We consider the integrated optimization problem of procurement, processing, and trade of commodities in a multiperiod setting. Motivated by the operations of a prominent commodity processing firm, we model a firm that procures an input commodity and has processing capacity to convert the input into a processed commodity. The processed commodity is sold using forward contracts, while the input itself can be traded at the end of the horizon. We solve this problem optimally and derive closed-form expressions for the marginal value of input and output inventory. We find that the optimal procurement and processing decisions are governed by price-dependent inventory thresholds. We use commodity markets data for the soybean complex to conduct numerical studies and find that approximating the joint price processes of multiple output commodities using a single, composite output product and using the approximate price process to determine procurement and processing decisions is near optimal. Compared to a myopic spread-option-based heuristic, the optimization-based dynamic programming policy provides significant benefits under conditions of tight processing capacities and high price volatilities. Finally, we propose an approximation procedure to compute heuristic policies and an upper bound to compare the heuristic against, when commodity prices follow multifactor processes.

W e consider how trade credit can coordinate a two-echelon supply chain in the presence of supplier moral hazard and costly working capital financing. While trade credit resolves moral hazard problems in the absence of working capital financing costs, we show that this is not necessarily true when financial frictions make financing trade credit costly. We then show that trade credit along with an appropriately designed reverse factoring program can restore supply chain efficiency.

We consider the dynamic risk management problem for a commodity processor facing risk costs. The firm procures an input commodity and processes it to produce an output commodity over a multi-period horizon. The processed commodity is sold using forward contracts while the input itself can be traded at the end of the horizon. The firm can also trade financial instruments to manage the commodity price risk, but cannot hedge the risk completely. Using the concept of conditional risk mappings, we extend the single period conditional value at risk (CVaR) measure to a dynamic setting and ensure a time-consistent representation of the firm's risk management objective. In a partially complete market framework, we show that the optimal financial trading policy is a CVaR-replicating portfolio. Contingent on optimal financial trading, we show that the optimal procurement and processing policies are characterized by price and horizon dependent inventory thresholds. We show, analytically, that the procurement threshold increases with risk costs during the horizon. Our numerical studies show that optimizing a time-consistent risk measure results in better risk control over the entire horizon when compared to optimizing the CVaR of total profits. We also find that myopic and risk-neutral optimal policies are poor substitutes for the optimal risk management policy, especially when the firm faces significant risk costs.

We study the funds allocation problem for a resource‐constrained non‐profit organization (NPO) that implements social development projects for public good. In addition to raising funds from donors who contribute prior to project implementation (“traditional donors”), the NPO uses a novel approach, which we term as the “ex‐post funding” approach, to also raise funds from donors who contribute based on the results delivered by the NPO (“ex‐post donors”). In this approach, the NPO uses its initial funds to implement early phases of the project, creates “results‐certificates” from the completed phases, and invites ex‐post donors to purchase these certificates. The donations raised from selling the results‐certificates are used to recover the NPO's own funds used in the project implementation. Operationalizing this approach is complicated when the project must incur a large fixed cost before any benefits are delivered by the project and the total benefit delivered is time sensitive. We show that for a given amount of initial funds available, there exists a threshold amount of funds that the NPO should raise from traditional donors before implementing the project phases so as to maximize the total expected benefit delivered. Through numerical studies, we analyze how the threshold of funds raised from traditional donors and the total benefit delivered vary with donor characteristics such as donor willingness to give and the proportion of donors who contribute prior to project implementation. Our numerical studies suggest that even with relatively small amount of initial funds, the NPO can deliver substantially higher benefit by using the ex‐post funding approach when compared to using a traditional approach that requires the NPO to raise all the funds required upfront.

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