Efficiency–resilience trade-offs in closed-loop supply chains: supply-side ripple propagation, alternative structures and inventory policies, and risk-aware tuning of the POUT controller

In a hybrid manufacturing/remanufacturing system managed by a proportional order-up-to (POUT) replenishment policy, a documented trade-off arises: tuning the inventory controller for cost efficiency (optimal time constant $T_I^* > 1$) erodes resilience to demand shocks (optimal $T_I = 1$), leaving a compromise interval $1 < T_I < T_I^*$. The source study (de Arquer, Ponte and Pino, Central European Journal of Operations Research, 2022) deliberately analysed only one configuration — a hybrid system with POUT control of the serviceable stock, push control of the recoverable stock, and demand-side shocks — and left open how the trade-off behaves under supply-side disruptions (the ripple effect), in other closed-loop structures (pure remanufacturing, recycling-dominant networks) and inventory-control combinations, and how its qualitative suggestion to place $T_I$ within the compromise interval according to disruption probabilities could be formalized into a decision rule. No later work quantifies how POUT tuning $T_I$ mediates supply-shock ripple propagation in closed-loop systems with remanufacturing, characterizes the trade-off in the alternative structures, or formalizes the probability-based $T_I$ rule; the problem is open.

Background

Closing the loop of a supply chain — collecting used products and recovering value through remanufacturing or recycling — is a core operational strategy of the circular economy. The archetypal setting is the hybrid manufacturing/remanufacturing system, in which customer demand can be met either by newly manufactured products or by remanufactured used products; both streams feed a common serviceable inventory, while returned used products accumulate in a recoverable inventory. In the study that poses this problem (de Arquer, Ponte and Pino, 2022), the serviceable stock is managed by a proportional order-up-to (POUT) replenishment policy: a periodic-review rule in which each period's manufacturing order covers the forecast of net demand (total demand minus remanufacturing completions) plus a correction of the inventory and work-in-progress gaps toward their targets, with the correction damped by a proportional gain $1/T_I$, where $T_I$ is the inventory controller time constant — a larger $T_I$ means slower reaction to inventory discrepancies. The recoverable stock follows a push policy: every returned unit is remanufactured as it arrives. The source study modelled this periodic-review system with difference equations and derived explicit transfer functions relating the manufacturing order rate and the serviceable inventory to demand, complementing that frequency-domain analysis with time-domain step-response and long-run stochastic simulation.

Efficiency is assessed with two variance-based dynamic metrics. The Bullwhip effect (BW) is the amplification of order variance relative to demand variance as orders move up the chain, and drives capacity, production-changeover and transportation costs; Net Stock Amplification (NSAmp) is the amplification of inventory variance relative to demand variance, and drives holding and stock-out costs. Both are combined into a single cost-weighted efficiency metric $J_e$ whose weights $k_{BW}$ and $k_{NSA}$ reflect the supply chain's cost structure. In the base scenario of the source study, $J_e$ is convex in $T_I$ with an optimum at $T_I^* > 1$ (approximately 2.2 or 6.5 for two illustrative cost weightings): smoothing the replenishment signal pays off for efficiency, consistent with earlier findings that POUT policies improve the dynamics of closed-loop chains (Cannella et al., 2021) and with the unified transfer-function theory of closed-loop supply chain dynamics (Hosoda and Disney, 2018).

Resilience is assessed by the transient response to a sudden demand shock (a step increase in demand), using a control-engineering metric adopted from supply chain resilience research (Spiegler et al., 2012): the integral of time-weighted absolute error (ITAE) of the serviceable inventory and of the manufacturing order rate, which jointly capture the time to recovery and the performance lost during recovery — two of the three dimensions that resilience metrics should ideally reflect (Behzadi et al., 2020). The source study finds that ITAE increases monotonically with $T_I$, so resilience is maximized at $T_I = 1$: smoothing helps efficiency but slows recovery from shocks. This produces the central trade-off — efficiency calls for $T_I^* > 1$, resilience for $T_I = 1$ — and leaves managers with a compromise interval $1 < T_I < T_I^*$. Two structural findings frame the trade-off: a higher return yield (the fraction of demand that returns for remanufacturing, i.e. the level of circularity) makes the system more efficient but less resilient, because long consumption lead times delay the reverse flow's contribution to recovery; and resilience is maximized when the remanufacturing lead time equals the manufacturing lead time — a resilience counterpart of the well-known lead-time paradox of hybrid systems (the counterintuitive finding that shortening the remanufacturing lead time does not uniformly improve performance, because it improves some dynamic metrics while worsening others).

The literature on disruption propagation and the costs of resilience has developed along parallel but separate lines. The ripple effect — the propagation of a disruption along the supply chain as its consequences cascade through the network — has been studied for forward chains and network-design models (Ivanov and Sokolov, 2019; Aldrighetti et al., 2021), and multi-echelon simulation studies of closed-loop chains have examined lead-time variability and information sharing (Dominguez et al., 2020). The closest prior work joins these lines to the reverse loop: de Arquer, Ponte, Pino and de la Fuente (2023) demonstrate, with an illustrative example, that control engineering can be used to analyse the propagation of disruptions — the ripple effect — in closed-loop supply chains, without quantifying how the POUT time constant $T_I$ mediates supply-shock propagation or linking it to the efficiency–resilience trade-off. None of these analyses addresses the efficiency–resilience trade-off at the level of inventory-controller tuning in a closed-loop system, which is precisely where the source study located it — and where it delimited its own scope: demand-side shocks only, one hybrid structure, one policy combination.

Problem Statement

Extend the control-theoretic characterization of the efficiency–resilience trade-off in closed-loop supply chains beyond the single configuration analysed by de Arquer, Ponte and Pino (2022) — a hybrid manufacturing/remanufacturing system with a POUT policy on the serviceable stock, a push policy on the recoverable stock, and demand-side shocks — and convert the qualitative compromise into a formal decision rule. The following three linked questions address one scientific objective: how to control closed-loop supply chains so that efficiency and resilience are balanced.

1. Supply-side resilience and the ripple effect. Model supply-side disruptions — upstream supply stoppages or raw-material shocks, and their propagation through the forward and reverse loops of the closed-loop system — and quantify how such shocks propagate into the serviceable inventory, the recoverable inventory, and the manufacturing and remanufacturing order rates. Determine how POUT controller tuning (the time constant $T_I$) mitigates or amplifies these upstream ripple effects, and establish whether the demand-side trade-off structure — resilience maximized at $T_I = 1$, efficiency at $T_I^* > 1$, with the compromise interval $1 < T_I < T_I^*$ — persists, reverses, or changes form under supply-side shocks.

2. Other closed-loop structures and inventory-control combinations. Repeat the efficiency–resilience trade-off analysis for the alternative closed-loop structures named by the source — pure remanufacturing systems (closed-loop systems in which demand is met exclusively from remanufactured returns, with no manufacturing stream for new products) and recycling-dominant networks (networks in which value recovery proceeds mainly through material recycling rather than product remanufacturing) — and for a bounded set of alternative inventory-control combinations replacing the POUT/push pairing: pull control of the recoverable stock with POUT control of the serviceable stock, POUT control on both the serviceable and the recoverable stock, and proportional control of the recoverable stock. These two structures and these three policy combinations delimit the settings considered here. For each such setting, establish whether the compromise-interval logic and the structural findings of the source study (the effect of the return yield, and resilience being maximized when the remanufacturing and manufacturing lead times are equal) carry over, and identify which structures or policy combinations permit a better integration of efficiency and resilience.

3. Risk-aware tuning rule. Formalize the decision rule that the source only sketches: an explicit procedure that takes as inputs the estimated probabilities of disruption events and the cost weights of the efficiency metric, and returns a prescribed $T_I$ within the compromise interval $1 < T_I < T_I^*$, together with the conditions under which the prescription is optimal or at least dominates the extreme choices $T_I = 1$ and $T_I = T_I^*$.

References

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