Modeling demand flexibility in electrified supply chains: optimizing manufacturing and transport under carbon pricing

1 Introduction

This study explores the untapped potential of fully electrified logistics ecosystems—encompassing both cargo movement and fabrication processes—to serve as mid-to-long horizon demand modulators for the power grid. The transition from fossil-fueled operations to electricity-driven systems in manufacturing and freight sectors has gained increasing attention as a strategy to decarbonize large-scale industrial activities. Unlike conventional fuels, electricity can be sourced from variable renewable energy (VRE) assets such as wind and solar, which are now supported by advanced low-carbon generation technologies.

However, the integration of such VRE resources introduces inherent volatility into the grid due to their stochastic and intermittent nature. Although battery-based energy storage technologies have emerged as a promising remedy to high-frequency fluctuations, their economic feasibility remains constrained by capital intensity and cycle dependency (Li et al., 2016; Hu et al., 2022; Mwasilu et al., 2014; Ma et al., 2024). These systems excel in short-term buffering but fall short in addressing multi-day generation troughs—common under sustained low-wind conditions. Pumped-hydroelectric storage is the most mature large-scale storage option and can provide multi-hour to multi-day balancing where suitable hydrological and siting conditions exist (Barbour et al., 2016). Nevertheless, its deployment is geographically constrained and permitting-intensive; other alternate long-duration storage modalities are generally in earlier stages of technical maturity (Wang et al., 2022; Jenkins and Sepulveda, 2021).

An alternative mitigation route is to adjust electricity consumption dynamically—a strategy broadly categorized as demand-side modulation. Among various flexible loads, electric mobility has shown particular promise. Charging of electric vehicles (EVs), especially underutilized during extended parking intervals, can be postponed to align with grid conditions without compromising user convenience (Mathieu et al., 2025). Research to date has demonstrated the technical viability of both uni-directional smart charging (Crozier et al., 2020b; Das et al., 2020; Fesli and Ozdemir, 2024) and bi-directional vehicle-to-grid (V2G) integration (Crozier et al., 2020a). Nevertheless, most implementations concentrate on residential EVs, whose mobility routines impose tight temporal constraints.

Fleet-oriented scenarios—spanning electric buses (Manzolli et al., 2022; Zhuang and Liang, 2021; Purnell et al., 2022), taxis (Yu et al., 2024), and logistics fleets (Mohammadian et al., 2025; Hill et al., 2012; Wang et al., 2024; Severiano and Crozier, 2024)—introduce greater operational elasticity. Here, tasks can be redistributed among vehicles, enabling more sophisticated temporal load-shifting strategies that unify routing, battery constraints, and energy optimization. Objectives across such frameworks differ widely, ranging from rapid recharge Schuller et al. (2014), base-only charging policies (Al-Hanahi et al., 2022), route-based energy minimization (Woo et al., 2024), to cost-optimal charging trajectories (Mohammadian et al., 2025). Still, these approaches are primarily constrained to short-term flexibility (typically within hours) (Gerritsma et al., 2019; Nolan and O’Malley, 2015).

Parallel efforts have examined production systems as candidates for longer-term responsiveness. In manufacturing domains with schedule slack, facilities can reshape operational timelines in response to energy market signals (Yang et al., 2020; Wang and Li, 2013; Lu et al., 2021; Huang et al., 2017). Yet, existing studies typically isolate a single plant without accounting for distribution logistics, limiting their applicability to broader supply networks. A critical insight arises when considering that production deferrals are only viable if downstream delivery windows remain unaffected. This motivates our central hypothesis: when transportation and manufacturing are jointly electrified and centrally orchestrated, their combined flexibility may unlock new forms of temporally extended grid support.

To investigate this hypothesis, we develop a unified optimization framework for managing electric-powered production and logistics under a shared objective. We test its efficacy using a stylized case focused on high-intensity material distribution across a regional corridor. Our contributions are threefold: (1) we present a system-level formulation for jointly scheduling electrified mobility and fabrication; (2) we demonstrate that temporally shifted electricity demand—on the order of days—can emerge as a cost-minimizing response to carbon-aware pricing signals; and (3) we perform a comprehensive sensitivity analysis to uncover which cost drivers and system properties most influence flexibility outcomes.

2 Model formulation

This section presents the proposed planning formulation for co-optimizing production and logistics activities within an electrified industrial network. The system is centrally orchestrated to harness latent flexibility across fabrication sites and zero-emission freight operations. As illustrated in Figure 1, the process pipeline is structured into three interconnected components: renewable-powered production, battery-electric distribution, and renewable resource interfacing.

2.1 Coordination perspective and modeling assumptions

The theoretical perspective combines integrated supply-chain planning with demand-response aggregation. Integrated planning internalizes the interdependence among production, inventory, and transport decisions that would otherwise be optimized separately (Stadtler, 2005); demand-response theory similarly treats portfolios of flexible loads as resources that can be scheduled against power-system conditions (Siano, 2014). The centralized formulation used here is therefore a system-planning benchmark: it estimates the physical and economic flexibility available when cross-stage coordination frictions are removed. It is not intended as a normative claim that a single public or private actor should control an entire regional supply chain.

The benchmark rests on five explicit coordination assumptions. First, a vertically integrated firm, logistics control tower, or authorized aggregator has decision rights over production starts, inventory, truck dispatch, and charging. Second, the coordinator receives complete and truthful operational data from participating sites and vehicles. Third, demand deadlines and renewable-availability traces are known over the 4-week planning horizon; the optimization is deterministic and does not represent forecast error or recourse. Fourth, schedules are enforceable and the model excludes strategic behavior, bilateral bargaining, privacy costs, transaction costs, and the distribution of gains among independently owned firms. Fifth, the aggregate power balance uses a copper-plate approximation and therefore does not represent local network congestion or node-specific electricity prices.

These assumptions define both the interpretation and the boundary of the results. Centralization provides an upper-bound estimate of coordinated flexibility rather than a prediction of what an uncoordinated market will deliver. In a decentralized supply chain, implementation would require contracts, time-varying tariffs, or an aggregator mechanism that aligns private incentives with the system objective; absent such mechanisms, realized flexibility may be lower. Decentralized and game-theoretic demand scheduling offers one possible extension for explicitly representing participant autonomy (Mohsenian-Rad et al., 2010). The present study deliberately isolates the physical scheduling potential before introducing those institutional frictions.

2.2 Renewable-energized production modules

Let P denote the set of discrete fabrication modules indexed by ϕ. Each module ϕ operates for a temporal window of δ ϕ scheduling intervals, consuming ξ ϕ kilowatts of electrical power per production unit throughout the process window. Each unit of fabrication draws λ ϕ kilograms of base input material and outputs ν ϕ kilograms of finished goods.

The system must also account for externally governed inflows and outflows—specifically, imported goods, unregulated raw material deliveries, and market-driven demand for output. These dynamics are treated as immutable with respect to the optimization process and thus excluded from the profit-cost structure.

To encode these exogenous flows, let Π i [ t ] denote the net exogenous balance of final goods at site i and timestep t. Here, Π i [ t ] > 0 represents supplemental inbound finished products (e.g., cross-border imports), while Π i [ t ] < 0 represents inelastic demand which must be fulfilled. Additionally, define F i [ t ] as the quantity of raw material (in kilograms) passively arriving at location i at time t.

These uncontrollable terms play a key role in constraining internal decision variables—ensuring that fabricated output and intra-network distribution remain consistent with external logistics realities.

2.3 Battery-powered freight coordination

We model a centralized pool of V electric freight vehicles, each equipped with a battery storage module of capacity Ω max kilowatt-hours. Let R i j denote the feasible routing matrix, where a path from node i to node j is admissible if the transit energy ε i j required does not exceed on-board capacity, i.e., ε i j ≤ Ω max.

Define ϒ i [ t ] as the count of idle vehicles stationed at node i during interval t, which are eligible for localized energy exchange with co-located infrastructure (e.g., vehicle-to-building load support). The model excludes any vehicle-to-grid (V2G) export capabilities to simplify power balance representation. Two distinct logistics flows are encoded: ψ i j [ t ] vehicles dispatching with cargo from node i to j, and ψ ̄ i j [ t ] denoting empty returns or repositioning trips. This distinction is critical because energy consumption scales with vehicular payload. The energy cost of an unloaded trip is weighted by a proportionality factor defined later in the energy accounting constraints. In the applied case study, the set of logistics nodes consists of the 20 demand centers listed in Table 1; Charlotte and Savannah are also modeled as manufacturing nodes. The freight network is fully connected subject to the battery-feasibility condition ε i j ≤ Ω max, and the distance inputs are derived from the nodal coordinate pairs shown in Figure 2. Renewable generation is treated as node-level availability: each demand or production node is assigned an hourly wind–solar profile, and the optimization decides when production and vehicle charging draw from this available renewable supply versus carbon-intensive backup.

TABLE 1. Demand-center nodes and manufacturing-plant locations used in the East Coast cement case study.

Monthly demand values are normalized shares used to allocate the USGS state-level cement consumption data; the absolute monthly totals are scaled from the January–June 2024 average.

2.4 Distributed renewable input layer

At each spatial node i and interval t, denote ρ i [ t ] as the renewable generation potential (kW), available from on-site or regionally allocated clean energy sources. The formulation embeds an implicit incentive mechanism favoring renewables by penalizing supplemental draw from carbon-intensive sources. This differentiation in power procurement cost is interpreted economically as a policy-induced emissions charge, comparable to a carbon levy. We analyze two distinct tax regimes: a moderate scenario σ low = $ 50 / ton - CO 2 and a stringent case σ high = $ 250 / ton - CO 2, both consistent with forward-looking global decarbonization frameworks (Barrage and Nordhaus, 2024). Assuming a marginal emissions factor φ = 0.389 k g C O 2 / k W h—consistent with combined-cycle gas turbines—the above tax rates yield per-unit clean energy incentives of θ low = $ 19.45 / M W h and θ high = $ 97.25 / M W h, respectively.

2.5 System-level optimization framework

We consider the joint coordination of energy, production, and freight operations over a discrete planning horizon consisting of T hor uniform intervals, each of duration Δ τ hours. The objective of the proposed supply-chain flexibility model is to minimize the total system cost J SC, encompassing both amortized infrastructure investments and dynamic operational expenditures:In Equation 1, C infra is a levelized capital-cost rate ($/h), whereas C oper is the total operating cost accumulated over the planning horizon. Therefore, all terms inside the parentheses have monetary units.

min J SC = Δ τ ⋅ T hor ⋅ C infra + C oper (1)

The capital expenditure component C infra includes all long-term assets deployed in the system:In Equation 2, κ veh, κ sto, and κ fab are the levelized unit cost rates of electric vehicles, warehouse storage, and production infrastructure, respectively. The term S n denotes storage capacity at node n, and P ϕ , n denotes the rated throughput of fabrication module ϕ at site n.

C infra = κ veh ⋅ V + ∑ n κ n sto ⋅ S n + ∑ ϕ κ ϕ fab ⋅ P ϕ , n (2)

Operational costs C oper are modeled based on energy consumption, distinguishing between renewable and non-renewable sources:In Equation 3 ζ carbon is the cost penalty per kWh of non-renewable usage, ω [ t ] is the grid power drawn from carbon-based generation at time t, and π n [ t ] is the total electric load (including both renewable and non-renewable) at site n and time t. A small coefficient η accounts for base electricity-consumption charges in $/kWh; the factor Δ τ is therefore included in both operating-cost terms.

C oper = ζ carbon ∑ t ω t Δ τ + η ∑ t , n π n t Δ τ (3)

To track the dynamic system evolution, we define the following state variables:

• Γ n [ t ]: aggregate battery charge level of vehicles parked at site n;
• ϒ n [ t ]: count of parked vehicles at site n;
• Σ n [ t ]: finished-goods inventory at site n;
• Φ n [ t ]: raw-material reserves at site n.

The transition constraints for these states are:

Γ n t − Γ n t − 1 = Δ τ π n t − ∑ ϕ ∑ δ = 0 δ ϕ ξ ϕ ⋅ μ ϕ , n t − δ − ∑ m ε n m ψ n m t + θ ⋅ ψ ̄ n m t ∀ n , t (4a)

ϒ n t − ϒ n t − 1 = ∑ m − ψ n m t − ψ ̄ n m t + ψ m n t − δ m n + ψ ̄ m n t − δ m n ∀ n , t (4b)

Σ n t − Σ n t − 1 = Π n t + Ω load ∑ m ψ m n t − δ m n − ψ n m t + ∑ ϕ ν ϕ ⋅ μ ϕ , n t − δ ϕ ∀ n , t (4c)

Φ n t − Φ n t − 1 = F n t − ∑ ϕ λ ϕ ⋅ μ ϕ , n t ∀ n , t (4d)

Here, μ ϕ , n [ t ] is the workload of fabrication unit ϕ at node n and time t, and δ m n denotes travel time from node m to n. The parameter θ = Ω empty Ω empty + Ω load accounts for weight-based energy adjustments between loaded and unloaded trips. Equations 4a–d track four coupled inventories. The first line is the aggregate vehicle-battery energy balance at node n: charging increases stored energy, active production consumes site electricity, and loaded or empty vehicle departures reduce the battery energy available at that node. The second line updates the number of parked vehicles by subtracting departures and adding arrivals after their travel-time lag. The third line is the finished-product inventory balance, where customer demand or exogenous inflow, loaded shipments, and completed production jointly determine stock. The fourth line updates raw-material inventory by adding exogenous material arrivals and subtracting material consumed by production.

We now impose coupling constraints among these variables:

Γ n t − Γ n t − 1 ≤ 1 τ chg ⋅ Δ τ ⋅ Ω max ⋅ ϒ n t − 1 ∀ n , t (5a)

Γ n t ≤ Ω max ⋅ ϒ n t ∀ n , t (5b)

S n ≥ Σ n t + Φ n t ∀ n , t (5c)

The local coupling constraints in Equations 5a–c prevent the model from creating unrealistic flexibility. Equation 5a limits the hourly increase in vehicle-battery energy by the number of parked trucks and their charging rate. Equation 5b ensures that the aggregate battery energy at a node cannot exceed the physical battery capacity of the trucks parked there. Equation 5c links the installed warehouse capacity to the maximum combined inventory of finished goods and raw material.

V ≥ ∑ n ϒ n t + ∑ n , m ∑ δ = 0 δ n m ψ n m t − δ + ψ ̄ n m t − δ ∀ t (6a)

P ϕ , n ≥ ∑ δ = 0 δ ϕ μ ϕ , n t − δ ∀ ϕ , n , t (6b)

Equations 6a,b, define the infrastructure sizing logic. The required fleet size must cover both parked vehicles and vehicles currently in transit, while the installed production capacity must cover all production jobs that are active during their process duration. These constraints are the reason that shifting production or transport in time can change capital requirements, not only hourly electricity use.

Additionally, to prevent exploitation of initial/final conditions, we enforce cyclical boundary constraints. In words, the model must end the horizon with the same finished-goods inventory and aggregate vehicle-battery energy with which it started. This avoids artificially improving the objective by depleting warehouses or vehicle batteries at the final time step:

Σ n 1 = Σ n T hor (7a)

Γ n 1 = Γ n T hor (7b)

Equation 7a and Equation 7b enforce cyclical boundary conditions for finished-goods inventory and aggregate vehicle-battery energy. All relevant decision variables are constrained to be non-negative:

ω t , ψ n m t , ψ ̄ n m t , μ ϕ , n t , Φ n t , Σ n t , S n , ϒ n t , V , Γ n t ≥ 0 (8)

Equation 8 enforces the non-negativity of all relevant decision variables. To guarantee physical feasibility, we impose the following system-level energy balance at each time step using a copper-plate approximation:

∑ n π n t ≤ ∑ n ρ n t + ω t ∀ t (9)

Equation 9 ensures that aggregate energy demand is supported by available renewable generation and dispatchable carbon-intensive backup. This ensures that aggregate energy demand is supported by available renewable generation ρ n [ t ] and dispatchable carbon-intensive backup ω [ t ].

2.6 Virtual energy buffering benchmark

To benchmark the effectiveness of intrinsic supply chain flexibility against conventional energy storage approaches, we introduce a comparative formulation based on a centralized Energy Reserve Model (ERS). This auxiliary model estimates the economic trade-offs of installing stationary batteries at logistics and production hubs under identical external conditions.

Unlike the flexible supply chain model, the ERS benchmark assumes a fixed operational profile for both freight scheduling and fabrication, derived from a baseline cost-minimizing configuration without emissions penalties (i.e., ζ carbon = 0). This isolates the economic value contributed by temporal arbitrage using grid-scale storage alone. The ERS problem is not a second objective in a multi-objective formulation; it is a separate benchmark solved after the supply-chain schedule is fixed. Its objective is to minimize the combined stationary-storage investment and electricity cost under the ERS strategy, denoted by J ERS:In Equation 10, JERS is the total ERS benchmark cost, Bcap represents the total installed stationary battery energy capacity (kWh), and κ^ERS denotes its levelized cost per unit capacity over the planning horizon. The variables ω [ t ] and χ [ t ] correspond to non-renewable procurement and total power consumption at time t, respectively.

min J ERS = κ ERS ⋅ B cap + ζ carbon ∑ t ω t Δ τ + η ∑ t χ t Δ τ (10)

The ERS dynamics are governed by the following energy storage evolution and feasibility constraints:

B t − B t − 1 = Δ τ − χ t + ρ t + ω t − ρ curt t ∀ t (11a)

B t ≤ B cap ∀ t (11b)

B 0 = B T hor (11c)

Equation 11a updates the internal energy level B [ t ] at each step, accounting for consumption χ [ t ], available renewable input ρ [ t ], non-renewable fallback ω [ t ], and any curtailed clean energy ρ curt [ t ]. Constraint Equation 11b ensures the storage level never exceeds its rated capacity. The cyclical constraint Equation 11c enforces temporal neutrality, avoiding exploitation of initial-final imbalances.

B cap , B t , ω t , χ t , ρ curt t ≥ 0 ∀ t (12)

Equation 12 enforces non-negativity for all ERS-related variables.

This formulation provides a reference case in which load shifting is achieved solely via electrochemical storage. It offers a clear economic contrast with the flexible supply chain design, where similar renewable-integration objectives are met through schedule adjustments and inventory/fleet buffers rather than through additional stationary batteries.

3 Experimental scenario configuration

This section details the setup, assumptions, and modeling parameters of the applied industrial case study designed to assess the performance of coordinated electrified supply chain operations. We selected cement production because the industry is characterized by highly energy-intensive thermal processing. Conventional cement production is thermal-energy dominated: high-temperature kiln heat is the major energy service, while electricity is mainly used for grinding, fans, material handling, and auxiliary equipment (International Energy Agency and Cement Sustainability Initiative, 2018). The present case study therefore should be read as an electrified, schedulable abstraction of the high-temperature process load, not as a detailed kiln-chemistry model. Additionally, the cement industry is a major contributor to global CO 2 emissions, thus offering substantial environmental benefits if thermal services can be electrified and powered via low-carbon electricity.

We construct and evaluate the system across a geographically distributed network, simulating operations of manufacturing and logistics in a renewable-integrated power environment.

3.1 Scenario parameterization

In this study, the cement production process is abstracted as a single-stage electrified thermal conversion unit characterized by the parameters listed in Table 2. The abstraction represents the clinker-related high-temperature stage as a controllable batch-equivalent electric load rather than modeling kiln chemistry, preheating, grinding, and cooling as separate sub-processes. One production unit consumes 56,667 kWh during one hourly scheduling interval and produces 150,000 kg of finished material; hence the modeled controllable electricity requirement is approximately 377.8 kWh/t. The 1-h process duration is therefore a dispatch interval for the batch-equivalent load, not a claim that a physical cement kiln completes the full thermal process in 1 h. Flexibility is represented through the number of active production units in each hour. If M i units are installed at plant i, the hourly production rate can vary between 0 and 150,000 M i kg/h, and the associated electrical load can vary between 0 and 56.667 M i MWh/h. Thus, in the optimization, production can be modulated at an hourly rate by switching integer/batch-equivalent production units on or off, while cumulative demand feasibility is maintained through warehouse inventory. This assumption is intended to capture medium-duration scheduling flexibility rather than sub-hourly ramping; minimum up/down times, kiln thermal inertia, and product-quality constraints are therefore not explicitly represented and are acknowledged as limitations of the case study.

TABLE 2. Assumed cement-process parameters used in the case-study abstraction, with conventional thermal and electrical energy benchmarks shown for context.

Demand estimation is based on state-level consumption data from the U.S. Geological Survey’s Mineral Industry Surveys, capturing monthly volumes for Portland and blended cement types (Survey, 2024). The case-study demand profile was derived in three steps. First, January–June 2024 state-level cement consumption was averaged to obtain a representative monthly demand level. Second, state-level demand was allocated to the selected urban demand nodes according to their population share within the corresponding state or regional service area. Third, the resulting nodal monthly total was imposed either as an end-of-month cumulative requirement or as four equal end-of-week cumulative requirements in the weekly-demand sensitivity case. Because the objective of the paper is to evaluate supply-chain flexibility rather than to forecast construction activity, intra-day stochastic demand fluctuations are not modeled; demand enters as cumulative fulfillment constraints. Table 1 reports the nodal demand-center definition used in the case study.

For freight operations, we model electric heavy-duty transport units with technical specifications aligned with the 2024 Tesla Semi (Ali, 2025). Each truck is assigned a full-charge duration of μ = 2 hours and equipped with a 900 kWh battery pack, translating to a peak charging rate of 450 kW. Each unit has a capital cost of $150,000 and a cargo capacity of 20,000 kg. The 30-year truck asset life is used only for levelizing the non-battery vehicle platform and logistics asset, not as a physical battery lifetime. Battery replacement and drivetrain maintenance are implicitly represented in the levelized vehicle-cost parameter. In the comparative ERS (Energy Reserve System) configuration, the stationary storage cost is assumed to be $400/kWh, with a 5-year economic lifespan. Because the vehicle-cost and battery-lifetime assumptions strongly affect the relative attractiveness of truck-based flexibility and ERS storage, Section 5 reports a one-order-of-magnitude sensitivity test for truck and manufacturing costs, and explicit battery-degradation modeling is identified as an important extension.

The transportation network spans 20 urban demand centers along the eastern seaboard of the United States, from Miami in the south to Boston in the north, and extending westward to Mobile, AL. Two central production hubs are located in Charlotte, NC, and Savannah, GA, operating under identical process constraints. Great-circle road-equivalent distances between all nodes are used to parameterize transport time and energy demand, and routes are configured such that any inter-city path can be traversed without intermediate charging. Figures 2 and 3 provide the physical nodal setup, including the assumed demand centers, the two manufacturing plants, representative freight corridors, and their geographical relationship to node-level renewable profiles.

Operational planning is performed at an hourly resolution, i.e., each optimization time step represents 1 h. The main simulations use a 4-week window (T = 672 hours), during which cumulative cement demand in each city must be satisfied by the end of the period. The use of 2024-era truck specifications together with a 2019 renewable trace is intentional: the truck data define a prospective technology scenario, while the renewable trace supplies a historical weather-driven generation profile. The model does not claim to reproduce a real 2019 freight system. The 2019 renewable profile was screened to select a 4-week interval that includes both diurnal solar variability and multi-day wind variability; therefore, the horizon is intended to test medium-duration shifting rather than only typical daily cycling. We did not optimize the renewable portfolio over a full year, and this limitation is now stated explicitly. With the present hourly 4-week formulation, a single scenario solve typically completes within minutes on a standard workstation, although run time varies with the number of active routes, integer relaxations, and solver settings.

The renewable power profile is constructed using 2019 hourly generation data for both photovoltaic and wind resources (Pfenninger and Staffell, 2016). In the baseline case, each node is assigned 276 MW of renewable nameplate capacity, split equally into 138 MW solar and 138 MW wind. This value was selected so that the aggregate 4-week renewable energy potential is of the same order as, but does not trivially exceed, the total electricity demand of production and transport; it therefore creates a non-degenerate flexibility problem in which scheduling decisions affect renewable utilization. The equal solar/wind split is a neutral benchmark rather than an optimized generation mix; equal capacity across nodes is not required by the mathematical formulation, but was imposed in the case study to isolate the scheduling effect from renewable siting and sizing effects. In the phrase “capacity factors were applied uniformly,” uniform means that the same hourly normalized solar and wind capacity-factor time series are multiplied by the assigned nameplate capacity at each node. This assumption removes local meteorological diversity and is used only for a controlled first comparison; a geographically resolved renewable dataset would be preferable for planning applications. Renewable investment cost is not included in the proposed supply-chain objective in Equation 1 because the model treats renewable availability as an exogenous regional resource and focuses on the incremental value of supply-chain scheduling flexibility. To avoid underinterpreting the results, we have clarified that the reported system cost should not be read as the full greenfield cost of building both the industrial supply chain and the renewable fleet. The assumed levelized renewable cost parameters used for contextual interpretation are summarized in Table 3. Future work should endogenize renewable siting, sizing, and technology mix in a year-long co-optimization.

TABLE 3. Renewable-energy cost assumptions used for contextual interpretation.

These costs are not included as decision variables in the baseline optimization because renewable generation is treated as an exogenous regional resource.

For computational efficiency in select analyses, we also employ a reduced seven-node network representing southeastern cities with similar infrastructure properties. The reduced network is used only for sensitivity screening; the main case-study results are based on the full 20-node demand network and two manufacturing hubs shown in Figure 3.

3.2 Computational complexity reduction strategy

The optimization framework presented in the preceding sections constitutes a mixed-integer linear programming (MILP) model. This arises primarily due to the integrality constraints associated with the logistics-related decision variables, including the number of full and empty trucks dispatched along each route ( y i j ( t ) , y i j ′ ( t ) ), the number of stationary vehicles at each location ( Y i ( t ) ), and the total fleet size ( Y ̂ ).

Solving MILP formulations at scale is computationally intensive, especially under large-scale settings involving extended planning horizons and expanded spatial networks. To mitigate this challenge and improve tractability, we adopt a relaxation strategy in which the integer constraints are relaxed to continuous domains. This approximation transforms the problem into a linear program (LP), significantly reducing solution time.

While the relaxation sacrifices integrality, the resulting solution provides a tractable lower-bound cost estimate for the original minimization MILP and a continuous dispatch schedule for comparative scenario analysis. This strategy is particularly beneficial for exploring the influence of various system configurations (e.g., extended geography or temporal resolution) without incurring prohibitive computational costs.

Table 4 consolidates the principal numerical inputs used in the baseline model before the results are discussed. Values not listed in the table are either scenario outputs or are defined directly in the equations above.

TABLE 4. Main baseline input data used in the case-study optimization.

4 Simulation results

Figure 4 illustrates how the capital investment requirements evolve across different carbon pricing scenarios. Across all cases, capital expenditure is overwhelmingly dominated by the cost of electric trucks, while the right panel reports the incremental cost relative to the zero-tax case. As the carbon tax increases, the model installs additional warehouse capacity and slightly reduces manufacturing equipment, indicating that stockpiling becomes a preferred mechanism for temporal flexibility. Figure 5 then shows that truck utilization remains near 80%, consistent with the operational ceiling imposed by recharging constraints; warehouse utilization falls because installed storage capacity expands. Figure 6 presents electricity consumption by energy source for manufacturing and transportation. The data confirm that manufacturing is the dominant electricity consumer in this abstraction, reflecting the electrified representation of thermal process energy in cement production. Both manufacturing and transport increase their renewable share under the carbon penalty, with wind providing most of the additional renewable uptake because its multi-day availability patterns align better with the longer demand-settlement windows than the daily solar cycle.

Figures 4–7 show that carbon taxation changes the timing of production and renewable use, but only within the flexibility envelope created by the demand deadlines, vehicle-charging feasibility, warehouse capacity, and the exogenous renewable profile. The carbon tax is therefore not interpreted as the sole or universal driver of flexibility; in real electricity systems, time-varying wholesale prices, congestion prices, or ancillary-service signals would provide more granular incentives. The present model uses a carbon penalty as a transparent proxy for the marginal value of avoiding carbon-intensive backup generation. Figure 7 investigates the temporal characteristics of electricity demand shifting by comparing cumulative energy-consumption trajectories under scenarios with and without a carbon tax. The upper panels remain close because total demand is fixed by the cumulative fulfillment constraints. The lower panels, rather than the final cumulative total, are the relevant flexibility metric: they report when energy use is advanced or delayed within the same overall production requirement. Two demand fulfillment structures are evaluated: one in which cumulative product demand is settled by the end of the month (monthly demand), and another with weekly settlement requirements (weekly demand), the latter imposing stricter temporal constraints on production scheduling. Under the weekly regime, deviations must reset at the conclusion of each week, thereby limiting flexibility. A positive deviation implies that production has been accelerated (i.e., energy demand advanced), whereas a negative deviation reflects deferred manufacturing activity.

In the monthly demand scenario, carbon taxation induces temporal shifts in electricity consumption, with the cumulative timing difference exceeding 20 GWh over periods longer than 1 week. This difference is less than 5% of the approximately 483 GWh total 4-week energy requirement, which explains why the upper cumulative curves appear visually close. The point is not that the carbon tax changes the total amount of cement produced; the demand constraints keep final production essentially constant. Rather, the tax changes when the same energy-intensive production is scheduled, allowing it to align better with wind availability. As anticipated, the weekly demand constraint imposes tighter flexibility limits, resulting in smaller volumes of temporal demand shifting, though bidirectional adjustments are observed in both cases.

The cumulative curves in Figure 7 aggregate several non-cumulative nodal time-series decisions. The largest hour-to-hour changes arise at the manufacturing hubs, Charlotte and Savannah, because production can be advanced into high-renewable hours or delayed during low-renewable periods while inventories preserve downstream service. Demand-only nodes do not create comparable process-load shifts; their hourly behavior is dominated by inbound shipment arrivals, finished-product inventory drawdown, and vehicle charging associated with departures or returns. Consequently, the 20 GWh-scale cumulative difference should not be interpreted as a uniform change at every city. It is the system-wide sum of production pulses at the two plants, freight-charging load distributed across the route network, and inventory timing at the demand centers. To make this mechanism transparent, the revised supplementary data package reports the hourly nodal values of production activity, charging load, finished-product inventory, and loaded shipments for each scenario; the main manuscript summarizes the dominant mechanism because plotting all 20 nodes over 672 hourly intervals would obscure rather than clarify the aggregate result.

Table 5 summarizes energy use and renewable integration under varying carbon tax levels for both weekly and monthly fulfillment schemes. While higher carbon taxes lead to greater renewable uptake, the marginal improvement between 50 / t n a n d250/tn is minimal. Total energy demand remains effectively constant across scenarios, primarily due to the fixed energy requirements of cement production. Minor variations in transport-related energy use are observed, with slightly longer distances traveled under weekly demand and modest reductions in all cases as carbon tax increases. Nevertheless, these changes are negligible compared to the dominant manufacturing energy footprint.

TABLE 5. East Coast cement case study results for weekly and monthly demand scenarios.

Importantly, the similar levels of renewable usage under $50/tn and $250/tn taxes do not imply that carbon price is generally unimportant. Rather, in this specific scenario, the $50/tn case is already high enough to activate nearly all feasible schedule adjustments available under the modeled demand and capacity constraints. Once this operational flexibility is saturated, increasing the tax to $250/tn cannot create additional renewable absorption unless new flexibility resources, such as larger warehouses, alternative routing, additional vehicle batteries, stationary storage, or a different renewable profile, are introduced. This saturation effect was consistent across multiple renewable generation profiles, although alternative resource mixes may still reveal differentiated impacts at higher tax levels.

Finally, Table 6 contrasts the effectiveness of exploiting supply chain flexibility versus deploying ERS. The proposed model includes only the batteries embedded in electric trucks; it does not allow additional stationary batteries unless the ERS benchmark is activated. Allowing stationary batteries and supply-chain flexibility simultaneously would likely increase renewable utilization, but that hybrid design is outside the current comparison and is identified as future work. Results indicate that supply chain-based flexibility achieves significantly higher renewable penetration under considerably lower carbon pricing. At low carbon taxes, no battery installations are observed, implying that operational flexibility is economically viable well before grid-scale storage becomes cost-effective. Even at 400 / t n, the total installed ERS capacity remains less than that of a single electric truck, further emphasizing the superior scalability and responsiveness of supply chain adaptations. Moreover, comparable renewable integration is attained at carbon prices as low as 1 / t n (or 0.39 / M W h), highlighting the economic efficiency of demand-side flexibility mechanisms.

TABLE 6. Renewable energy utilization for the Proposed Model (Supply Chain Flexibility) and ERS under varying carbon tax levels.

5 Sensitivity analysis

The results above are based on a specific case study of electrified cement production on the U.S. East Coast. To assess their generalizability, we conduct a sensitivity analysis focusing on capital costs—specifically, truck and manufacturing equipment costs, which exert the greatest influence on system behavior. Cost changes may also serve as proxies for different product characteristics, such as transport intensity or energy density.

We explore nine cost scenarios by scaling truck and manufacturing costs by factors of 0.1, 1, and 10 relative to baseline values. Results are summarized in Tables 7, 8.

TABLE 7. Sensitivity results, part A: energy, renewable utilization, and fleet size under truck and manufacturing cost variations.

^† Indicates the lowest feasible value that still meets the system’s basic requirements.

TABLE 8. Sensitivity results, part B: manufacturing capacity, warehouse capacity, and distance under truck and manufacturing cost variations.

^† Indicates the lowest feasible value that still meets the system’s basic requirements.

In all cases, a carbon tax leads to a notable increase in renewable energy use, despite structural differences across supply chain configurations. The table shows why electric freight costs are pivotal. When trucks are inexpensive (truck-cost scale factor 0.1), the optimizer can add many vehicles and use the fleet as a scheduling resource; under the carbon-tax case, fleet size increases from 19,900 to 28,400 vehicles in the low-truck-cost cases, while total distance falls from 4.87 to 1.71 million km. This indicates that additional electric freight capacity allows the model to choose shorter and better-timed shipment patterns rather than forcing every plant to operate close to a fixed schedule.

By contrast, when truck costs are at the baseline or high level, the fleet is held at the minimum feasible level in the tested scenarios, and the adjustment shifts toward production and storage. For example, in the baseline cost case, renewable utilization rises from 38.2% to 74.3% under the carbon tax while fleet size and transport distance remain effectively unchanged; the change is instead achieved through lower installed manufacturing capacity and larger warehouse capacity. When manufacturing equipment is expensive, the model installs fewer production units and compensates with storage and shipment timing. Thus, different cost structures change not only the total cost but also the physical configuration of the optimal supply chain: cheap trucks favor transport-enabled flexibility, expensive trucks favor inventory and production-timing flexibility, and expensive manufacturing favors flatter production with larger buffers.

In each case, the objective function becomes dominated by one or two capital terms, while the rest of the system adapts to minimize their impact. This results in latent flexibility in non-dominant components, which can be leveraged to respond to power grid variability. These findings suggest that supply chains with strong cost asymmetries inherently possess temporal slack, offering untapped potential for renewable energy integration.

6 Stakeholder relevance and scope

The case study should be interpreted as a boundary-case experiment rather than a near-term deployment forecast. It assumes a fully electric heavy-duty fleet, electrified and schedulable production modules, centralized coordination, and cumulative demand deadlines. These assumptions are intentionally strong because the purpose is to identify whether a coupled manufacturing-transport system can, in principle, provide multi-day demand flexibility, and which physical or economic constraints determine the size of that flexibility. The results therefore do not imply that today’s cement supply chains can immediately operate in this way without plant retrofits, charging infrastructure, operational data integration, and market mechanisms that compensate flexible load.

The study is most directly addressed to three stakeholder groups. For industrial firms and logistics operators, the model provides a planning tool for evaluating whether investments in electric trucks, warehouse capacity, and flexible production equipment create operational value beyond emissions reduction. For grid operators and electricity-market designers, the results show that large industrial supply chains could become long-duration flexible loads if settlement rules, carbon prices, or time-varying electricity tariffs reward shifting over several days rather than only within a single day. For policymakers, the central lesson is that freight-electrification incentives and industrial demand-response policy should be considered jointly: the same electric trucks that decarbonize transport can also change the flexibility value of manufacturing and inventory decisions.

The practical implication is therefore not that every stakeholder should adopt the exact configuration in this stylized network. Rather, stakeholders can use the framework to test where their own system sits in the cost-structure space shown in Tables 7 and 8. If electric freight capacity is inexpensive relative to production equipment, transport scheduling becomes an important flexibility lever. If freight capacity is expensive, the value shifts toward warehouse buffers and production timing. If manufacturing equipment is expensive or technically inflexible, the attainable flexibility narrows and may require other resources such as stationary storage, procurement contracts, or demand-window renegotiation.

7 Conclusion

This work developed a cost-minimizing optimization framework for a fully electrified supply chain in which manufacturing, vehicle charging, freight dispatch, and inventory are scheduled jointly. In the East Coast cement case study, the model shows that the value of electrification is not limited to replacing fossil-fueled equipment: once production and transport are coordinated, the same cumulative demand can be served with materially different hourly electricity profiles. Under monthly demand settlement, the $250/tn CO₂ case creates a cumulative timing difference exceeding 20 GWh while total 4-week electricity use remains approximately 483 GWh. This demonstrates a multi-day load-shifting mechanism, not a change in final production volume.

The quantitative added value of the proposed formulation is threefold. First, renewable utilization rises from 59.9% to 73.5% in the monthly case and from 59.5% to 73.5% in the weekly case once the carbon penalty activates feasible schedule shifts. Second, the ERS benchmark shows that stationary batteries alone remain unattractive at low carbon prices in this parameterization, whereas supply-chain scheduling reaches 74.3% renewable utilization without additional stationary storage. Third, the sensitivity analysis shows that electric truck capital cost determines the physical source of flexibility: when truck cost is scaled to 0.1 of the baseline, the carbon-tax case expands the fleet from 19,900 to 28,400 vehicles and reduces total distance from 4.87 to 1.71 million km, whereas at baseline or high truck cost the adjustment shifts toward warehouse buffers and production timing.

These findings indicate that electrified freight vehicles should be evaluated not only as transport assets, but also as components that reshape the feasible operating space of industrial supply chains. The present case is deliberately stylized and should not be read as a deployment forecast for today’s cement sector. Future work should include plant-specific kiln dynamics and ramping limits, battery degradation, geographically resolved renewable profiles, charging-infrastructure constraints, integer-feasible fleet dispatch, and hybrid designs that combine supply-chain flexibility with pumped-hydro or electrochemical stationary storage.

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Footnotes

Edited by: Solomon Giwa, Olabisi Onabanjo University, Nigeria

Reviewed by: Henrique A. Matos, University of Lisbon, Portugal

Miguel Ángel Morales Mora, College of Puebla, Mexico

Sgouris Sgouridis, Dubai Electricity and Water Authority, United Arab Emirates