Internal Transfer Pricing for a Decentralized Operation with a Shared Supplier
We consider an operation comprised of multiple autonomous agents that satisfy external stochastic demand using locally managed inventory. Each agent orders discrete replenishments over discrete time from a common internal supplier, and pays internal transfer prices as a function of order quantity. The supplier operates as a cost center whose cost function may depend arbitrarily on the entire vector of orders placed across agents in each period, i.e. there can be technological dependence and fixed costs. We consider the problem faced by central management, which is how to set the internal transfer prices so as to maximize the operation’s total long-run average expected profit, given that the agents choose ordering policies that maximize their local profits minus transfer payments.
We show that within the class of all decentralized stationary policies, an optimal one is induced by our transfer pricing mechanism. We give various examples that illustrate optimal transfer price behaviour. We develop three approaches to computing transfer prices: a nonlinear program solved by sequential linear programming, math programming relaxations, and a scalable adaptive algorithm. We motivate and apply our ideas in the context of stochastic inventory routing, where the supplier’s cost function is given by optimal solutions to the capacitated vehicle routing problem.
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