Numerical Study of a Queuing-Inventory System with Two Supply Sources and Destructive Customers

Models of queuing-inventory systems with two inventory replenishment policies (IRPs) are studied: with a fixed supply volume and with a variable supply volume. Inventories can be replenished from two sources with different lead times and inventory delivery costs. If the inventory level drops to the ordering point s, then a regular inventory order is generated to the slow source. If inventory levels fall below a certain threshold r, where r < s, then the system instantly cancels the regular order and an emergency order to the fast source is generated. The system also accepts destructive customers (d-customers), as a result of which inventory levels are instantly reduced. Random variables involved in the formation of the model have exponential distribution functions (dfs) with finite means. The ergodicity conditions for the systems under study are found, their stationary distributions are calculated, and formulas are proposed for finding their characteristics. The problems of minimizing the total cost of the studied systems are solved by choosing the appropriate values of the ordering point s and threshold value r when using different inventory replenishment policies.