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

Abstract

We introduce capital flow constraints, loss of good will and loan to the lot sizing problem. Capital flow constraint is different from traditional capacity constraints: when a manufacturer launches production, its present capital should not be less than its present total production cost; otherwise, it must decrease production quantity or suspend production. Unsatisfied demand in one period may cause customer's demand to shrink in the next period considering loss of goodwill. Fixed loan can be adopted in the starting period for production. A mixed integer model for a deterministic single-item problem is constructed. Based on the analysis about the structure of optimal solutions, we approximate it to a traveling salesman problem, and divide it into sub-linear programming problems without integer variables. A forward recursive algorithm with heuristic adjustments is proposed to solve it. When unit variable production costs are equal and goodwill loss rate is zero, the algorithm can obtain optimal solutions. Under other situations, numerical comparisons with CPLEX 12.6.2 show our algorithm can reach optimal in most cases and has computation time advantage for large-size problems. Numerical tests also demonstrate that initial capital availability as well as loan interest rate can substantially affect the manufacturer's optimal lot sizing decisions.

Influences of supply chain finance on the mass customization program: risk attitudes and cash flow shortage

“…Besides, different from the case of the manufacturer, the capital constraint of which is usually related to the long lead time in the production processes, the capital constraint in the MC brand level can be a result of the MC brand itself. That is, the MC brand can be small or medium firms, which have a higher chance to suffer from cash flow shortage (Chen and Zhang, ). This can consequently limit the flexibility in the product modularity level design, especially in the case when the MC brand is risk averse.…”

“…In the meantime, the high requirements of the huge amount of financial resources for MC schemes (e.g., the extra costs spent on the production and inventory management of components and the opportunity costs of advanced high capital investments in MC productions; Agrawal et al., ; Reichwald et al., ) also lead to high operations risks of involved supply chain members. Especially, for some SMEs, which may suffer from cash flow shortage (Chen and Zhang, ), considerable risks can be induced in operations such as the production process, for example, when an MC garment manufacturer received a million dollar order from the retailer, and the retailer paid a certain proportion of the deposit. Thus, the manufacturer must fulfill the order from the retailer according to the contract.…”

Modeling and Simulation for Supply Chain Finance Under Uncertain Environment

“…Specifically, some factors (such as agency issues, bankruptcy costs, information asymmetry) make operational and financing decisions interact in different ways. Recently, a few papers have begun to examine external credit from e-commerce platform (e.g., Chen & Zhang, 2019;Wang et al, 2019), or the combination of bank loan and other credit (e.g., Jin et al, 2018;Huang et al, 2019;Lu et al, 2019).…”

Planning Production and Workforce in a Discrete-Time Financial Model Using Scenarios Modeling

“…Note that we do not need to impose limitations on the periods t > max i∈H {n − h i }, because they are dominated by the inequality defined for t = max i∈H {n − h i }. Further, constraints (6) and 7describe cash-flow conservation, where (6) involves period t = 1 and (7) characterizes the remaining periods. In these equalities, we set all the cash income in the left-hand side and the outgoing cash is placed in the right-hand side.…”

“…Then, we use one of the scenarios modeling techniques described in [8] and in [7] for discussing these three elements' uncertainty in the entire system. Another work in the literature that also integrates single lot-sizing, cash-flow constraints and loan strategies can be found in [6], addressing adequate balance on inventory level planning and customers goodwill on small online retailers acting on e-commerce platforms.…”