Effective Network Flow Approach for Solving Uncapacitated Dynamic Lot Sizing Problems with Time -Varying Cost

Abstract

This study aims to improve performance for solving uncapacitated dynamic lot sizing
problems with time-varying holding , material and ordering cost . In particular the prices
of some materials depend on seasoning factors arised in agricultural products and
apparel products. The right decisions are required for making benefit in these dynamic
demands and prices. Therefore, this study introduced network system modeling and
solving for its shortest path with the lowest total path cost. The proposed network are
created with huge number of arcs and nodes depending on the quantity combination of
dynamic demands. The shortest path of network can be solved using dynamic
programming with efficient performance .It generates lot sizing which get the minimum
total cost in varying demands, raw material , ordering and holding cost comparing with
Wagner-Whitin and linear programming algorithms. However, it takes prolonged time for
running MATLAB code. The maximum problem size of dynamic programming could be
achieved on range [200 1000] of dynamic demands in 12 periods with 56,754x 56,754
array size. Nevertheless, memory performance test can be depended to RAM of the tested
computer.