Optimal stopping and restarting times for multi item production inventory systems with resource constraints

Most of production inventory systems is interested in determining the optimal stopping and restarting times of producing certain commodity. In this paper, a multi-item production inventory model under resource constraints is considered. For any product, each of the production, the demand, and the deterioration rates in any cycle as well as all cost parameters are treated as known and arbitrary functions of time. Shortage for each product is allowed but it is partially backlogged. All cost components are affected by both inflation and time value of money. The existence of resource constraints implies the use of Linear Programming in order to determine the optimal production rates for each item. The objective is to find the optimal production and restarting times for each product in any cycle so that the overall total inventory cost for all products is minimized. A formulation of the problem is developed and rigorous optimization techniques are used to show the uniqueness and global optimality of the solution. An illustrative example which show the applicability of the theoretical results is provided. KeywordsLinear programming, Inventory control, Multiitem production, Varying Parameters, Optimality.