# Heuristic Mathematical Programming Methods for Lot-sizing, Inventory Control, and Distribution Cost Estimation in the Supply Chain

Sammanfattning: The supply function has an important role to support the business to create a customer value. Two important parts of this process is to have the warehouses and production sites in the right location and to have the right items stocked at the right level. This thesis is concerned with those two parts of the supply chain management.Three different areas of inventory control are dealt with. In the first part we consider the classical dynamic lot size problem without backlogging. The second part deals with estimation of holding and shortage costs in two-level distribution inventory systems. In the third part of the thesis we consider the localisation problem in a multi-level supply network system where items are consolidated at a warehouse and distributed to customers on routes. Within the area of inventory control we have evaluated a method earlier suggested by Axsäter (1988), the method is evaluated using a set of test problems and compared other heuristic methods, including the well-known Silver-Meal’s method (Silver and Meal, 1973).  The result shows that the method suggested by Axsäter does perform better than the other methods. In the latest contribution we point to the important differences between Least Period Cost and Silver-Meal when several periods have zero demand. In the area of inventory control we have also studied a two-echelon inventory system where we present methods for estimating the shortage- and stockholding costs in such inventory systems. The second part subject of the thesis concerns supply network optimization. We present a MIP formulation of the problem and evaluate in detail the approximation of the distribution cost when customers are delivered on multi-stop routes. An improved method for estimating the distribution is presented. Besides this introductory overview five research papers are included in the thesis. The first and the last paper consider evaluation of dynamic lot sizing heuristics. The second and third paper deals with cost evaluation of a stochastic two-echelon inventory system and the forth paper with evaluation of methods for estimating distribution costs in a supply network.

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