable energy consumption on the German economic growth: Evidence from combined cointegration test. Renew Sust Energy Rev 75: 1130-1141. doi: 10.1016/j.rser.2016.11.093
![]() |
[69] |
Salahuddin M, Gow J, Ozturk I (2015) Is the long-run relationship between economic growth, electricity consumption, carbon dioxide emissions and financial development in gulf cooperation council countries robust? Renew Sust Energy Rev 51: 317-326. doi: 10.1016/j.rser.2015.06.005
![]() |
[70] | Saud S, Chen S, Haseeb A (2019a) The role of financial development and globalization in the environment: accounting ecological footprint indicators for selected one-belt-one-road initiative countries. J Clean Prod 26: 2253-2269. |
[71] |
Shahbaz M, Solarin SA, Mahmood H, et al. (2013) Does financial development reduce CO2 emissions in Malaysian economy? A time series analysis. Econ Model 35: 145-152. doi: 10.1016/j.econmod.2013.06.037
![]() |
[72] | Shin Y, Yu B, Greenwood-Nimmo M (2014). Modelling asymmetric cointegration and dynamic multipliers in a nonlinear ARDL framework, In: Festschrift in honor of Peter Schmidt, Springer, New York, NY, 281-314. |
[73] |
Sinani E, Meyer KE (2004) Spillovers of technology transfer from FDI: the case of Estonia. J Comp Econ 32: 445-466. doi: 10.1016/j.jce.2004.03.002
![]() |
[74] |
Sinha A, Shahbaz M (2018) Estimation of environmental Kuznets curve for CO2 emission: role of renewable energy generation in India. Renew Energy 119: 703-711. doi: 10.1016/j.renene.2017.12.058
![]() |
[75] | Soederberg S (2014) Debtfare States and the Poverty Industry: Money, Discipline and the Surplus Population, New York: Routledge. |
[76] |
Stern DI (2004) The rise and fall of the environmental Kuznets curve. World Dev 32: 1419-1439. doi: 10.1016/j.worlddev.2004.03.004
![]() |
[77] |
Sugiawan Y, Managi S (2016) The environmental Kuznets curve in Indonesia: Exploring the potential of renewable energy. Energy Policy 98: 187-198. doi: 10.1016/j.enpol.2016.08.029
![]() |
[78] | Ulucak R, Khan SUD, Baloch MA, et al. (2020) Mitigation pathways toward sustainable development: Is there any trade‐off between environmental regulation and carbon emissions reduction? Sust Dev 28: 813-822. |
[79] |
Wang Z, Gerstein M, Snyder M (2009) RNA-Seq: a revolutionary tool for transcriptomics. Nature Rev Gene 10: 57-63. doi: 10.1038/nrg2484
![]() |
[80] |
Westerlund J (2007) Testing for error correction in panel data. Oxf B Econ Stat 69: 709-748. doi: 10.1111/j.1468-0084.2007.00477.x
![]() |
[81] | WDI T (2019) World development indicators (DataBank). Available from: https://databank.worldbank.org/source/world-development-indicators. |
[82] | Xing T, Jiang Q, Ma X (2017) To facilitate or curb? The role of financial development in China's carbon emissions reduction process: A novel approach. Int J Environ Res Public Health 14: 1222. |
[83] |
Yeh JC, Liao CH (2017) Impact of population and economic growth on carbon emissions in Taiwan using an analytic tool STIRPAT. Sust Environ Res 27: 41-48. doi: 10.1016/j.serj.2016.10.001
![]() |
[84] |
Zafar MW, Shahbaz M, Hou F, et al. (2019) From nonrenewable to renewable energy and its impact on economic growth: the role of research & development expenditures in Asia-Pacific economic cooperation countries. J Clean Prod 212: 1166-1178. doi: 10.1016/j.jclepro.2018.12.081
![]() |
[85] | Zaidi SAH, Wei Z, Gedikli A, et al. (2019) The impact of globalization, natural resources abundance, and human capital on financial development: Evidence from thirty-one OECD countries. Resour Policy 64: 101476. |
[86] |
Zambrano-Monserrate MA, Silva-Zambrano CA, Davalos-Penafiel JL, et al. (2018) Testing environmental Kuznets curve hypothesis in Peru: the role of renewable electricity, petroleum and dry natural gas. Renew Sust Energy Rev 82: 4170-4178. doi: 10.1016/j.rser.2017.11.005
![]() |
[87] |
Zoundi Z (2017) CO2 emissions, renewable energy and the environmental Kuznets curve, a panel cointegration approach. Renew Sust Energy Rev 72: 1067-1075. doi: 10.1016/j.rser.2016.10.018
![]() |
1. | Biswajit Sarkar, Bikash Koli Dey, Is online-to-offline customer care support essential for consumer service?, 2023, 75, 09696989, 103474, 10.1016/j.jretconser.2023.103474 |
Index | |
i | Number of products i=1,2,...,M;i=0 represents shared-production of all products |
Decision | variables |
t | Production cycle length (time unit) |
N | Number of shipments of finished products in each cycle (integer) |
q1,i | Production rate of product i (units/time unit) |
q2,i | Remanufacturing rate for product i (units/time unit) |
Parameter | |
δi | Market demand of product i (units/time unit) |
Ai | Production lot size of product finished product i (units/cycle) |
Bi | Production setup cost of product i ($/setup) |
Fi | Unit production cost of product i ($/unit) |
Cm1,i | Unit material cost of product i for production ($/unit) |
Cm2,i | Unit material cost of product i for remanufacturing ($/unit) |
CD1,i | Unit development cost of product i for production ($/unit) |
CD2,i | Unit development cost of product i for remanufacturing ($/unit) |
H1,i | Unit holding cost of new produced product i ($/unit/unit time) |
H2,i | Unit holding cost per remanufactured item i ($/unit/unit time) |
H3,i | Unit holding cost for storing finished product i ($/unit/unit time) |
H4,i | Unit holding cost for safety stocks for product i ($/unit/unit time) |
FR,i | Unit remanufacturing cost for product i ($/unit) |
T1,i | Production uptime for product i (time unit) |
T2,i | Remanufacturing time for product i (time unit) |
T3,i | Delivery time of product i (time unit) |
hi | Inventory level of common components for product i (units) |
h1,i | Perfect quality item i at the end of the production up time (units) |
h2,i | Perfect quality items i at the end of remanufacturing process (units) |
g1,i | Random defective rate of product i in Stage 1 |
g2,i | Random defective rate of product i in Stage 2 |
yi | Defective percentage of product i in production |
B1,i | Fixed delivery cost per shipment for product i ($/shipment) |
FT,i | Unit delivery cost per unit product i ($/unit) |
TN,i | Fixed interval of time between each of shipment of finished item i during T3,i |
(time unit) | |
I(T)i | On-hand inventory level of perfect quality items i at any time T (units) |
Ig(T)i | On-hand inventory level of imperfect items i at any time T (units) |
Ic(T)i | On-hand inventory level of finished product i at any time T (units) |
li | Leftover finished product i in each TN,i (units) |
Gi | Number of delivered finished product i in each shipment (units) |
β | Completion rate of common component of products as compared to the finished |
product | |
α | scaling parameter of unit production cost |
TC | Total cost of the production system ($) |
E[t] | Expected production cycle length (time unit) |
E[TCU] | Expected total cost ($/cycle) |
Index | |
i | Number of products i=1,2,...,M;i=0 represents shared-production of all products |
Decision | variables |
t | Production cycle length (time unit) |
N | Number of shipments of finished products in each cycle (integer) |
q1,i | Production rate of product i (units/time unit) |
q2,i | Remanufacturing rate for product i (units/time unit) |
Parameter | |
δi | Market demand of product i (units/time unit) |
Ai | Production lot size of product finished product i (units/cycle) |
Bi | Production setup cost of product i ($/setup) |
Fi | Unit production cost of product i ($/unit) |
Cm1,i | Unit material cost of product i for production ($/unit) |
Cm2,i | Unit material cost of product i for remanufacturing ($/unit) |
CD1,i | Unit development cost of product i for production ($/unit) |
CD2,i | Unit development cost of product i for remanufacturing ($/unit) |
H1,i | Unit holding cost of new produced product i ($/unit/unit time) |
H2,i | Unit holding cost per remanufactured item i ($/unit/unit time) |
H3,i | Unit holding cost for storing finished product i ($/unit/unit time) |
H4,i | Unit holding cost for safety stocks for product i ($/unit/unit time) |
FR,i | Unit remanufacturing cost for product i ($/unit) |
T1,i | Production uptime for product i (time unit) |
T2,i | Remanufacturing time for product i (time unit) |
T3,i | Delivery time of product i (time unit) |
hi | Inventory level of common components for product i (units) |
h1,i | Perfect quality item i at the end of the production up time (units) |
h2,i | Perfect quality items i at the end of remanufacturing process (units) |
g1,i | Random defective rate of product i in Stage 1 |
g2,i | Random defective rate of product i in Stage 2 |
yi | Defective percentage of product i in production |
B1,i | Fixed delivery cost per shipment for product i ($/shipment) |
FT,i | Unit delivery cost per unit product i ($/unit) |
TN,i | Fixed interval of time between each of shipment of finished item i during T3,i |
(time unit) | |
I(T)i | On-hand inventory level of perfect quality items i at any time T (units) |
Ig(T)i | On-hand inventory level of imperfect items i at any time T (units) |
Ic(T)i | On-hand inventory level of finished product i at any time T (units) |
li | Leftover finished product i in each TN,i (units) |
Gi | Number of delivered finished product i in each shipment (units) |
β | Completion rate of common component of products as compared to the finished |
product | |
α | scaling parameter of unit production cost |
TC | Total cost of the production system ($) |
E[t] | Expected production cycle length (time unit) |
E[TCU] | Expected total cost ($/cycle) |