Integration of sales, inventory, and transportation resource planning by dynamic-demand joint replenishment problem with time-varying costs

This paper addresses the joint replenishment problem in the context of sales and operations planning. Unlike traditional ones that assume static demands, unit costs, and transportation capacity, we consider dynamic-deterministic demands from sales plans and time-varying unit costs and transportation capacity to deal with the recent logistics conditions. We then introduce the capacitated dynamic-demand joint replenishment problem with time-varying costs. To efficiently solve this problem, a three-phase approach is proposed: (1) simplifying the problem and determining ideal inventory quantities using mixed integer linear programming, (2) estimating policy variables for each item using the covariance matrix adaptation evolution strategy, and (3) updating the ideal inventory quantities based on evaluated shortages until all demands are satisfied. Our method outperforms conventional approaches with at least 12 times faster solution runtimes in tests with up to 100 items. We also obtain the insight that the cost-efficient replenishment plan changes according to the increase rate of the unit transportation cost.