Assessing the cost structure of component reuse in a product family for remanufacturing

Abstract

Component reuse is a crucial remanufacturing strategy that assists manufacturers to achieve sustainable supply chain management. However, few manufacturers obtain economic benefits from component reuse strategies due to the demand for increasing product variety and its related complex cost structure. In this paper, we propose an integrated quantitative decision model to assess the economic aspects of component reuse for remanufacturing management. Given numerous cost factors, such as component manufacturing, reverse logistics, reprocessing, disposal and penalty costs, we derive the optimal acquisition cost to retrieve end-of-life products for component reuse. Then, we identify the component commonality effects to quantify the component reuse rate from a variety of end-of-life products. Finally, our models and results are demonstrated through an industrial case study. Accordingly, the cost savings from reusing components could be achieved by 25 % of the manufacturing cost offered to acquire the used products from customers at a low reverse logistics cost. Based on the 80 % yield rate observed in the case study, the commonality of components in a product family would affect 35 % of the total cost savings of component reuse for remanufacturing.

Appendix: Proof of proposition

When $Q_{reuse}^{\prime } =\frac{\pi BM(T-\tau )}{T}\cdot \frac{c_{ac} -a}{b-a}$, the objective function can be rewritten as the following:

$$\begin{aligned} CS= & {} Q_{reuse}^{\prime } \left[ {d+\rho -\frac{1}{\beta }(\alpha +\mu +\gamma )-\frac{1-\beta }{\beta }\sigma } \right] c_{man} \\= & {} \frac{\pi \beta M(T-\tau )}{T}\cdot \frac{c_{ac} -a}{b-a}\\&\quad \left[ {d+\rho -\frac{(\alpha +\mu +\gamma )-(1-\beta )\sigma }{\beta }} \right] c_{man} \\= & {} \frac{\pi \beta M(T-\tau )}{T}\cdot \frac{c_{ac} -a}{b-a}\\&\quad \left\{ {\left[ {d+\rho -\frac{(\mu +\gamma )-(1-\beta )\sigma }{\beta }} \right] c_{man} -\frac{1}{\beta }c_{ac} } \right\} \\= & {} \frac{\pi \beta M(T-\tau )}{T}\left\{ -\frac{c_{ac}^2 }{(b-a)\beta }+\frac{\left[ {d+\rho -\frac{(\mu +\gamma )-(1-\beta )\sigma }{\beta }} \right] c_{man} \cdot c_{ac} }{b-a}\right. \\&\left. +\frac{a\cdot c_{ac} }{(b-a)\beta }-\frac{a}{(b-a)}\frac{\left[ {d+\rho -\frac{(\mu +\gamma )-(1-\beta )\sigma }{\beta }} \right] c_{man} }{b-a} \right\} \\ \end{aligned}$$

Since $\frac{dCS}{dc_{ac} }=-\frac{2c_{ac} }{(b-a)\beta }+\frac{\left[ {d+\rho -\frac{(\mu +\gamma )-(1-\beta )\sigma }{\beta }} \right] c_{man} }{b-a}+\frac{a}{(b-a)\beta }$ and $\frac{d^{2}CS}{dc_{ac} }<0$ implies that the objective function is strictly concave. Therefore,

$$\begin{aligned} \frac{dCS}{dc_{ac} }= & {} -\frac{2c_{ac} }{(b-a)\beta }+\frac{\left[ {d+\rho -\frac{(\mu +\gamma )-(1-\beta )\sigma }{\beta }} \right] c_{man} }{b-a}\\&+\frac{a}{(b-a)\beta }=0 \\ \Rightarrow \quad c_{ac}^*= & {} \frac{a+\left[ {\beta (d+\rho -\sigma )-(\mu +\gamma -\sigma )} \right] c_{man} }{2} \\ \end{aligned}$$

When $c_{ac}^*>b$, the optimal acquisition cost will be equal to b, the optimal acquisition cost becomes: $\min \left\{ {\frac{a+\left[ {\beta (d+\rho -\sigma )-(\mu +\gamma -\sigma )} \right] c_{man} }{2},b} \right\}$ such that all end-of-life products can be returned.

Such objective value is feasible when $\left[ {\beta (d+\rho -\sigma )-(\mu +\gamma -\sigma )} \right] c_{man} >a$. Otherwise, the optimal value of the acquisition cost is equal to zero for avoiding net loss in the remanufacturing operations. The proposition is proved.