  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.
