Sripad K. Devalkar

Integrated Optimization of Procurement, Processing, and Trade of Commodities

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.

The Impact of Working Capital Financing Costs on the Efficiency of Trade Credit

One of the arguments given to explain the widespread use of costly trade credit in supply chains is that trade credit enhances efficiency by resolving moral hazard problems. In this paper, we consider the impact of demand shocks on this efficiency role of trade credit. We show that as the probability of a negative demand shock increases, the amount of trade credit necessary to resolve moral hazard also increases. In other words, as economic conditions weaken (i.e. as the probability of low demand increases), more trade credit is required to coordinate the supply chain. The working capital financing costs associated with trade credit can impose a burden that makes it infeasible to coordinate the supply chain. We show that an appropriately designed reverse factoring program can provide suppliers with access to inexpensive credit necessary to finance the working capital associated with trade credit and restore supply chain efficiency.

Payment for Results: Funding Non-Profit Operations

The non-profit sector (NPO) faces two critical challenges in delivering public goods effectively and raising funds for developmental projects. The first challenge arises due to donors being uncertain about the NPOs efficiency to deliver the expected output (information asymmetry), and the second because the actual benefit provided is subject to uncertain exogenous shocks (outcome uncertainty). To partially address these challenges, the sector has seen the growth of the payment for results (PfR) funding approach, where the donor funds the NPO after the project is implemented and the outcome is observed, compared to the traditional funding (TF) approach where the donor contributes ex-ante. While the PfR approach addresses the donors challenge, the NPO still faces a significant risk of shortfall in funds. In this paper we model the interaction between the donor and a NPO as a Stackelberg game and characterize the conditions under which TF and PfR emerge as the equilibrium outcomes when there is information asymmetry and outcome uncertainty. The donor moves first and decides the donation amount if the NPO were to opt for TF and the NPO responds by choosing TF or PfR. Counter to initial intuition, we find that the donor does not prefer PfR under all conditions. We find that incentivizing the NPO to choose TF increases the donors expected utility when the negative impact of uncertainty and the donors willingness to contribute are high. On the other hand, the donor prefers the NPO to use PfR when the impact of outcome uncertainty is relatively small. Using numerical studies, we find that PfR does not always maximize the expected benefit provided. We find that the gap between the maximum possible expected benefit and expected benefit at equilibrium is significant when outcome uncertainty and donors willingness to contribute are high.

Delayed Payments in Supply Chains: The Role of Moral Hazard vs. Bankruptcy

Performance-based contracting is gaining widespread acceptance in supply chains where moral hazard might prevent either or both supply chain entities from exerting the first-best effort that improves supply chain outcomes. We analyze the use of delayed payments as a performance-based contract when supply chain payoffs are lead time dependent. The buyers margin depends on lead time which is governed by costly supplier effort. For a cash-constrained supplier, the delayed payment offered by the buyer (principal) raises the possibility of bankruptcy and incentivizes the supplier (agent) to exert effort. We study the optimal balance between moral hazard and bankruptcy risk in the context of a delayed payment contract whose objective is to reduce the lead time from supplier to buyer. Modeling the buyer--supplier interaction as an infinite--horizon principal--agent game, we find that suppliers with high cost of effort are able to use the threat of bankruptcy to extract better payment terms from the buyer. Further, these suppliers also exert less effort than what would be optimal for the supply chain as a whole. We show that a payment structure that involves a bonus payment for timely delivery combined with a delayed payment coordinates the supply chain. This payment structure effectively implies buyer cost-sharing in the suppliers effort, contingent on adequate supplier performance. Our results provide buyers with a roadmap on when and how to implement delayed payments as a function of different supplier parameters such as the cost of operational effort and the wholesale price.

Using Procurement Service Providers in Supplier Screening

A buyer engages a procurement service provider (PSP) to short-list pre-screened suppliers for final selection. The PSP can exert costly effort to include promising candidates that have a higher probability to be deemed qualified by the buyer. The buyer optimizes two key decision variables in her contract with the PSP: the short-list size and the performance bonus. We solve a mixed-integer program to characterize the optimal solution and provide a fast algorithm to compute the optimal decisions. We find that the number of candidates short-listed and the PSPs effort are substitutes in the sense that they both increase the probability of the buyer finding a qualified supplier. The buyer prefers to offer a performance bonus if and only if the fixed fees are sufficiently high. We also find that when the buyer has the choice to re-engage the PSP until finding a qualified supplier, the buyer may still prefer a single engagement when using a performance bonus. These managerial insights are robust when the buyer seeks multiple qualified suppliers to form a supply base.