Constrained Joint Replenishment Problem with Refrigerated Vehicles

Abstract

We study a constrained joint replenishment problem with a multi-commodity refrigerated road transport in cold chain logistics. Each truck may have multiple temperature zones, since products in full truckload shipment may have different temperature requirements. In the proposed mathematical programming model, we want to minimize the expected total cost that includes the inventory cost and the transportation cost as well as the penalty cost if temperature violation occurs subject to the full truckload constraint. Under the deterministic demand, the cycle time of each product, the temperature of each zone in each truck and the allocation plan (the number of units of each product to be shipped in each zone in each truck) are obtained from the mixed-integer nonlinear optimization model. Under the stochastic demand, we assume that the inventory is controlled using a periodic review system, and the order-up-to level is chosen to maintain the desired cycle service level of each product. In the case study of one of the largest modern grocery retailers in Thailand, our model is applied to obtain the optimal replenishment policy. Currently, the company’s fleet consists of single-temperature trucks. We estimate the monetary benefit obtained by switching from a single-temperature truck to a multi-temperature truck. We also estimate the cost reduction from reducing the lead time. Finally, our model can be used to quantify the trade-off between the service level and the inventory cost to help the company choose the appropriate service levels.