Dynamic lot-sizing with short-term financing and external deposits for a capital-constrained manufacturer

The interface between operations and finance has recently been of interest to both practitioners and academics, who recognize that coordinating decisions from both functions provides a great opportunity to improve the performance of firms. However, the link between dynamic lot-sizing and financing decisions remains largely unexplored in the literature. This paper investigates a dynamic lot-sizing problem with short-term financing and external deposits for a capital-constrained manufacturer. In each period, the manufacturer finances its operations using a combination of internal cash, short-term loans, and short-term capital subscriptions from shareholders. Furthermore, the manufacturer decides on an amount to send to an external depository to take into consideration the opportunity cost of carrying cash. Two formulations for this integrated problem are presented, structural properties of the optimal solution are derived, and a dynamic programming algorithm is developed to solve the problem. Subsequently, the integrated problem, analysis, and solution procedure are extended to consider the case of a per-period loan limit. A numerical study is conducted to derive insights on the effect of financial and operational parameters, which are then validated using extensive computational experiments. Our results show that integration leads to significant savings, smoother production, and smaller capital subscriptions and external deposits. In addition, while the discount factor affects the number of setups, inventory levels, capital subscriptions, and external deposits, the short-term interest rate determines the choice between using internal cash or short-term loans from the lender.