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We study a single-product setting in which a firm can source from two suppliers, one that is unreliable and another that is reliable but more expensive. Suppliers are capacity constrained, but the reliable supplier may possess volume flexibility. We prove that in the special case in which the reliable supplier has no flexibility and the unreliable supplier has infinite capacity, a risk-neutral firm will pursue a single disruption-management strategy: mitigation by carrying inventory, mitigation by single-sourcing from the reliable supplier, or passive acceptance. We find that a supplier’s percentage uptime and the nature of the disruptions (frequent but short versus rare but long) are key determinants of the optimal strategy. For a given percentage uptime, sourcing mitigation is increasingly favored over inventory mitigation as disruptions become less frequent but longer. Further, we show that a mixed mitigation strategy (partial sourcing from the reliable supplier and carrying inventory) can be optimal if the unreliable supplier has finite capacity or if the firm is risk averse. Contingent rerouting is a possible tactic if the reliable supplier can ramp up its processing capacity, that is, if it has volume flexibility. We find that contingent rerouting is often a component of the optimal disruption-management strategy, and that it can significantly reduce the firm’s costs. For a given percentage uptime, mitigation rather than contingent rerouting tends to be optimal if disruptions are rare.

Disruptive events that halt production can have severe business consequences if not appropriately managed. Business interruption (BI) insurance offers firms a financial mechanism for managing their exposure to disruption risk. Firms can also avail of operational measures to manage the risk. In this paper, we explore the relationship between BI insurance and operational measures. We model a manufacturing firm that can purchase BI insurance, invest in inventory, and avail of emergency sourcing. Allowing the insurance premium to depend on the firm's insurance and operational decisions, we characterize the optimal insurance deductible and coverage limit as well as the optimal inventory level. We prove that insurance and operational measures are not always substitutes, and we establish conditions under which they can be complements; that is, insurance can increase the marginal value of inventory and can increase the overall value of emergency sourcing. We also find that the value of insurance is higher for those firms less able to absorb financially significant disruptions. As disruptions become longer but rarer, the value of emergency sourcing increases, and the value of inventory and the value of insurance increase before eventually decreasing. This paper was accepted by Martin Lariviere, operations management.

We connect the mix-flexibility and dual-sourcing literatures by studying unreliable supply chains that produce multiple products. We consider a firm that can invest in product-dedicated resources and totally flexible resources. Product demands are uncertain at the time of resource investment, and the products can differ in their contribution margins. Resource investments can fail, and the firm may choose to invest in multiple resources for a given product to mitigate such failures. In comparing a single-source dedicated strategy with a single-source flexible strategy, we refine the common intuition that a flexible strategy is strictly preferred to a dedicated strategy when the dedicated resources are costlier than the flexible resource. We prove that this intuition is correct if the firm is risk neutral or if the resource investments are perfectly reliable. The intuition can be wrong, however, if both of these conditions fail to hold, because there is a resource-aggregation disadvantage to the flexible strategy that can dominate the demand pooling and contribution-margin benefits of the flexible strategy when resource investments are unreliable and the firm is risk averse. We investigate the influence that resource attributes, firm attributes, and product-portfolio attributes have on the attractiveness of various supply-chain structures that differ in their levels of mix flexibility and diversification, and we investigate the influence these attributes have on the optimal resource investments within a given supply-chain structure. Our results indicate that the appropriate levels of diversification and flexibility are very sensitive to the resource costs and reliabilities, the firm's downside risk tolerance, the number of products, the product demand correlations and the spread in product contribution margins.

Process flexibility, whereby a production facility can produce multiple products, is a critical design consideration in multiproduct supply chains facing uncertain demand. The challenge is to determine a cost–effective flexibility configuration that is able to meet the demand with high likelihood. In this paper, we present a framework for analyzing the benefits from flexibility in multistage supply chains. We find two phenomena, stage–spanning bottlenecks and floating bottlenecks, neither of which are present in single–stage supply chains, which reduce the effectiveness of a flexibility configuration. We develop a flexibility measure g and show that increasing this measure results in greater protection from these supply–chain inefficiencies. We also identify flexibility guidelines that perform very well for multistage supply chains. These guidelines employ and adapt the single–stage chaining strategy of Jordan and Graves (1995) to multistage supply chains.

Dual sourcing and inventory are two prevalent and widely studied strategies firms use to manage yield risk. A pervasive but implicit assumption in the literature is that a firm knows its suppliers' yield distributions with certainty. This is a strong assumption in many circumstances. A firm is more likely to have a forecast of a supplier's yield distribution and to update that forecast based on its experiences with the supplier. We introduce and analyze a Bayesian model of \"supply learning\" (i.e., distribution updating) and investigate how supply learning influences both sourcing and inventory strategies in dual-sourcing and single-sourcing models, respectively. In the case of Bernoulli all-or-nothing yield distributions, we completely characterize the firm's optimal sourcing and inventory decisions for the supply-learning model. Among other results, we prove that for a given expected supplier reliability (i.e., the mean of the firm's forecast for the probability of successful delivery) an increase in the reliability forecast uncertainty increases the attractiveness of a supplier, but it reduces the firm's desire to invest in inventory to protect against future supply failures. We extend our analysis to allow for general yield distributions, multiple sourcing (i.e., more than two suppliers), and inventory carryover in the dual-sourcing model.

Operations managers do not typically have full information about the demand distribution. Recognizing this, data-driven approaches have been proposed in which the manager has no information beyond the evolving history of demand observations. In practice, managers often have some partial information about the demand distribution in addition to demand observations. We consider a repeated newsvendor setting, and propose a maximum-entropy based technique, termed Second Order Belief Maximum Entropy (SOBME), which allows the manager to effectively combine demand observations with distributional information in the form of bounds on the moments or tails. In the proposed approach, the decision maker forms a belief about possible demand distributions, and dynamically updates it over time using the available data and the partial distributional information. We derive a closed-form solution for the updating mechanism, and highlight that it generalizes the traditional Bayesian mechanism with an exponential modifier that accommodates partial distributional information. We prove the proposed approach is (weakly) consistent under some technical regularity conditions and we analytically characterize its rate of convergence. We provide an analytical upper bound for the newsvendor’s cost of ambiguity, i.e., the extra per-period cost incurred because of ambiguity, under SOBME, and show that it approaches zero quite quickly. Numerical experiments demonstrate that SOBME performs very well. We find that it can be very beneficial to incorporate partial distributional information when deciding stocking quantities, and that information in the form of tighter moment bounds is typically more valuable than information in the form of tighter ambiguity sets. Moreover, unlike pure data-driven approaches, SOBME is fairly robust to the newsvendor quantile. Our results also show that SOBME quickly detects and responds to hidden changes in the unknown true distribution. We also extend our analysis to consider ambiguity aversion, and develop theoretical and numerical results for the ambiguity-averse, repeated newsvendor setting.

In this paper, we investigate price-only contracts in supply chain capacity procurement games. For a two-party supply chain, comprising a manufacturer and a supplier that both invest in capacity, we prove the existence of a class of coordinating price-only contracts that arbitrarily allocate the supply chain profit. Moreover, if the supplier's reservation profit is below a certain threshold, the manufacturer's optimal contract is a quantity-premium price-only schedule, that is, the average wholesale price per unit increases in the order size. We prove that the manufacturer prefers simple piecewise-linear quantity-premium contracts to linear contracts and show numerically that such contracts are highly efficient. We extend our results for piecewise-linear price schedules to N -supplier assembly systems. We also enrich the voluntary compliance regime of Cachon and Lariviere (2001). With this enrichment, we prove that share-the-pain contracts, such as firm commitment and options contracts, increase supplier capacity in the full information case, a result that contrasts with that of Cachon and Lariviere. Finally, we investigate when a manufacturer prefers single-breakpoint quantity premiums to firm commitments.

The simultaneous production of different outputs (coproducts) is observed in the chemical, material, mineral, and semiconductor industries among others. Often, as with microprocessors, the outputs differ in quality in the vertical sense and firms classify the output into different grades (products). We analyze product line design and production for a firm operating a vertical coproduct technology. We examine how the product line and profit are influenced by the production cost and output distribution of the technology. We prove that production cost influences product line design in a fundamentally different manner for coproduct technologies than for uniproduct technologies where the firm can produce products independently. For example, with coproducts, the size and length of the product line can both increase in the production cost. Contrary to the oft-held view that variability is bad, we prove the firm benefits from a more variable output distribution if the production or classification cost is low enough. Data, as supplemental material, are available at http://dx.doi.org/10.1287/mnsc.2013.1738 . This paper was accepted by Serguei Netessine, operations management.

We examine technological systems that display the following characteristics: (i) unplanned outages incur significant costs, (ii) the system experiences an outage if one or more of its subsystems fails, (iii) subsystem failures may occur simultaneously, and (iv) subsystem recovery requires specific resources and capabilities that are provided by different firms. Firms may invest in two measures to enhance system availability-namely, failure prevention and recovery capacity. If recovery capacity investment is the only option, we find that the firms in a decentralized setting overinvest in capacity, resulting in higher system availability but at a higher cost. If both investments can be made, we find that the firms underinvest in failure prevention and overinvest in recovery capacity. That is, firms in a decentralized setting shift their focus from preventing failures to responding to failures. The net effect is lower system availability, reversing the conclusion above. We also find that, unexpectedly, firms are more willing to let their subsystems fail if a joint failure is more likely to occur. This paper was accepted by Martin Lariviere, operations management.

Coproduction systems, in which multiple products are produced simultaneously in a single production run, are prevalent in many industries. Such systems typically produce a random quantity of vertically differentiated products. This product hierarchy enables the firm to fill demand for a lower-quality product by converting a higher-quality product. In addition to the challenges presented by random yields and multiple products, coproduction systems often serve multiple customer classes that differ in their product valuations. Furthermore, the sizes of these classes are uncertain. Employing a utility-maximizing customer model, we investigate the production, pricing, downconversion, and allocation decisions in a two-class, stochastic-demand, stochastic-yield coproduction system. For the single-class case, we establish that downconversion will not occur if prices are set optimally. In contrast, we show that downconversion can be optimal in the two-class case, even if prices are set optimally. We consider the benefit of postponing certain operational decisions, e.g., the pricing or allocation-rule decisions, until after uncertainties are resolved. We use the term recourse to denote actions taken after uncertainties have been resolved. We find that recourse pricing benefits the firm much more than either downconversion or recourse allocation do, implying that recourse demand management is more valuable than recourse supply management. Special cases of our model include the single-class and two-class random-yield newsvendor models.