Multi - Product , Multi - Constraint Single - Period Inventory Problem : a Hierarchical Solution Procedure

A single period inventory model, also popularly known as the Newsboy or Christmas tree problem, is to decide the quantity of a single product to be manufactured or purchased for a single period such that the quantity maximizes (minimizes) the expected profit (cost) under stochastic demand. The earliest works in this area were those by Hadley and Whittin (1963) and Hodges and Moore (1970). The later authors solved the product-mix problem with stochastic demand competing for a number of limited resources. Among the many extensions to the classical single period inventory problems developed after the 80’s, the optimization techniques to solve multiproduct, multi-constraint single period inventory problem are of relevance to the present work. Khouja (1999) in his review paper has classified the above extensions into eleven categories. To these, one can add another category, namely the application of techniques like marginal analysis [Hodges and Moore (1970)], Lagrange multipliers [Karmarkar (1981), and [Lau and Lau (1995), etc.], heuristics [Nahmias and Schmidt (1984), etc.], and analytical solution procedures [BenDaya and Raouf (1993), etc.] to solve the constrained newsboy problem.