Abstract
Every organisation has an upper limit to the number of orders or products that it can manufacture or remanufacture per unit time. In reverse logistics operations, capacity limits can lead to inefficiencies in the remanufacturing process. In this paper, comparisons were made of the Bullwhip effect (BWE) in closed-loop systems that have collection and remanufacturing capacity limits and those that do not. Collection and remanufacturing capacity limits were introduced for a system where a company had to collect ‘enough’ products before remanufacturing can begin. This introduced collection backlogs, remanufacturing backlogs and remanufacturing downtimes to the closed loop supply chain (CLSC). By adopting a systems dynamics approach, the research performed ‘what-if’ analyses of the closed-loop system under different levels of the factors under investigation. Two case studies were investigated: one remanufacturing electric vehicle batteries (low demand, slow moving item) and the other remanufacturing kitchen appliances (high demand, fast moving item). Firstly, introducing collection and remanufacturing capacity limits in the reverse chain increased the BWE to a level higher than the reverse chain without any capacity limits, but not to the level of the forward chain without any product returns. Secondly, introducing collection and remanufacturing capacity limits for a closed-loop system where a company had to collect ‘enough’ products before remanufacturing begins had different impacts depending on the product demand size and speed. The presence of external returns by other parties not regulated by an organisation had an impact of lowering the BWE in the closed-loop system and it also impacted how the other factors under investigation affected the Bullwhip effect. These findings were used to provide managerial insights for organisations venturing into reverse logistics.
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Appendix
Appendix
Stock and flow diagrams and model equations
Model equations
STOCKS
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1.
Collected products
$$ Collected\ products(t)= collected\ products\left(t- dt\right)+\left( total\ collection\ rate- acce\ rate\ for\ reuse- reje\ rate\ for\ reuse\right)\times dt $$
Inflows
Outflows
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2.
Components inventory
$$ Components\ inventory\ (t)= components\ inventory\ \left(t- dt\right)+\left( comp\ prdn\ rate+ comp\ reman\ rate+ comp\ acce\ rate\ for\ dir\ reuse- comp\ used\ for\ prdn\right)\times dt $$
Inflows
Outflows
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3.
Components rejected for direct reuse
$$ comp\ reje\ for\ dir\ reuse\ (t)= comp\ reje\ for\ dir\ reuse\ \left(t- dt\right)+\left( comp\ repla\ rate+ comp\ reje\ rate\ for\ dir\ reuse- recycle\ rate- coomp\ reman\ rate- disposal\ rate\right)\times dt $$
Inflows
Outflows
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4.
Controllable disposal
$$ controllable\ disposal\ (t)= controllable\ disposal\ \left(t- dt\right)+\left( disposal\ rate\right)\times dt $$
Inflows
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5.
Distributor orders backlog
$$ distributor\ orders\ backlog\ (t)= distributor\ orders\ backlog\ \left(t- dt\right)+\left( distributor\ orders- distributor\kern0.5em backlog\ red\ rate\right)\times dt $$
Inflows
Outflows
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6.
Distributor inventory
$$ distributor\ inventory\ (t)= distributor\ inventory\ \left(t- dt\right)+\Big( shipments\ to\ distributor- shipments\ to\ wholesaler\times dt $$
Inflows
Outflows
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7.
Inventory of components from rejected products
$$ inv\ of\ comp\ from\ reje\ prdcts\ (t)= inv\_ of\_ comp\_ from\_ reje\_ prdcts\left(t- dt\right)+\left( comp\_ from\_ reje\_ prodcts- comp\_ reje\_ rate\_ for\_ dir\_ reuse- comp o\_ acce\_ rate\_ for\_ dir ect\_ reuse\right)\times dt $$
Inflows
Outflows
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8.
Products for remanufacturing
$$ products\ for\ remn\ (t)= products\ for\ reman\ \left(t- dt\right)+\left( acce\ rate\ for\ reman- reman\ rate- produsctscotremanufactured\right)\times dt $$
Inflows
Outflows
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9.
Products for cannibalisation
$$ prod\ for\ cannibalisation\ (t)= prod\ for\ cannibalisation\ \left(t- dt\right)+\left( reje\ rate\ for\ reman\right)\times dt $$
Inflows
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10.
Raw material inventory
$$ raw\ mat\ inventory\ (t)= raw\ mat\ inventory\ \left(t- dt\right)+\left( recycling\ rate- comp\ prod\ rate\right)\times dt $$
Outflows
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11.
Rejected products for reuse
$$ reje\ prod\ for\ reuse\ (t)= reje\ prod\ for\ reuse\ \left(t- dt\right)+\left( reje\ rate\ for\ prod\ reuse- acce\ rate\ for\ reman- reje\ rate\ for\ reman\right)\times dt $$
Inflows
Outflows
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12.
Remanufacturing backlogs
$$ remanufacturing\ backlogs\ (t)= remanufacturing\ backlogs\ \left(t- dt\right)+\left( products\ not\ remanufactured\right)\times dt $$
Inflows
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13.
Retailer orders backlog
$$ retaile{r}^{\prime } s order\ backlog\ (t)= retailer\ orders\ backlog\ \left(t- dt\right)+\left( retaile{r}^{\prime } s order s- retailer\ backlog\ red\ rate\right)\times dt $$
Inflows
Outflows
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14.
Retailer inventory
$$ retailer\ inventory\ (t)= retailer\ inventory\ \left(t- dt\right)+\left( shipments\ to\ retailer- retail\ sale\right)\times dt $$
Inflows
Outflows
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15.
Serviceable inventory
$$ serviceable\ inventory(t)= serviceable\ inventory\ \left(t- dt\right)+\left( production\ rate+ reman\ rate+ acce\ prod\ for\ reuse- shipments\ to\ distributor\right)\times dt $$
Inflows
Outflows
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16.
Wholesaler inventory
$$ wholesaler\ inventory(t)= wholesaler\ inventory\ \left(t- dt\right)+\left( shipments\ to\ wholesaler- shipments\ to\ retailer\right)\times dt $$
Inflows
Outflows
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17.
Wholesaler orders backlog
$$ wholesaler\ orders\ backlog\ (t)= wholesaler\ orders\ backlog\ \left(t- dt\right)+\left( wholesaler\ orders- wholesaler\ backlog\ redu\ rate\right)\times dt $$
Inflows
Outflows
AUXILLIARY VARIABLES
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Tombido, L., Louw, L., van Eeden, J. et al. A system dynamics model for the impact of capacity limits on the Bullwhip effect (BWE) in a closed-loop system with remanufacturing. Jnl Remanufactur 12, 1–45 (2022). https://doi.org/10.1007/s13243-021-00100-7
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DOI: https://doi.org/10.1007/s13243-021-00100-7