Impact of carbon emission policies on manufacturing, remanufacturing and collection of used item decisions with price dependent return rate

Abstract

Industries across the world today are looking for cost effective solutions to reduce waste and curb the carbon emission, due to heightened awareness about ecological responsibility coupled with stringent government regulation and legislations, through operational adjustments in manufacturing/remanufacturing and collection (used products) policy. This paper presents a production, remanufacture and waste disposal EPQ model under different carbon regulatory mechanisms of a firm that sells new and repaired versions of its product at two different markets and it is assumed that remanufactured items are of poorer quality; i.e., not ’as-good-as new’. In reality, the return rates of used product from the end customers of both markets are influenced by the purchasing price, and therefore this study suggests that the return flow of used product as an increasing function of purchasing price. We studied the optimization model under two scenarios: (i) no carbon emission policy (ii) carbon emission norms (a. carbon tax; b. strict carbon cap; c. carbon cap and trade). Mathematical modeling followed by numerical analysis is carried out to examine the impact of regulatory policies on optimal decisions and overall emissions. The results indicate that remanufacturing is an effective strategy to decrease carbon emission compared to manufacturing process.

Appendix: Inventory level of repairable item in shop-2

As illustrate in Fig. 2,the inventory differential equations of repairable item during $T_{R1},$ $I_1(t)$, can be expressed as

$$\begin{aligned} \frac{dI_{1}}{dt}+a I_1(t)=k_2-R,\,\,\,\,0<t<T_{R1} \end{aligned}$$

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with boundary condition: (i)$I_1(0)=\beta _1$ and (ii) $I_1(T_{R1})=0$

The inventory differential equations of repairable item during production period $T_{R2}$ is

$$\begin{aligned} \frac{dI_{2}}{dt}+a I_2(t)=k_2,\,\,\,\,0<t<T_{R2} \end{aligned}$$

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with boundary condition:(i)$I_1(0)=0$ and (ii) $I_2(T_{R2})=\alpha _1$

The inventory differential equations of repairable item during production period $T_M$ is

$$\begin{aligned} \frac{dI_{3}}{dt}+a I_3(t)=k_1,\,\,\,\,0<t<T_M \end{aligned}$$

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with boundary condition:$I_3(0)=\alpha _1$

where $k_1=(1-\alpha )\delta _p\beta _p\gamma _pD_m$ and $k_2=((1-\alpha )\delta _s\beta _s\gamma _sD_r$

The differential equations are solved as

$$\begin{aligned} I_1(t)= & {} \frac{R-k_2}{a}\bigg [\exp (a (T_{R1}-t))-1\bigg ],\quad 0<t<T_{R1} \end{aligned}$$

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$$\begin{aligned} I_2(t)= & {} \frac{k2}{a}\bigg [1-\exp (-a t)\bigg ],\quad 0<t<T_{R2}\end{aligned}$$

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$$\begin{aligned} I_3(t)= & {} \alpha \exp (-a t)+\frac{k_1}{a}\bigg [1-\exp (-a t)\bigg ],\quad 0<t<T_M \end{aligned}$$

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where $\beta _1=\frac{R-k_2}{a}\bigg [\exp (a T_{R1})-1\bigg ]$ and $\alpha _1=\frac{k2}{a}\bigg [1-\exp (-a T_{R2})\bigg ]$

The value of $\gamma _1$ is $\beta _1-I(T_{R2})$ that is  $\gamma _1=\beta _1-\alpha _1$

The inventory holding of repairable item during the time interval [0, T] in shop-2 is

$$\begin{aligned} I_R= & {} n\int _0^{T_{R1}}I_1(t) dt+n\int _0^{T_{R2}}I_2(t) dt+\int _0^{T_M}I_3(t)dt+\sum _{i=1}^{n-1}i\gamma _1 \bigg (\frac{T_R}{n}\bigg ) \end{aligned}$$

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