General Model for Single-item Lot-sizing with Multiple Suppliers, Quantity Discounts, and Backordering

Lot-sizing is a very important problem in production and inventory planning under variable demand. In this work, a general model is proposed for a single-item lot-sizing problem with multiple suppliers, quantity discounts, and backordering of shortages. Mixed integer programming (MIP) is used to formulate the problem and obtain the optimum solution for small problems. Due to the large number of variables and constraints in practical problems, the model is too difficult for an optimal solution. Therefore, an effective heuristic method is developed by modifying the well-known silver-meal heuristic. This heuristic method is shown to be effective for this problem, producing near-optimal solutions much faster than MIP.