Development of a Bi-Objective Mathematical Model for Optimizing Credit Allocation an‎d Maximizing Profit in Supply Chain Considering Operational Constraints (case study: SAPCO company)

10/19/2026 12:00:00 AM

In today’s highly competitive environment, making joint decisions on supplier order allocation an‎d credit allocation is essential to balance profit an‎d risk. Using a real automotive case, this study addresses the problem of meeting a deterministic deman‎d of 4,099.5 units under a purchasing budget of 217,276,400,000 rial (IRR) an‎d supplier-specific credit ceilings. A common gap in the literature treating order allocation separately from credit policy leads to misaligned decisions. We bridge this gap by proposing an integrated framework that simultaneously optimizes profit an‎d a composite operational-risk index (lead time–cost), subject to capacity, liquidity, an‎d credit constraints. Our approach is a multi-objective mathematical model with two objectives: maximizing profit an‎d minimizing a normalized composite risk. We generate the Pareto frontier via the epsilon-constraint method an‎d, for comparison, report weighted-sum solutions. The preferred solution is selec‎ted by minimizing distance to the ideal point, which makes the managerial trade-offs transparent. To assess robustness, we design “what-if” scenarios over deman‎d, budget, an‎d credit ceilings, an‎d vary risk weights (0.8/0.2, 0.5/0.5, 0.2/0.8). In addition, a global Sobol sensitivity analysis quantifies the contribution of key parameters to profit an‎d risk. Solving the model over an epsilon grid yields a set of nondominated solutions. In the baseline scenario, we achieve a perfect fill rate (FR = 1) with 100% budget utilization; total profit reaches 33,617,820,000 IRR, an‎d the risk index is 0.530989. The recommended allocation exhibits meaningful diversification most notably a controlled concentration on two key suppliers (≈25.62% an‎d 10.71%) which preserves profitability while curbing concentration risk. Scenario results clarify the profit–risk trade-off an‎d provide actionable guidance for tuning credit ceilings, allocating budgets, an‎d designing the supplier portfolio.

تأمين مالي زنجيره‌اي , تخصيص اعتبار , تركيب وزني , بهينه‌سازي چندهدفه , ريسك عملياتي

supply chain finance , credit allocation , Weighted Combination , multi-objective optimization , operational risk

Kiarash Ramazani

Dr. Ebrahim Teymouri