Evaluating cost impacts on reverse logistics using an Economic Order Quantity (EOQ) model with environmental and social considerations

Abstract

Societal awareness and legislation changes concerning sustainability have affected how organizations generate value for stakeholders, as well as their processes, products, and public relations. In the context of increasing environmental and social awareness, more studies are needed regarding reverse logistics lot-sizing control taking into account sustainability principles. The contribution of this study is the incorporation of sustainable costs in reverse logistics processes using the Economic Order Quantity (EOQ) model. This paper proposes the extension of a mathematical model for lot-sizing in the reverse logistics that considers environmental, social, and economic parameters. A numerical example and sensitivity analyses are presented to evaluate the sustainable EOQ. Our results indicate that carbon prices have a significant impact on the remanufacturing tax, i.e. the proportion of reusable items in a reverse supply chain that are successfully remanufactured. Additionally, a perspective on the social impact on lot sizing is discussed by noting that high social costs, calculated as a function of ergonomic conditions, can invalidate a high remanufacturing tax. As a consequence, poorly planned labour conditions in reverse logistics can lead to lower recycling rates due to inefficient use of social resources.

Appendix

As proposed in Battini et al. (2017), the following assumptions are made for the Rest Allowance.

(RA) costs:

• The worker needs to rest for a certain amount of time dependent on the previous work load;

• During transportation, the worker adopts a standing position;

• Tasks such as picking and storing demand the same amount of time for completion; and

• The opportunity cost (σ) of the RA time can be higher than the regular worker hourly wage

The parameters adopted are the same as those proposed in the original study.

• Q: Total amount to be handled

• q: Lot-size

• w: Item weight

• d: Distance between stock points

• s: Speed of a person during the carrying task

• t_ps= t_p = t_s: Time for stocking/picking

• c_op: Unitary worker cost

• ${\dot{\text{E}}}_{\text{ps}}$(w) = Ep(w) = Es(w): Metabolic cost for the picking/stocking activity

• ${\dot{\text{E}}}_{\text{t}}$: Metabolic cost for transportation

• $\upalpha$: Cost impact of the RA, as a multiplier of the unitary worker cost

The RA is then modelled as follows:

$$ {\text{RA}}\left( {\text{q}} \right) =\upalpha c_{op} 2t_{ps} Q\frac{{{\dot{\text{E}}}_{\text{ps}} - 4.3}}{{4.3 - {\dot{\text{E}}}_{\text{t}} }} -\upalpha c_{op} \frac{2d}{s}\frac{Q}{q} $$

where the metabolic cost, ${\dot{\text{E}}}_{\text{ps}}$, is a function of the load weight, w:

$$ {\dot{\text{E}}}_{\text{ps}} = 0.1743w + 3.7206. $$

Parameter	Value/denomination	Units
α	σ	–
cop	15	€/h
tps	8	s
Q	λμ	–
d	25	m
s	1	m/s
q	$Q_{r/m}$	–
w	6	kg
${\dot{\text{E}}}_{\text{ps}}$	4.765	kcal/min
${\dot{\text{E}}}_{\text{t}}$	1.86	kcal/min