Dynamic lot-sizing in a two-stage supply chain with liquidity constraints and financing options

Dynamic lot-sizing has typically been studied in the context of optimizing the physical flow of goods to minimize supply chain costs, assuming that there is always enough cash to finance operations. In practice, small-and medium-sized firms are more likely to be financially constrained and find themselves making sub-optimal production and inventory decisions. We consider a supply chain with two capital-constrained firms - a supplier and a manufacturer - and present a model to jointly optimize lot-sizing, initial endowment and short-term amounts to borrow, the capital to subscribe from shareholders, and deposits to invest. The objective is to maximize the net present value of supply chain cash flows subject to operational and financial constraints. Structural properties of the optimal solution are derived, and a dynamic programming algorithm is developed to solve the supply chain problem. Through numerical experiments on available data and a case study from the literature, we compare the profitability and planning decisions of a coordinated supply chain, in which the production and financial decisions of the supplier and manufacturer are jointly optimized, with those of an uncoordinated supply chain, in which the supplier and manufacturer locally optimize their decisions. The results indicate that there is an added value of supply chain coordination for financially constrained stages, and that the traditional profit-maximizing production plan which assumes financially unconstrained stages may result in an important deterioration of the objective value. It is found that considering financial decisions and constraints with lot -sizing increases the number of setups and decreases the average inventory. This results in higher short-term loans and lower capital subscriptions and deposits. For financially constrained supply chains, coordinating production plans leads to fewer setups without increasing the supply chain's average inventory. Furthermore, financial and operational parameters have a smaller impact on production and financial plans when the supply chain is coordinated.Dynamic lot-sizing has typically been studied in the context of optimizing the physical flow of goods to minimize supply chain costs, assuming that there is always enough cash to finance operations. In practice, small-and medium-sized firms are more likely to be financially constrained and find themselves making sub-optimal production and inventory decisions. We consider a supply chain with two capital-constrained firms - a supplier and a manufacturer - and present a model to jointly optimize lot-sizing, initial endowment and short-term amounts to borrow, the capital to subscribe from shareholders, and deposits to invest. The objective is to maximize the net present value of supply chain cash flows subject to operational and financial constraints. Structural properties of the optimal solution are derived, and a dynamic programming algorithm is developed to solve the supply chain problem. Through numerical experiments on available data and a case study from the literature, we compare the profitability and planning decisions of a coordinated supply chain, in which the production and financial decisions of the supplier and manufacturer are jointly optimized, with those of an uncoordinated supply chain, in which the supplier and manufacturer locally optimize their decisions. The results indicate that there is an added value of supply chain coordination for financially constrained stages, and that the traditional profit-maximizing production plan which assumes financially unconstrained stages may result in an important deterioration of the objective value. It is found that considering financial decisions and constraints with lot -sizing increases the number of setups and decreases the average inventory. This results in higher short-term loans and lower capital subscriptions and deposits. For financially constrained supply chains, coordinating production plans leads to fewer setups without increasing the supply chain's average inventory. Furthermore, financial and operational parameters have a smaller impact on production and financial plans when the supply chain is coordinated.A