A cash-constrained dynamic lot-sizing problem with loss of goodwill and credit-based loan

Abstract

We consider a small retailer that manages its inventory under a strict cash constraint. At each period, the retailer's available cash restricts the maximum inventory level that it can replenish. These retailers are nanostores, which are widely present in emerging markets, or small online retailers in some Chinese e-commerce platforms. We assume that the retailer can decide the satisfied demand quantity even if it has enough inventory, but unsatisfied demand in one period may cause customer demand to decrease in the next period considering the loss of goodwill. The retailer could adopt a credit-based loan provided by its suppliers or e-commerce platforms to alleviate cash shortages. A profit maximization single-item lot-sizing model is constructed for this problem. Numerical tests demonstrate that cash-flow constraint is different from traditional capacity constraint, and that cash availability, as well as loan interest rate, can substantially affect a retailer's optimal lot-sizing decisions. Our model can help a retailer decide at the beginning of the planning horizon whether it is worth applying for a credit-based loan with a given loan policy. We prove that the zero-inventory-ordering property still holds for certain situations, and propose a polynomial algorithm with heuristic adjustments to solve this problem when customers' payment delay length can be neglected. If unit variable ordering costs are equal and the loss of goodwill rate is zero, the algorithm can obtain optimal solutions. Under other situations, comparisons with CPLEX 12.6.2 show that our algorithm can reach optimal performance in most cases, and it has a computation time advantage for large-sized problems.