A generalized stock control formulation for stock management problems involving composite delays and secondary stocks

It is well established in the system dynamics literature that if the stock management formulation ignores the supply line delay, the behavior of a system can be highly oscillatory. But there are no general decision rules to handle other types of delays in stock management systems, such as information delays in decision processing and delays implicit in controlling a primary stock indirectly via a secondary stock. In this research, it is first shown that the consequence of ignoring information delays or ignoring the delays implicit in secondary stock control is equivalent to ignoring the supply line delay in the standard case: large oscillations. Next, the notion of “virtual supply line” is introduced and a generalized stock control heuristic that does take into account these indirect or composite delays is derived; it is shown that the result is a stabilized dynamic behavior. Finally, the decision heuristic is implemented on an example involving all three types of delays, demonstrating the “generic” nature of the proposed formulation structure. The combined result is a significant improvement in the stability of the system, when compared with the standard formulation that considers the supply line delays only. It is also shown that the stability of the results is quite insensitive to even large errors in parameter estimates. The proposed policy is compared with some other standard stabilizing policies used in system dynamics and it is shown that the proposed policy can be conveniently combined with such policies to yield superb stability results. Finally some implementation issues and potential solutions are discussed.