تعیین اندازه دسته تولید پویای چند آیتمی با سیاست های حمل و نقل تأخیری

We optimize ordering and inbound shipment decisions for a manufacturer that sources multiple items from a single supplier. The objective is to satisfy the requirements in the production plan with minimum transportation and inventory holding costs over a multi-period planning horizon. Transportation costs are charged to the manufacturer on a per truck shipment basis. We investigate the option of delaying a less-than-full truckload shipment to the next period, by utilizing the safety stocks as needed. We analyze the impact of delaying shipments on both cost and service levels in stochastic environments through experiments with data from a bus manufacturer. The results indicate that the proposed policy reduces both holding and transportation costs without creating much stock-out risk.

The importance of coordinating the shipment of parts from suppliers with the production schedule has long been recognized by manufacturing companies, with added emphasis in the context of supply chain management, e.g., Jung and Lee (2010) and Sawik (2009). In this paper, we address the inbound shipment of manufacturing parts to facilitate a production plan. We focus on a multi-item dynamic lot-sizing problem where the cost of shipments from the supplier is charged to the manufacturer. We encountered this problem at a leading coach bus manufacturer in Turkey, and found it to be common with other manufacturers that pay for shipments from the suppliers. The bus manufacturer relies on a Material Requirements Planning (MRP) system to generate the dependent demand for parts and subassemblies over a planning horizon. A majority of the required items are procured from local suppliers that are at most several hours of drive away. The manufacturer prefers to source each item from a single supplier and maintain a long-term relationship with its suppliers. Reduction of the supplier base has been a prevalent trend, as pointed out by Minner (2003), due to benefits such as decreased coordination efforts and more attractive contract terms as a result of large purchasing volume. A supplier provides several types of items and when the manufacturer places an order that consists of different quantities of multiple items with given due dates, the supplier arranges a shipment plan. The supplier either takes care of the shipment with its own fleet, or as a common practice, utilizes a third party logistics service provider. The parts to be shipped on the same day are packed into trucks and directly shipped to the manufacturer. The transportation cost consists of a fixed cost per truck and a variable cost that depends on the distance traveled, and thus, can be represented by a per truck–per trip cost. Clearly, this cost structure calls for high truck utilizations. However, the bus manufacturer observed that most suppliers ship partial orders, sometimes as frequently as several times in a day, in less-than-full truckloads (LTL shipments). Hence, significant transportation costs accumulate in the long run when all suppliers are considered. As a remedy, the manufacturer wants to control its suppliers' delivery schedules, in addition to its own parts ordering process, to minimize the sum of transportation and inventory holding costs. We propose and analyze a shipment strategy called the Delayed Transportation Policy (DTP) that aims to achieve truck utilization efficiency. The main idea of this strategy is as follows. Manufacturers keep safety stocks as a buffer against demand variability and possible schedule changes. We investigate the option of delaying LTL shipments to the next period by pulling items from the safety stock, considering that the items are ready at the supplier and could be delivered quickly when needed. We find the optimal ordering and transportation schedule under this policy, and without the policy for comparison purposes, by solving Mixed Integer Programming (MIP) models. The models minimize total transportation and inventory holding costs over a multi-period planning horizon, for which time-varying demands of multiple items are given. We analyze the benefits and risks of the proposed policy by computational tests with data from the bus manufacturer. The remainder of the paper is organized as follows. We review the related literature in Section 2 and present the mathematical models in Section 3. Results of the computational analysis are given in Section 4. Section 5 presents the conclusions.

We studied the problem of finding a cost-efficient ordering and shipment plan for a manufacturer that sources multiple items from a supplier. Given a multi-period planning horizon, we determine how many units of each item should be ordered and shipped in how many trucks in each period to minimize the total inventory holding and transportation costs by solving a MIP model. We proposed a policy called DTP that allows delaying the shipment of trucks with a small truckload percentage to increase vehicle utilization while still satisfying the requirements. This policy takes advantage of safety stocks and short lead times. We investigated benefits and risks of DTP using data from a bus manufacturer by simulation experiments and found that it is beneficial especially when frequent shipments occur. In all data sets, DTP improved the total cost with a small decrease in the service level in case of unexpected random changes in the manufacturer's procurement plans. The potential savings could be significant for manufacturers requiring a large variety of components, as in the automotive industry, and could be weighed against possible risks by the approach demonstrated in this study. The proposed policy can be extended to cases where multiple vehicle types having different capacities and costs are available by modifying the given MIP formulations.