Joint Finance-Based Scheduling for Two Concurrent Projects: A Nash Bargaining Framework

Abstract

We develop a joint finance-based scheduling (JFBS) model for two concurrent projects that pools line-of-credit (LOC) headroom and allocates the cooperative surplus via the Nash bargaining solution. Each project’s cash flow and precedence relations are modeled in a discrete, finance-constrained schedule; the joint problem co-optimizes the schedule and bargaining allocation, yielding Pareto-efficient and individually rational outcomes. We use a genetic algorithm to solve the mixed discrete–nonlinear search. In an illustrative case, JFBS outperforms individually optimized FBS. Financing costs decline for both contractors. Pooling unused LOC capacity reduces the worst simultaneous shortfall and thus the combined peak external credit. Portfolio-level schedule distortion also eases, with total activity shift dropping considerably, suggesting that partnering is not necessarily burdensome. These results indicate that credit pooling with Nash bargaining offers a practical and fair mechanism to cut financing cost and LOC size while preserving schedule quality. Given deterministic input and two parties, next steps include sensitivity analysis on key parameters, handling stochastic cash flows, and extending to multi-contractor coalitions. Implementation will require a clear internal-credit agreement, auditable exposure tracking, and possibly a neutral administrator or smart-contract automation. Further research can explore field pilots and institutional design questions.