Optimal control of procurement policy optimization with limited storage capacity

Abstract

This research aims to minimize the cost of inventory procurement, i.e raw material procurement. Companies must be able to determine when to order supplies, when to use inventory in the warehouse, and when to postpone buyers demand based on prices, demand, and limited storage capacity. Therefore, the optimal control theory is used to find the optimal solution of inventory procurement problem by combining JIT (just-in-time), warehousing, and backlogging procurement policy. The necessary conditions of Pontryagin’s Maximum Principle (PMP) and Karush-Kuhn-Tucker (KKT) are met in order to obtain the optimal raw material procurement cost. The Hamiltonian is locally optimal along a singular arc. A numerical example is given to compare the generated optimal policy and simple procurement strategy. The cost of inventory procurement that is combining JIT, warehousing, and backlogging policies is more optimal than the cost of inventory procurement that just applies JIT procurement policy. The inventory procurement problem with JIT, warehousing, and backlogging policies can be divided into two cases, i.e. zero final stock and non-zero final stock. The cost of inventory procurement with zero final stock is more optimal than non-zero final stock.