The vehicle routing problem with partial outsourcing

This paper introduces the vehicle routing problem with partial outsourcing (VRPPO) in which a customer can be served by a single private vehicle, by a common carrier, or by both a single private vehicle and a common carrier. As such, it is a variant of the vehicle routing problem with private fleet and common carrier (VRPPC). The objective of the VRPPO is to minimize fixed and variable costs of the private fleet plus the outsourcing cost. We propose two different path-based formulations for the VRPPO and solve these with a branch-and-price-and-cut solution method. For each path-based formulation, two different pricing procedures are designed and used when solving the linear relaxations by column generation. To assess the quality of the solution methods and gain insight in potential cost improvements compared with the VRPPC, we perform tests on two instance sets with up to 100 customers from the literature

The Inventory routing problem with demand moves

ABSTRACT: In the Inventory Routing Problem, customer demand is satisfied from inventory which is replenished with capacitated vehicles. The objective is to minimize total routing and inventory holding cost over a time horizon. If the customers are located relatively close to each other, one has the opportunity to satisfy the demand of a customer by inventory stored at another nearby customer. In the optimization of the customer replenishments, this option can be included to lower total costs. This is for example the case for ATMs in urban areas where an ATM-user that wants to withdraw money could be redirected to another ATM. To the best of our knowledge, the possibility of redirecting end-users is new to the operations research literature and has not been implemented, but is being considered, in the industry. We formulate the Inventory Routing Problem with Demand Moves in which demand of a customer can (partially) be satisfied by the inventory of a nearby customer at a service cost depending on the quantity and the distance. We propose a branch-price-and-cut solution approach which is evaluated on problem instances from the literature. Cost improvements over the classical IRP of up to 10% are observed with average savings around 3%

The Dynamic-Demand Joint Replenishment Problem with Approximated Transportation Costs

In a vendor-managed inventory setting, a supplier determines the timing and size of replenishments for its customers. In the Dynamic-Demand Joint Replenishment Problem (DJRP), one assumes that the supplier pays a fixed fee for replenishing a customer which often occurs if the supplier outsources transportation. Hence, there is no incentive for the supplier to schedule replenishments for nearby customers in the same period. This results in higher transportation costs for the carrier, decreased vehicle utilization and increased future fees for the supplier. To lower costs for both parties, this paper extends the traditional DJRP to the DJRP with Approximated Transportation Costs (DJRP-AT) by taking transportation considerations into account. Since routing problems are difficult to solve and it is not necessary to know the sequence of the deliveries to the customers as these are outsourced, the transportation costs for a given set of customers are approximated using classical schemes. A solution approach for the DJRP-AT based on Branch-and-Cut-and-Price is validated using test instances from the literature. Results show improvements of 4% on average and up to 14.4% for individual instances compared with the DJRP. Moreover, when the DJRP-AT is compared with the DJRP on instances derived from a real-life case, similar savings are obtained. Comparing the DJRP-AT to an equivalent problem with actual routing costs, the solution values of the DJRP-AT are on average only 0.77% higher showing the value of the approximation

The Inventory Routing Problem with Demand Moves

In the Inventory Routing Problem, customer demand is satisfied from inventory which is replenished with capacitated vehicles. The objective is to minimize total routing and inventory holding cost over a time horizon. If the customers are located relatively close to each other, one has the opportunity to satisfy the demand of a customer by inventory stored at another nearby customer. In the optimization of the customer replenishments, this option can be included to lower total costs. This is for example the case for ATMs in urban areas where an ATM-user that wants to withdraw money could be redirected to another ATM. To the best of our knowledge, the possibility of redirecting end-users is new to the operations research literature and has not been implemented, but is being considered, in the industry. We formulate the Inventory Routing Problem with Demand Moves in which demand of a customer can (partially) be satisfied by the inventory of a nearby customer at a service cost depending on the quantity and the distance. We propose a branch-price-and-cut solution approach which is evaluated on problem instances from the literature. Cost improvements over the classical IRP of up to 10 % are observed with average savings around 3 %