Optimal lot sizing in a non‐cooperative material manager–controller game

It is important for manufacturing companies to optimise purchase order quantities. Inaccurate lot size planning raises costs and lowers profits, which top management of course attempts to avoid through controlling processes. The lot size decision becomes even more relevant in the case of just‐in‐time delivery within a supply chain. The interaction between lot sizing and auditing can be described in terms of a modified inspection game. This paper considers how probabilities, which are the basis for the mixed strategies at equilibrium in the inspection game, will change if the level of penalties accruing to the two players (material manager and controller) depends on the cost deviation caused by the material manager's poor lot‐size planning. It is evident that the Nash equilibrium shifts to the strategy combination (methodically determined decision and low auditing level), if the penalties imposed on the controller and material manager increase. Penalties that depend on such deviations, and an accurate audit of the controller's report by top management, prove to be the best instruments for avoiding mismanagement by the material manager and poor controller work, both of which lead to high costs.