NONLINEAR-PROGRAMMING ANALYSIS TO ESTIMATE IMPLICIT INVENTORY BACKORDER COSTS

In this paper, we use nonlinear programming to provide an alternative treatment of the economic order quantity problem with planned backorde rs. Many businesses, such as capital-goods firms that deal with expens ive products and some service industries that cannot store their servi ces, operate with substantial backlogs. In practical problems, it is u sually very difficult to estimate accurately the values of the two typ es of backorder costs, i.e., the time-dependent unit backorder cost an d the unit backorder cost. We redefine the original problem without in cluding these backorder costs and construct a nonlinear programming pr oblem with two service measure constraints which may be easier to spec ify than the backorder costs. We find that, with this different formul ation of our new problem, we obtain results which give implicit estima tes of the backorder costs. The alternative formulation provides an ea sier-to-use model and managerially meaningful results. Next, we show t hat, for a wide range of parameter values, it usually suffices to cons ider only one type of backorder cost, or equivalently, only one type o f service measure constraint. Finally, we develop expressions which br acket the optimal values of the decision variables in a narrow range a nd provide a simple method for computing the optimal solution. In the most complicated case, this method requires finding the unique root of a polynomial.