Dual Sourcing for Critical Energy Equipment under Exchange-Rate and Fuel-Price Volatility

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1. Introduction

Critical energy equipment is characterised by high unit value, long manufacturing cycles, a small number of qualified suppliers and severe consequences of non-availability. A failed generator step-up transformer or an unavailable set of turbine blades can idle hundreds of megawatts for months, and the cost of that idle capacity (lost energy sales, contractual penalties, emergency rental generation and reputational damage) typically dwarfs the purchase price of the missing part. Procurement teams therefore face a problem that is not well captured by price-focused tendering: they must trade off purchase cost against the reliability and timing of supply.

Studies of energy facilities in emerging markets link spare-parts availability directly to plant uptime (Okonkwo et al., 2018b; Okonkwo, Agbabiaka, et al., 2021) [198, 201], and reliability and maintenance research on power infrastructure shows that failures of high-value assets are frequent enough to make spare provisioning a recurring decision rather than a rare event (Adaramola et al., 2018; Gideon et al., 2019) [2, 102]. The year 2021 made this trade-off unusually sharp for buyers in emerging and import-dependent markets. Several currencies depreciated against the US dollar, raising the local-currency cost of imported equipment that is invoiced in dollars. Oil prices recovered from their 2020 lows to an average of roughly 70 US dollars per barrel, which raised freight and bunker surcharges and, for thermal-heavy power systems, increased dispatch hours and wear on rotating equipment. At the same time, the pandemic-era disruption of container shipping lengthened and destabilised lead times from overseas manufacturers. Buyers that had consolidated purchases with a single low-cost foreign supplier discovered that the lowest quoted price could be the most expensive choice once delays, currency moves and shortages were counted. Port congestion and demurrage were already a recognised cost driver for importers in West Africa before the pandemic (Okonkwo et al., 2020) [197], and import procedures, documentation and access to foreign exchange add further delay and uncertainty (Jones & Ominyi, 2020) [124]. Reviews of post-disruption supply chains and of force majeure practice in energy supply contracts show how quickly such shocks reach buyers (Anene, 2021; Uchechi et al., 2020) [37, 260].

Dual sourcing is the natural response, but it raises a quantitative question that practitioners often settle by rule of thumb: how much should be allocated to each source? A 50/50 split is easy to defend but rarely optimal. Procurement frameworks developed for the energy sector emphasise strategic sourcing, vendor evaluation and bid selection (Okonkwo et al., 2018a; Ahiaeke Patrick et al., 2021) [14, 200], but they seldom quantify how volume should be split when prices, lead times and supplier reliability are all uncertain. This paper develops a decision model to answer that question. The model is a single-period, two-supplier procurement problem that jointly captures currency-denominated purchase prices with partial indexation of the domestic supplier, fuel-price pass-through into freight and into demand for replacement units, stochastic lead times evaluated against a hard planning window, random domestic capacity, foreign shipment disruptions and an explicit supplier-concentration constraint. The buyer minimises a mean-CVaR objective, which expresses aversion to rare but very costly outcomes, and the analysis yields an interpretable first-order condition linking the foreign order to an effective yield that combines disruption and lateness. To our knowledge, these sources of risk have not previously been combined in a single allocation model for critical energy equipment. We illustrate the model with a numerical study calibrated to 2021 conditions, with sensitivity analysis on exchange-rate volatility, fuel-price volatility, their correlation, disruption probability, lead-time mean and variability, the domestic price premium and domestic capacity, and we translate the results into procurement guidance.

The remainder of the paper is organised as follows. Section 2 synthesises the related literature. Section 3 presents the conceptual model. Section 4 sets out the methodology, including the formal model, its structural properties, the solution approach and the calibration. Section 5 reports the results. Section 6 discusses the findings in light of prior work, Section 7 draws out theoretical, managerial and policy implications, Section 8 states the limitations, Section 9 outlines directions for future research and Section 10 concludes.

2. Literature Synthesis

2.1. Multiple Sourcing, Lead Times and Supply

Uncertainty The value of using more than one supplier has been studied extensively. Minner (2003) [158] surveys multiple-supplier inventory models and distinguishes between price-driven, lead-time-driven and reliability-driven reasons for diversification. Random-yield models, reviewed by Yano and Lee (1995) [277], treat supplier unreliability as a random fraction of the order that is delivered. Dada et al. (2007) [72] analyse a newsvendor who chooses among unreliable suppliers and show that cost is the order qualifier while reliability determines how much is ordered from each supplier beyond the cheapest. Federgruen and Yang (2008) [96] study supplier portfolio selection under demand and supply risk. Our model inherits the newsvendor structure of this stream but makes reliability depend on two distinct mechanisms, capacity shortfall and late arrival, which behave differently in the analysis.

Early analytical studies showed that, under random yield, spreading orders across suppliers can lower expected cost even when one supplier is cheaper (Anupindi & Akella, 1993; Gerchak & Parlar, 1990; Henig & Gerchak, 1990; Parlar & Wang, 1993) [40, 100, 110, 215]. Agrawal and Nahmias (1997) [12] examine how many suppliers to keep when yields are uncertain, and Swaminathan and Shanthikumar (1999) [246] show that the benefit of diversification depends on the shape of the demand distribution. Babich et al. (2007) [54] add competition and supplier default risk, and Ahiska et al. (2013) [15] characterise optimal policies under unreliable sourcing with a Markov decision process. Surveys of multiple-supplier inventory control by Svoboda et al. (2021) [245] and of newsvendor extensions by Khouja (1999) [130] and Qin et al. (2011) [218] confirm that single-period models remain the standard tool for one-off procurement of high-value items, which is the setting adopted here. A second stream studies dual sourcing between a fast, expensive source and a slow, cheap one. Classic results go back to Fukuda (1964) [98] and Whittemore and Saunders (1977) [272], who analyse two supply options with different lead times. Veeraraghavan and Scheller-Wolf (2008) [268] propose a simple dual-index policy for capacitated systems, Allon and Van Mieghem (2010) [30] introduce tailored base-surge allocation between offshore and near-shore production, and Xin and Goldberg (2018) [275] prove its asymptotic optimality, while Sun and Van Mieghem (2019) [241] extend the analysis to robust capped dual-index policies. Tomlin and Wang (2005) [253] and Wang et al. (2010) [270] compare dual sourcing with mix flexibility and with process improvement, Tomlin (2009) [252] considers learning about supplier reliability, and Yang et al. (2009) [276] study backup production under asymmetric information. Disruption-oriented dual-sourcing models are developed by (Hu et al., 2013; Silbermayr & Minner, 2014; Xanthopoulos et al., 2012; Yu et al., 2009) [113, 237, 274, 279]. The domestic-foreign structure of the present model mirrors the base-surge logic with the roles reversed: the near source carries the base load because it is reliable, and the distant source supplies the surge. Stochastic lead times have their own literature. Kaplan (1970) [127] and Zipkin (1986) [280] derive optimal policies when lead times are random, and Song (1994) [240] shows that greater lead-time variability does not always raise costs or stock levels, a result that anticipates the effective-yield finding of Section 4.4. Order splitting across suppliers to pool lead-time risk is examined by Sculli and Wu (1981) [229] and Ramasesh et al. (1991) [219] and reviewed critically by Thomas and Tyworth (2006) [250]. Capacity uncertainty, which we use to model the domestic supplier, is treated by Ciarallo et al. (1994) [70]. Textbook treatments of these models appear in (Arrow et al., 1951; Chopra & Meindl, 2016; Porteus, 2002; Silver et al., 2017; Zipkin, 2000) [43, 65, 217, 238, 281].

2.2. Disruption Risk and Supply Chain Resilience

Tomlin (2006) [251] compares mitigation strategies (inventory, sourcing) and contingency strategies (rerouting, volume flexibility) for a firm exposed to supplier disruptions, and shows that the preferred strategy depends on disruption frequency and duration and on the firm's risk attitude. Kleindorfer and Saad (2005) [132] propose a broader framework for disruption risk, and Sheffi and Rice (2005) [233] emphasise redundancy and flexibility as sources of resilience. Snyder et al. (2016) [239] review operations research models of supply chain disruption. Most of this work treats prices as known; the present paper adds price risk from currency and fuel markets.

Empirical evidence shows why disruptions deserve explicit modelling: announcements of supply chain glitches are followed by significant falls in shareholder value and by lasting increases in equity risk (Hendricks & Singhal, 2003, 2005) [108, 109]. Conceptual frameworks for supply risk and resilience were developed by (Chopra & Sodhi, 2004; Christopher & Peck, 2004; Craighead et al., 2007; Ponomarov & Holcomb, 2009; Tang, 2006a, 2006b) [67, 69, 71, 216, 247, 248], and Chopra et al. (2007) [66] argue that recurrent and disruption risks call for different responses. Ho et al. (2015) [112] organise the supply chain risk management literature, and the COVID-19 pandemic renewed interest in ripple effects and in the viability of intertwined supply networks (Ivanov & Dolgui, 2020; Ivanov et al., 2019) [121, 122].

For imported equipment, lead-time variability largely reflects maritime schedule reliability. Liner services frequently miss their scheduled arrival times, and these delays propagate into hinterland supply chains (Notteboom, 2006; Vernimmen et al., 2007) [160, 269]; the pandemic magnified the effect through port congestion and capacity withdrawals (Notteboom et al., 2021) [161]. Import compliance and customs interdiction regimes add further variability (Aneke & Adesemoye, 2021) [36], while integrated procurement information systems and chain-of-custody frameworks improve the planning and traceability of inbound orders (Ahiaeke Patrick et al., 2020; Aneke & Adesemoye, 2019) [13, 34].

2.3. Price Risk and Risk-Averse Procurement

Kazaz et al. (2005) [128] show how exchange-rate uncertainty shapes global production and allocation decisions, and Ding et al. (2007) [81] integrate operational decisions with financial hedging in global markets. These papers establish that operational flexibility, including the ability to switch supply sources, acts as a real option against currency movements. Our setting differs in that the buyer is in a weak-currency economy procuring capital equipment, the domestic price is itself partially indexed to the exchange rate, and there is no assumption that financial hedges are available or cheap, which is realistic for many emerging-market utilities. Exchange-rate exposure in global sourcing has often been framed as a real option. Kogut and Kulatilaka (1994) [134] value the flexibility of a multinational production network, Huchzermeier and Cohen (1996) [114] quantify the value of switching production under currency risk, Dasu and Li (1997) [80] derive optimal operating policies under exchange-rate variability, and Lowe et al. (2002) [149] screen location strategies for currency risk. Kouvelis (1999) [138] reviews global sourcing under exchange-rate uncertainty, and Van Mieghem (2003) [267] links capacity investment to operational and financial hedging. The real-options perspective of (Dixit & Pindyck, 1994; Trigeorgis, 1996) [82, 256] provides the conceptual basis for treating a second supplier as an option on supply.

Commodity and input-price risk has been studied in procurement with spot markets (Haksöz & Seshadri, 2007; Seifert et al., 2004) [106, 230], portfolio and option contracts (Fu et al., 2010; Martínez-de-Albéniz & Simchi-Levi, 2005) [97, 151], stochastic purchase prices (Berling & Martínez-de-Albéniz, 2011; Goel & Gutierrez, 2011) [57, 104] and joint inventory and financial hedging (Caldentey & Haugh, 2006; Gaur & Seshadri, 2005; Kouvelis et al., 2013) [61, 99, 139]. Oil price shocks have long been shown to affect macroeconomic activity, with effects that differ according to whether they originate in supply or demand (Hamilton, 1983; Kilian, 2009) [107, 131], and energy prices are among the most volatile of all commodity prices (Regnier, 2007) [220]. Fuel prices also shape shipping operations, because carriers adjust vessel speed and fleet size when bunker costs rise (Ronen, 2011) [225]. These links motivate the joint modelling of fuel and exchange-rate shocks in Section 4.

We measure tail risk with Conditional Value-at-Risk, introduced for optimisation by Rockafellar and Uryasev (2000, 2002) [223, 224]. CVaR is coherent, easy to communicate (the average cost in the worst 5 percent of scenarios) and admits a linear-programming representation under sampled scenarios, which makes it attractive for procurement committees that must justify decisions to boards and regulators.

CVaR satisfies the axioms of coherent risk measures (Artzner et al., 1999) [44] and is often preferred to Value-at-Risk because it accounts for the size of losses beyond the quantile (Jorion, 2007; Sarykalin et al., 2008) [126, 228]. Its optimisation properties are summarised by Rockafellar (2007) [222] and applied to portfolio selection by Krokhmal et al. (2002) [140], building on the mean-variance tradition of Markowitz (1952) [150]. In inventory theory, risk aversion has been introduced through expected utility (Eeckhoudt et al., 1995) [88], mean-variance criteria (Choi et al., 2008) [64], Value-at-Risk (Tapiero, 2005) [249] and CVaR (Chen et al., 2009; Gotoh & Takano, 2007; Wu et al., 2013) [63, 105, 273], and Chen et al. (2007) [62] characterise risk-averse policies in a multi-period setting. Our formulation follows the CVaR newsvendor of Chen et al. (2009) [63] and the random-capacity extension of Wu et al. (2013) [273], adding currency, fuel and lead-time uncertainty.

2.4. Procurement of Critical Equipment in Emerging

Energy Markets A growing applied literature addresses procurement and supply risk for energy and infrastructure operators in emerging economies. Agbabiaka et al. (2019) [7] propose a supply chain risk management model for engineering, procurement and construction (EPC) and gas processing projects, and Ogunwole et al. (2021) [193] develop a resilience framework for critical infrastructure and gas processing plants. Okonkwo et al. (2018a) [200] set out a framework for strategic procurement optimisation in oil and gas operations, while Okonkwo et al. (2018b) [201] and Okonkwo, Agbabiaka, et al. (2021) connect inventory availability and materials readiness to plant uptime and maintenance performance. Contract and vendor governance are treated by Okonkwo et al. (2019) [202], regulatory compliance in high-risk energy procurement by Okonkwo, Ogunwole, et al. (2021), and data-driven vendor evaluation by Ahiaeke Patrick et al. (2021) [14]. On the logistics side, Okonkwo et al. (2020) [197] model demurrage and port efficiency in emerging economies, and Nnabueze et al. (2021) [159] and Ike et al. (2021) [116] examine end-to-end visibility and supplier relationship management as sources of resilience. Contractual risk allocation for high-value energy services and the role of force majeure clauses are reviewed by Uchechi and Ominyi (2019) [259] and Uchechi et al. (2020) [260]. Currency risk from the buyer's perspective is addressed in work on tiered treasury architecture and foreign-exchange control (Dada et al., 2021a) [73] and on cross-border strategic finance (Isiekwu et al., 2021) [120]. These contributions are largely conceptual or framework-based; they identify the relevant risks and governance levers but do not provide a quantitative rule for splitting volume between suppliers. The present model is intended to supply that rule.

Related applied work examines capital project delivery and programme management for high-risk infrastructure (Aminu-Ibrahim et al., 2019, 2021; Nwafor et al., 2019b; Ogbete et al., 2021) [32, 33, 162, 191], capital budgeting in upstream energy (Nwangwu et al., 2021) [163], and statutory and regulatory compliance in energy licensing and bidding (Ominyi et al., 2020; Uchechi & Ominyi, 2020; Uchechi et al., 2019) [204, 259, 260]. Studies of contractor governance and operational integrity in high-risk energy operations (Arumosoye & Obriki, 2020; Nwangwu et al., 2018; Obogo, Uduokhai, et al., 2021) [47, 164, 181] and of agile supply chain digital transformation with embedded IT risk controls (Mbonu et al., 2020a) [155] complete the picture of the operating environment in which critical equipment is procured.

Supplier selection has been studied for decades, and Weber et al. (1991) [271] summarise the criteria and methods used in early work. Multi-criteria methods such as the analytic hierarchy process combined with linear programming remain popular (Ghodsypour & O'Brien, 1998) [101], and reviews by Ho et al. (2010) [111] and Aissaoui et al. (2007) [21] document the shift from pure selection towards joint selection and order-quantity allocation. Applied work in emerging markets has examined procurement process automation and transparency (Akinleye & Adeyoyin, 2021) [24], analytics for procurement profitability (Akin-Oluyomi et al., 2020) [23], data-driven operations management (Efobi et al., 2021) [89], ESG-integrated and circular-economy procurement decisions (Okojie & Abioye, 2020; Okojie et al., 2020) [195], and supply chain talent and capability building (Falemi et al., 2020) [95]. Supplier concentration is commonly measured with the Herfindahl-Hirschman Index (Rhoades, 1993) [221], which we adopt as a governance constraint.

Power systems in Sub-Saharan Africa have long been constrained by under-investment, weak utility finances and unreliable supply (Eberhard et al., 2008, 2016; Trimble et al., 2016) [86, 87, 257], and the Nigerian sector in particular has suffered from low availability of installed capacity (Emodi & Boo, 2015; Oseni, 2011; Oyedepo, 2012) [90, 211, 213]. The International Energy Agency (2019) [117] outlook highlights the region's growing equipment needs, and global analyses point to rising demand for grid equipment and the materials it requires as energy transitions accelerate (International Energy Agency, 2021a, 2021b) [118, 119]. Within utilities, spare-transformer provisioning has been modelled probabilistically (Chowdhury & Koval, 2005; Li et al., 1999) [68, 148] and set within transformer asset management practice (Abu-Elanien & Salama, 2010) [1] and power system reliability evaluation (Billinton & Allan, 1996) [58]. Spare-parts inventory theory provides further foundations, from the multi-echelon METRIC model (Sherbrooke, 1968) [234] to reviews of the special characteristics of maintenance spares and of system-oriented models (Basten & van Houtum, 2014; Huiskonen, 2001; Kennedy et al., 2002) [56, 115, 129]. Local studies of grounding design, voltage control, solar integration and microgrids show how equipment requirements evolve with the network (Adeniji et al., 2020; Komi & Adeniji, 2020; Oshevire et al., 2017; Sunday & Omoegun, 2018, 2019; Yeboah & Ike, 2020) [4, 137, 212, 242, 243, 278], supported by solar-resource and wind-power forecasting models (Komi, 2021; Odejobi & Ahmed, 2018a) [135, 188], peer-to-peer energy trading (Shittu et al., 2021) [236] and hydrogen integration (Shittu et al., 2019) [235].

Read together, these strands lead to three observations. First, operational models of multiple sourcing treat yield, lead-time and disruption risk in depth but usually take purchase prices as known. Second, models of currency and commodity risk treat prices as stochastic but rarely consider supply that is unreliable or late. Third, the applied literature on energy procurement in emerging economies identifies the full set of risks and the governance levers available to buyers, yet remains largely conceptual and offers no quantitative rule for splitting volume between suppliers.

The gap that this paper addresses is therefore the joint treatment of currency, fuel, lead-time and disruption risks in a supplier-allocation model for critical energy equipment, together with an explicit concentration constraint that mirrors governance rules many utilities adopted after 2020.

3. Conceptual Model

Figure 1 summarises the conceptual model that guides the analysis. Five exogenous risk drivers act on the attributes of the two supply sources: exchange-rate volatility, fuel-price volatility and its correlation with the exchange rate, foreign lead-time uncertainty, shipment disruption and domestic capacity uncertainty. The exchange rate acts on landed cost, fully for the foreign supplier and partially, through the indexed share of its cost base, for the domestic supplier. Fuel prices act on freight costs and, through higher dispatch and asset stress, on demand for replacement units. Lead-time uncertainty and disruption combine into the foreign effective yield, the share of each ordered unit that arrives usable within the planning window, while capacity uncertainty limits what the domestic supplier can deliver.

Fig 1: Conceptual model linking risk drivers, supplier attributes, moderators, the allocation decision and procurement outcomes.

These supplier attributes determine the value of each unit ordered from each source, and the allocation decision is moderated by the buyer's risk attitude and by governance limits on supplier concentration and service level. The decision in turn produces four outcomes: expected total cost, tail cost measured by CVaR, service level measured by the fill rate, and supplier concentration measured by the HHI. The structure draws on the random-yield view of supplier unreliability (Dada et al., 2007; Yano & Lee, 1995) [72, 277], the real-options view of sourcing flexibility under currency risk (Kogut & Kulatilaka, 1994; Kouvelis, 1999) [134, 138] and the resilience perspective in which assured supply has value beyond its price (Sheffi & Rice, 2005; Tomlin, 2006) [233, 251]. The conceptual model implies three expected relationships that the formal analysis examines. First, the foreign order should fall as the foreign effective yield falls, whether because lead times become longer or more variable or because disruption becomes more likely. Second, currency volatility should raise tail cost more than it changes the allocation, because it alters the dispersion of the foreign landed cost rather than its mean. Third, reliable domestic capacity should be used first, and expanding it should reduce tail cost more than any reallocation of a fixed capacity.

4. Methodology

The study follows a quantitative decision-modelling design in four steps. First, the decision setting implied by the conceptual model is specified (Section 4.1). Second, it is formalised as a single-period stochastic program with a mean-CVaR objective (Sections 4.2 and 4.3), and its structural properties are derived analytically (Section 4.4). Third, the program is solved by sample average approximation over Monte Carlo scenarios (Section 4.5). Fourth, the model is calibrated to stylised 2021 conditions and examined through one-factor-at-a-time sensitivity analysis (Section 4.6), with the results reported in Section 5.

4.1. Problem Setting

Consider a power utility (the buyer) that must secure a stock of a critical, standardised equipment item, for example distribution and generator step-up transformers of a given rating, or a family of turbine hot-gas-path components, for a 12-month planning horizon. Orders are placed at the start of the year. Units that arrive within a planning window of T = 9 months can be installed or held as strategic spares in time to protect against the year's failures and planned replacements; units arriving later cannot cover this year's needs and are carried at no value to the current period. Items of this kind are usually governed by asset integrity and reliability programmes that determine when replacements are needed (Atta et al., 2020, 2021; Obetta, 2018, 2019, 2020) [51, 52, 166, 167, 168], and their failure rates rise with operating intensity and harsh service conditions (Obetta & Ninduwezuor-Ehiobu, 2018, 2019; Obetta et al., 2020, 2021) [168, 169, 170, 172]. Two qualified suppliers are available. The first is a domestic or regional supplier (D), a local or near-shore assembler with a short lead time (mean 3 months). Its price is quoted in local currency units (LCU), but a fraction θ of its cost base consists of imported components, so its price is partially indexed to the exchange rate. Its nominal annual allocation to the buyer is KD units, and realised capacity is random because of component shortages and competing orders. The buyer pays only for units delivered.

The second is a foreign original equipment manufacturer (F), an established firm with a lower dollar price but a long and variable lead time (mean 6 months, standard deviation 2 months) and exposure to shipment disruption (port congestion, vessel incidents, export delays) that destroys or indefinitely delays part of the consignment. Following common practice under letters of credit, the buyer commits to the full dollar payment for the ordered quantity, converted at the spot rate prevailing at payment. This payment structure is typical of import transactions where access to foreign exchange is administratively controlled (Jones & Ominyi, 2020) [124].

Demand for the item over the horizon is uncertain. It is driven by failures, planned replacements and network expansion, and it rises with fuel prices because high fuel prices in 2021 coincided with higher dispatch of thermal units and greater stress on assets. Failure-prediction work on energy assets supports treating demand for replacements as a function of operating intensity (Komi & Adamolekun, 2021) [136]. A shortfall triggers a large penalty per unit representing downtime, emergency procurement at spot premiums and rental generation. Excess units incur a holding cost covering storage, insurance and capital.

The buyer's governance policy may also impose a maximum supplier concentration, measured by the HHI of quantity shares, to avoid dependence on any single source. The decision is the pair of order quantities (qD, qF).

4.2. Notation and Uncertainty

Table 1: Notation Symbol Meaning qD, qF Order quantities from domestic and foreign suppliers (decision variables, units) S, S0 Exchange rate at payment (LCU per USD) and its reference value P, P0 Fuel price at shipment (USD per barrel) and its reference value D Demand for units within the planning window LD, LF Random lead times of the two suppliers (months) T Planning window within which units are usable (months) K̃D Realised domestic capacity available to the buyer (random) δ, ℓ Foreign disruption indicator and fraction of shipment lost if disrupted pD, θ Domestic base price (LCU) and its share indexed to the exchange rate pF Foreign unit price (USD) fD, fF Freight cost per unit at reference fuel price (LCU, USD) h, b Holding cost and shortage (downtime) penalty per unit (LCU) λ, α Weight on CVaR and CVaR confidence level Hmax Maximum allowed supplier concentration (HHI) Let Z1 and Z2 be standard normal variables with correlation ρ. The exchange rate and fuel price are lognormal with unit mean multipliers:

A positive ρ reflects the tendency, observed for oil importers, of currency weakness to coincide with higher dollar fuel costs; for oil exporters ρ can be negative. Demand responds to fuel prices with elasticity η:

Lead times LD and LF are lognormal with given means and standard deviations. The foreign disruption indicator δ is Bernoulli with probability π, and the lost fraction ℓ is uniform on [0.3, 0.9]. Realised domestic capacity is K̃D = KD·κ, where κ is a truncated normal multiplier with mean 1 and coefficient of variation 0.15.

4.3. Costs, Objective and Constraints

The first two terms are purchase costs, with the foreign order paid in full irrespective of disruption or lateness. The last two terms are the holding and shortage costs. Because cF is the product of a dollar price and a random exchange rate, foreign purchasing carries direct currency exposure; the domestic price carries a smaller, indexed exposure θ. The buyer solves minq Φ(q) = (1 − λ) E[C(q, ξ)] + λ CVaRα[C(q, ξ)] (6)

where si = qi / (qD + qF) are quantity shares, the HHI constraint limits concentration (Hmax = 1 means no restriction and Hmax = 0.5 forces an equal split), and FR(q) = 1 − E[(D − Y)+]/E[D] is an optional fill-rate service constraint. Using the representation of Rockafellar and Uryasev (2000) [223], The HHI is the standard concentration measure in competition analysis (Rhoades, 1993) [221]; applied here to quantity shares, it records how dependent the buyer is on its largest supplier.

so that, with N sampled scenarios, problem (6) to (7) becomes a mixed-integer program with auxiliary variables un ≥ Cn − τ, un ≥ 0.

4.4. Structural Properties

Define the foreign effective yield RF = (1 − δℓ)·1{LF ≤ T}, the fraction of each ordered foreign unit that is usable within the window. Then YF = qFRF.

Proposition 1 (Risk-Neutral Optimality Condition): Let λ = 0 and suppose demand has a continuous distribution. At an interior optimum the foreign order satisfies E[cF] = b · E[RF 1{D > Y}] − h · E[RF 1{Y > D}] (9)

Argument. Differentiating (5) with respect to qF gives ∂C/∂qF = cF + RF[h·1{Y > D} − b·1{D > Y}], which is non-decreasing in qF because Y increases in qF. Hence E[C] is convex in qF; setting its derivative to zero gives (9). Condition (9) is a generalised critical-fractile rule: the marginal landed cost of a foreign unit must equal the expected shortage cost it avoids minus the expected holding cost it creates, both scaled by the probability that the unit actually arrives usable. It has three implications. First, lead-time risk acts as a loss of yield rather than as a reason to over-order. Raising the variability of LF increases Pr(LF > T) and lowers E[RF], which shrinks the right-hand side of (9). Because the buyer pays for late units in full, the optimal foreign order falls rather than rises. This contrasts with classical safety-stock logic, where lead-time variability increases stock levels.

Second, exchange-rate volatility enters mostly through the tail of the cost distribution. With the mean-preserving specification in (1), E[cF] is unchanged by σS, so the risk-neutral allocation is nearly insensitive to currency volatility. It matters for λ > 0, because CVaR penalises scenarios where a weak currency coincides with high demand or disruption. Third, fuel prices act on both sides of the trade-off. A higher P raises cF and cD through freight but also raises D through (2), increasing the shortage term. With freight a small share of landed cost, the demand channel dominates and the net effect on the allocation is small.

Proposition 2 (Preference for The Reliable Source): If the domestic supplier's expected landed cost per usable unit, E[cD]/Pr(LD ≤ T), is below the shortage penalty b and the domestic supply is less correlated with the shortage event than foreign supply, then under λ ≥ 0 the domestic order is at its upper bound KD whenever the foreign order is positive. Sketch. Exchanging one foreign unit for one domestic unit reduces the probability of a usable-supply shortfall by more than the price premium in penalty-weighted terms, so the objective decreases until the capacity bound binds. The numerical results in Section 5 are consistent with this property: in every case with KD of 44 units or less, the domestic order equals KD; only at 54 units, when domestic capacity alone exceeds expected demand, does the bound stop binding.

4.5. Solution Approach: Sample Average Approximation

Because equipment is ordered in whole units and the feasible region is small, we solve the sample average approximation (SAA) of (6) to (7) by exhaustive enumeration over integer pairs (qD, qF) with qD ∈ {0,., KD}, qF ∈ {0,.., 60} and qD + qF ≥ 30. For each candidate we evaluate the empirical mean and the empirical CVaR at α = 0.95 over N = 20,000 scenarios drawn with common random numbers, so that differences between candidates are not driven by sampling noise. Enumeration guarantees a global optimum of the SAA problem despite the non-convexity introduced by the capacity minimum in (4); for larger instances (more suppliers or multiple items) the mixed-integer formulation based on (8) can be solved with a commercial solver.

Sample average approximation is an established method for stochastic discrete optimisation with known convergence properties (Kleywegt et al., 2002) [133], and its foundations are set out in standard texts on stochastic programming (Birge & Louveaux, 2011; Shapiro et al., 2009) [59, 232]. It has been applied to supply chain design under uncertainty by Santoso et al. (2005) [227]. Scenario generation uses standard Monte Carlo techniques for correlated lognormal variables (Glasserman, 2004) [103]. For larger instances, heuristic and approximation methods developed for cloud and network resource allocation offer scalable alternatives to full enumeration (Ahmed & Odejobi, 2018b; Ahmed et al., 2019, 2020; Odejobi et al., 2019) [16, 17, 18, 189].

4.6. Parameter Calibration

The instance is stylised, representing a standardised distribution-class equipment item bought in volume, but anchored to conditions faced by an import-dependent utility in 2021. The reference exchange rate is 410 LCU per USD and the reference fuel price is 70 USD per barrel, which are close to the official naira rate and the average Brent price in that year. Prices are expressed in millions of LCU per unit. Table 2 lists the base-case parameters.

Table 2: Base-case parameters Parameter Value Interpretation S0, σS 410 LCU/USD; 0.25 Reference rate; annual FX volatility P0, σP, ρ 70 USD/bbl; 0.40; 0.35 Fuel reference, volatility and correlation with FX μD, σD, η 40; 8; 0.15 Mean and SD of demand; fuel elasticity of demand pD, θ, fD 0.95; 0.35; 0.010 Domestic price (LCU m), FX-indexed share, freight pF, fF USD 1,850; USD 100 Foreign price and freight per unit (see note) KD, CV of capacity 34 units; 0.15 Domestic allocation and its reliability LD (mean, SD) 3; 0.8 months Domestic lead time LF (mean, SD) 6; 2.0 months Foreign lead time T 9 months Usable planning window π, ℓ 0.10; U[0.3, 0.9] Disruption probability; fraction lost h, b 0.10; 6.0 Holding cost and downtime penalty (LCU m per unit) λ, α 0.5; 0.95 CVaR weight and confidence level Note to Table 2: the instance represents a standardised distribution-class transformer and protection package. The foreign price of USD 1,850 per unit (0.00185 USD million in model units) and freight of USD 100 per unit at the reference fuel price give a landed foreign cost of about 0.80 LCU million per unit at the reference exchange rate, roughly 17 percent below the domestic price. Only relative magnitudes matter for the allocation. With these values about 8.3 percent of foreign shipments arrive after the window, versus essentially none of the domestic deliveries.

5. Results

5.1. Optimal Allocation Versus Sole Sourcing

Table 3 compares the optimal risk-averse policy with the two sole-sourcing benchmarks and with the risk-neutral optimum. Sole domestic sourcing is capped by capacity, so it leaves a large expected shortfall and the lowest fill rate. Sole foreign sourcing is optimised over the order size; it achieves the lowest purchase cost per unit but has the highest volatility and by far the worst tail, because a single disruption or a late vessel exposes the buyer to large shortage penalties at the same time that it has already paid in full in dollars.

Table 3: Policy comparison (costs in LCU million; 20,000 scenarios) Policy qD / qF Foreign share % E[C] SD[C] CVaR0.95 Fill rate % P(no shortage) % Sole domestic 34 / 0 0.0 81.6 43.9 184.9 78.6 19.6 Sole foreign 0 / 45 100.0 74.2 76.0 310.3 84.2 61.9 Risk-neutral dual (λ = 0) 34 / 16 32.0 54.8 25.5 142.0 95.6 74.8 Risk-averse dual (λ = 0.5) 34 / 20 37.0 55.5 23.5 139.7 96.7 82.3 The risk-averse dual-sourcing policy orders the full domestic allocation of 34 units plus 20 foreign units. Relative to sole foreign sourcing, expected cost falls from 74.2 to 55.5 LCU million (−25 percent) and CVaR falls from 310.3 to 139.7 (−55 percent). The fill rate rises to 96.7 percent. Moving from the risk-neutral to the risk-averse policy adds four foreign units as insurance: expected cost rises by only 0.74 LCU million while CVaR falls by 2.37 and the probability of no shortage rises from 74.8 to 82.3 percent. The cost decomposition of the optimal policy is instructive: purchase costs account for 46.7 LCU million, expected shortage penalties for 7.7 and holding costs for 1.1. The dollar-denominated share of purchase spending is 16.0 LCU million, about 34 percent, which defines the buyer's residual currency exposure.

Fig 2: Expected cost, CVaR, objective and fill rate as functions of the foreign order, with the domestic order at capacity.

Figure 2 shows why the optimum is interior. The first foreign units are extremely valuable because they cover demand that domestic capacity cannot; expected cost and CVaR fall steeply. Beyond roughly 16 units the expected-cost curve turns up because additional foreign units are increasingly likely to be surplus. CVaR keeps falling a little longer because extra units still protect against joint domestic shortfall and foreign disruption scenarios, which places the mean-CVaR optimum at 20 units. Fill rate saturates near 98 percent, showing that the remaining shortages stem from disruptions and late arrivals that additional ordering cannot fix cheaply.

Fig 3: Objective surface Φ(qD, qF) for λ = 0.5. The star marks the optimum; the dashed line marks an equal 50/50 split.

Figure 3 maps the full objective surface. The basin around the optimum is relatively flat along the qF axis but steep along the qD axis: under-ordering from the reliable domestic source is far more costly than mis-sizing the foreign order by a few units. The 50/50 line passes well away from the optimum except at very high total quantities, which illustrates the cost of equal-split heuristics.

5.2. Risk Attitude and Concentration Limits

Table 4: Effect of risk aversion λ and concentration cap Hmax Setting qD / qF HHI E[C] CVaR0.95 Fill rate % λ = 0 34 / 16 0.56 54.80 142.04 95.6 λ = 1 34 / 22 0.52 56.47 139.40 97.1 Greater risk aversion monotonically increases the foreign order (16 to 22 units), trading small increases in expected cost for reductions in CVaR. Concentration caps of 0.62 and 0.55 are not binding because the unconstrained optimum already has an HHI of 0.53. A strict equal-split rule (Hmax = 0.5) forces 34 foreign units, raising expected cost by 9.8 LCU million and the objective by 7.0, while CVaR actually worsens slightly because surplus dollar purchases add currency-driven cost in bad scenarios. A concentration constraint is therefore valuable as a guardrail against single sourcing but costly if written as a rigid equal split.

5.3. Exchange-Rate, Fuel-Price and Disruption Sensitivity

Table 5: Sensitivity of the optimal policy to market and disruption risks (λ = 0.5) Parameter qD / qF E[C] CVaR0.95 Objective Fill rate % ρ = -0.30 34 / 20 55.46 138.04 96.75 96.8 Exchange-rate volatility: Raising σS from 0.10 to 0.55 increases CVaR from 138.7 to 146.0 LCU million but changes the foreign order only from 20 to 18 units. Consistent with Proposition 1, currency risk raises the price of the foreign hedge in bad states without changing its expected cost, so the response is a modest shift toward the domestic source, which in the base case is already at capacity. The practical message is that currency volatility should be managed mainly through contract terms (local-currency pricing, indexation caps, staged payments) and financial instruments where available, rather than by large changes in sourcing shares.

Fuel-price volatility and correlation: Fuel-price volatility and its correlation with the exchange rate have almost no effect on the allocation. Freight is a small fraction of landed cost, and the demand channel raises shortage risk for both suppliers alike. Fuel risk therefore matters more for budgeting than for allocation.

Disruption probability: As π rises from 0 to 0.30, CVaR rises from 131.3 to 151.6 and the fill rate falls from 97.5 to 95.0 percent, yet the foreign order barely changes (20 to 19). Since the disruption hits the foreign consignment as a block, extra units ordered from the same source are lost together with the rest; the cure for higher disruption risk is not to order more from the same supplier but to add independent capacity.

5.4. Lead-Time Uncertainty

Fig 4: Optimal foreign order and resulting fill rate as functions of foreign lead-time variability (left) and mean (right).

Lead-time parameters have the largest effect on the allocation. When the standard deviation of the foreign lead time increases from 1 to 4 months, the optimal foreign order drops from 25 to 16 units, CVaR rises from 100.0 to 156.8 and the fill rate falls from 99.0 to 94.0 percent. A one-month increase in the mean lead time, from 6 to 7 months, lowers the optimal foreign order from 20 to 16 units; at 8 months it falls to 13. This is the effective-yield mechanism of Proposition 1: units that are likely to miss the window are paid for but provide no protection, so the buyer rationally buys fewer of them. The flip side is a falling fill rate, which shows that in 2021-type conditions buyers could not order their way out of shipping delays; the value of a shorter or more predictable lead time is substantial. Comparing the 1- month and 2-month SD cases, reducing foreign lead-time variability by one month lowers the objective by 20.2 LCU million, which is a benchmark for what the buyer could rationally pay for expedited or guaranteed delivery terms.

5.5. Domestic Price Premium and Capacity

Table 6: Effect of the domestic price and of domestic capacity Setting qD / qF Foreign share % E[C] CVaR0.95 Fill rate % Raising the domestic base price from 0.95 to 1.60 LCU million, so that the domestic unit costs roughly double the landed foreign cost, does not change the allocation: domestic capacity remains fully used. With a downtime penalty of 6 LCU million per unit, the reliability advantage of the domestic source outweighs even large price premiums, in line with Proposition 2. The premium is simply passed through to cost.

Fig 5: Optimal orders and CVaR as domestic qualified capacity expands.

Capacity, by contrast, is decisive (Figure 5). With only 24 units of domestic capacity the buyer must split evenly and CVaR reaches 185.7. Expanding domestic capacity to 44 units cuts the foreign share to 25.4 percent and CVaR to 99.8, almost halving tail cost relative to the 24-unit case, at nearly constant expected cost. At 54 units the buyer does not use all available capacity (it orders 50), yet still keeps 8 foreign units, because foreign supply hedges against the domestic capacity shortfall. Dual sourcing therefore remains optimal even when one source could in principle cover all demand.

6. Discussion

The results align with, and in places qualify, findings in the literature. The finding that the reliable source is filled to capacity despite a sizeable price premium is consistent with Dada et al. (2007) [72], who show that cost determines which suppliers qualify while reliability determines how much each supplies, and with Yu et al. (2009) [279] and Silbermayr and Minner (2014) [237], who find dual sourcing valuable when disruption risk is material. The allocation also resembles the tailored base-surge structure of Allon and Van Mieghem (2010) [30], with the difference that here the near source provides the base volume because it is reliable rather than because it is cheap.

The lead-time result qualifies standard inventory intuition. In continuous-review settings more variable lead times usually call for more safety stock, although Song (1994) [240] showed that the relationship is not always monotone. In the present setting the hard planning window and full prepayment turn lateness into a loss of yield, so more variable foreign lead times make each foreign unit less valuable and the optimal order falls. This mechanism differs from the order-splitting benefit discussed by Thomas and Tyworth (2006) [250], which relies on independent lead times reducing the variability of the effective replenishment time.

The weak allocation response to exchange-rate volatility is consistent with the real-options literature (Huchzermeier & Cohen, 1996; Kouvelis, 1999) [114, 138], in which volatility raises the value of flexibility mainly when production or sourcing can be switched after the uncertainty is resolved. Here the order is committed before the exchange rate is known, so volatility shifts the cost distribution rather than the optimal split. The risk-averse response, a modest increase in foreign units as insurance against joint domestic shortfall and disruption, differs from the order reduction typically found for risk-averse newsvendors with reliable supply (Chen et al., 2009) [63]; the difference arises because supply itself is uncertain, as in the random-capacity setting studied by Wu et al. (2013) [273].

Finally, the strong effect of domestic capacity supports the emphasis on supplier development and resilience in applied work on energy infrastructure in emerging markets (Agbabiaka et al., 2019; Ogunwole et al., 2021) [7, 193] and gives it a quantitative basis: in the calibrated instance, moving from 24 to 44 units of qualified domestic capacity nearly halves tail cost at almost unchanged expected cost. All three expected relationships of the conceptual model in Section 3 are therefore borne out by the numerical analysis.

7. Implications

7.1. Theoretical Implications

For research on supplier allocation, the analysis shows that lead-time risk and disruption risk can be represented jointly through an effective yield whenever a hard usage window applies, which connects stochastic lead-time models with the random-yield literature. It also shows that, when the order is committed once, exchange-rate volatility acts as a driver of tail risk rather than of allocation. Models that combine operational and financial hedging should therefore be evaluated with risk measures that capture the tail of the cost distribution rather than with expected cost alone.

7.2. Managerial Implications

The results suggest several guidelines for procuring critical equipment under conditions like those of 2021. The first is to allocate for reliability before price. When downtime penalties are large relative to price gaps, the reliable short-lead-time source should be filled to its qualified capacity before the cheaper distant source is used. Price differences of the size typically observed between regional assemblers and global OEMs do not overturn this. This is consistent with resilience frameworks for critical gas and power infrastructure that place assured supply ahead of unit price (Agbabiaka et al., 2019; Ogunwole et al., 2021) [7, 193]. The second is to size the foreign order with an effective-yield rule. The foreign order should be set using the probability that a unit arrives usable within the window, not the nominal quantity. Ordering extra foreign units to compensate for lateness is counterproductive when late units are paid for in full. Shipment-level visibility of the kind described by Nnabueze et al. (2021) [159] provides the data needed to estimate this probability. Third, investment in capacity and lead-time reliability is worth more than buffer volume. Qualifying additional domestic or regional capacity and negotiating firm delivery windows (with liquidated damages or staged payments tied to delivery) reduce tail risk far more than adjusting order quantities. The lead-time sensitivity provides a willingness-to-pay benchmark for such terms. Supplier development and relationship management (Ike et al., 2021) [116] and contract structures that allocate delay risk and liability clearly (Okonkwo et al., 2019; Uchechi & Ominyi, 2019) [202, 259] are the practical routes to these gains. Fourth, concentration limits work best as guardrails. An HHI cap in the region of 0.6 prevents single sourcing without forcing costly equal splits. Rigid 50/50 rules raised cost without improving tail risk in our calibration. Such caps fit naturally into compliance-based procurement governance for high-risk energy environments (Okonkwo, Ogunwole, et al., 2021) [198]. Fifth, currency risk is better handled through contracts and finance than through volume. Because exchange-rate volatility shifts cost distributions more than optimal shares, local-currency pricing, indexation formulas with caps and floors, and where possible forward cover are better tools than reallocating volume. Tiered treasury structures and CFO-led cross-border finance provide the organisational means to apply them (Dada et al., 2021a; Isiekwu et al., 2021) [73, 120]. Finally, fuel risk should be budgeted mainly through its effect on demand. Fuel prices affect equipment requirements via higher dispatch and asset stress more than via freight. Planning scenarios should link fuel price assumptions to failure and replacement forecasts. Predictive demand and maintenance analytics can supply these linked forecasts (Adaramola et al., 2018; Aifuwa et al., 2020) [2, 20].

7.3. Implementation and Policy Implications

Applying the model requires reliable inputs. Failure and demand forecasts can draw on predictive maintenance and condition monitoring (Mayo et al., 2021; Sunday et al., 2020) [152, 244], on inspection data from unmanned aerial vehicles, LiDAR and geographic information systems for grid and corridor assets (Dagodzo, 2018a, 2018b; Dagodzo & Ahiaeke Patrick, 2020, 2021a, 2021b) [75, 76, 77, 78, 79], and on machine-learning forecasting methods developed for revenue, cash flow, customers and markets (Basnet et al., 2021; Dada et al., 2021b; Oziri et al., 2020; Sanni et al., 2020a; Seyi-Lande et al., 2020; Tonoyan et al., 2021a, 2021b) [55, 74, 214, 226, 231, 254, 255], including comparative reviews of predictive forecasting for operational resource allocation (Unamma et al., 2018) [264]. The quality of these inputs depends in turn on data-quality and single-source-of-truth frameworks for reporting across organisational units, on the analytics capacity of the institutions that use them (Unamma et al., 2019, 2021) [265, 266], and on methods for extracting usable information from unstructured maintenance, procurement and financial records (Iziduh et al., 2020) [123]. Forecasting and risk-stratification techniques from reservoir engineering, public health and environmental risk modelling offer transferable methods for estimating rare-event probabilities (Azeez & Badmus, 2018; Lamidi & Olamide, 2018; Nwangwu et al., 2020; Oparah et al., 2021) [53, 141, 165, 210], as do data-driven policy and value-chain models in agricultural economics (Jones & Ominyi, 2021; Michael & Ogunsola, 2021c) [125, 157]. The data and decision tools must run on secure, well-governed information systems. Utilities face specific operational technology risks (Adegbite et al., 2020; Ahmed et al., 2021) [3, 19], and enterprise frameworks address security audit, intrusion detection, incident response, insider threat and data availability (Akeju et al., 2018; Dosunmu & Ogundele, 2019, 2020, 2021; Fadayomi et al., 2019; Mbonu et al., 2019) [22, 83, 84, 85, 94, 156]. Data protection governance, risk-based business intelligence and continuous performance visualisation support transparent procurement decisions (Mbonu et al., 2018, 2021a; Ogbole et al., 2021) [153, 154, 192], and IT support models determine whether such tools stay available across dispersed sites (Anyanwu, 2019, 2020) [41, 42].

On the financial side, procurement allocations interact with budgeting, accounting controls and treasury. Frameworks for strategic accounting, financial analytics, executive decision systems and cost management (Bola-Sadipe et al., 2019; Lawal & Oduleye, 2018a, 2019b, 2021b; Oduleye & Medon, 2021) [60, 142, 145, 147, 190] and for tax governance and transfer pricing in cross-border operations (Lawal & Oduleye, 2018b, 2019a) [143, 144] help translate the expected-cost and CVaR outputs into budgets. Treating the cost of poor quality as a governance metric offers a practical way to express the shortage and downtime penalty in terms that boards and regulators already monitor (Ashore-Onisemo et al., 2021) [49]. Internal audit and risk-based control models (Akomolafe & Agu, 2018, 2019a, 2019b, 2019c) [26, 27, 28, 29], ethics and compliance training and tamper-proof regulatory recordkeeping (Anichukwueze et al., 2020, 2021) [38, 39], and trade finance, transaction banking and relationship banking arrangements (Agboada et al., 2018b, 2020; Ezeako et al., 2019; Okafor et al., 2021) [8, 9, 93, 194] govern how letters of credit and foreign-exchange purchases are executed. Scenario analysis of fiscal measures such as finance bills can inform assumptions about import duties and currency policy (Akinola et al., 2020) [25].

Contracting and compliance also shape which allocations are feasible. Frameworks for cross-border mergers, post-merger compliance integration, privacy by design in corporate restructuring and multi-jurisdictional supply chain governance (Ominyi, 2020, 2021; Ominyi & Anichukwueze, 2020; Ominyi et al., 2021) [204, 205, 206], anti-money laundering, anti-bribery and financial crime controls (Atakpa, 2021; Ominyi & Anichukwueze, 2021) [50, 207], stamp duty and contract-review standardisation (Uchechi, 2018; Uchechi et al., 2021) [258, 263], and risk-based decision-making, traceability and lean distribution in regulated supply chains (Aneke & Adesemoye, 2020; Obukadata et al., 2021a, 2021b) [35, 186, 187] all bear on how foreign and domestic suppliers are qualified and paid.

Finally, critical equipment is installed and maintained in high-hazard environments, so procurement timing must be coordinated with safety management. Research on heat stress, near-miss reporting, hazard recognition, safety culture, contractor governance, management walkthroughs, human error and incident prevention in industrial and construction settings (Arumosoye & Obriki, 2018, 2019, 2021; Obogo et al., 2020a, 2020b, 2020c; Obogo, Arumosoye, & Obriki, 2021; Obogo, Obriki, & Arumosoye, 2021; Obogo, Ozobu, et al., 2019a, 2019b; Obogo, Uduokhai, et al., 2019; Obriki & Arumosoye, 2018, 2019, 2020, 2021) [45, 46, 48, 173, 174, 175, 176, 178, 179, 182, 183, 184, 185], together with work on adaptive safety management and predictive compliance monitoring in aviation (Adeyelu, 2018, 2019) [5, 6], shows that late equipment deliveries often translate into compressed and riskier installation schedules. When supply failures do occur, root-cause and thematic analysis of major incidents provides a structured way to learn from them and to update the lead-time and disruption parameters used in the model (Okwesa et al., 2021) [203]. Standard operating procedures, lean methods, digital operations, joint-venture governance and compliance workflows (Agboada et al., 2018a, 2019; Ambali et al., 2021; Eyetsemitan et al., 2020, 2021) [10, 11, 31, 91, 92] provide the organisational routines through which the allocation policy proposed here can be institutionalised.

For policy makers, regulators and development finance institutions, the capacity result suggests that support for qualifying local and regional manufacturers of grid equipment can reduce utilities' exposure to currency and shipping shocks more effectively than measures that act only on prices, and that access to foreign exchange for letters of credit is itself a source of supply risk that public policy can reduce.

8. Limitations

The study has several limitations. The model is single-period and treats the order decision as made once, so it ignores rolling re-orders, the carry-over of late units and emergency purchases on the spot market, all of which would add flexibility and partly offset the penalty on late foreign units. Financial hedging is not modelled, so the buyer's only response to currency risk is operational. Supplier disruption is assumed independent of the exchange rate, whereas currency crises can coincide with import restrictions or foreign-exchange rationing. The demand response to fuel prices is captured by a single elasticity. Finally, the calibration is stylised: the parameters approximate 2021 conditions for an import-dependent utility but are not estimated from a particular firm's data, so the numerical results should be read as illustrative of the mechanisms rather than as forecasts.

9. Future Research

Several extensions would be valuable. A multi-period version with carry-over of late units, rolling re-orders and an emergency spot-purchase option would show how much of the penalty on late foreign units can be recovered through dynamic decisions. Adding forward contracts as decision variables would allow joint operational and financial optimisation in the spirit of Ding et al. (2007) [81]. Modelling dependence between currency crises and import disruption would test whether the case for domestic capacity strengthens further. Empirical calibration using utility maintenance records, failure data and supplier delivery histories would allow the model to be validated and used for actual tenders. Embedding the allocation in a wider capital-allocation process would let procurement risk be weighed against other uses of scarce foreign exchange (Lawal & Oduleye, 2021a) [146]. Finally, extending the model to several suppliers and several equipment classes, using the mixed-integer formulation based on (8), would make it applicable to full procurement portfolios.

10. Conclusion

This paper has developed a mean-CVaR decision model for dual sourcing of critical energy equipment that integrates exchange-rate risk, fuel-price risk, stochastic lead times, domestic capacity uncertainty, foreign shipment disruptions and supplier-concentration constraints. A newsvendor-type optimality condition shows that lead-time uncertainty enters as a loss of effective yield, which leads to the counterintuitive but practically important result that more variable foreign lead times call for smaller, not larger, foreign orders. In a calibrated 2021 setting, the optimal policy fills domestic capacity and sources about 37 percent of volume abroad, reducing expected cost by a quarter and tail cost by more than half relative to sole sourcing from the cheapest-landed supplier. Exchange-rate volatility mainly raises cost and tail risk, fuel volatility has a second-order effect on allocation, and the largest gains come from expanding reliable capacity and securing predictable delivery. The framework can be implemented with standard simulation and optimisation tools and offers procurement committees a transparent basis for balancing cost, concentration and reliability.

Appendix a. Simulation Procedure For each scenario n = 1,.., 20,000: (i) draw correlated normals (Z1, Z2) and compute S and P by (1); (ii) draw demand by (2), truncated at zero; (iii) draw lognormal lead times with the stated means and standard deviations by moment matching; (iv) draw the disruption indicator, lost fraction and domestic capacity multiplier (truncated to [0.3, 1.2]); (v) for each candidate (qD, qF) compute (3) to (5). The same scenario set is used for all candidates within a run (common random numbers, fixed seed). Empirical CVaR is the mean of costs at or above the empirical 95th percentile. Sensitivity runs regenerate scenarios with the altered parameter and the same seed. Monte Carlo standard errors of expected cost at the optimum are below 0.2 LCU million, small relative to the differences reported.