A multi-item multi-echelon inventory system with quantity-based order consolidation

The efficient management of a distribution system requires coordination between transportation planning and inventory control. Small and frequent shipments can reduce inventory levels while maintaining high customer service levels, but they increase unit transportation costs due to inappropriate utilization of the vehicles and more handling costs. On the other hand shipment consolidation policies reduce unit shipping cost because of economies of scale but they require higher inventory levels to maintain high service levels. Hence, it is of considerable interest to understand the trade-off between shipment consolidation policies and inventory levels. In this paper we consider a distribution network under a quantity based shipment consolidation policy, which means that all orders for a particular destination are held and shipped when a predetermined weight or volume is reached. The studied system is a divergent multi-item multi-echelon network with stochastic demand at the lowest echelon. The stockpoints are controlled by continuous review (s,Q) installation stock policies where the replenishment leadtime is dependent on the shipment consolidation policy. We derive approximations for the first two moments of the leadtimes, the reorder levels, the average inventory levels and the service levels which enables the evaluation of the relevant performance characteristics as well as the allocation of safety stocks for given target service levels. In a numerical study we test our approximations using computer simulation and we illustrate that the estimated service and inventory levels are close to the actual ones

A stochastic inventory policy with limited transportation capacity

In this paper we consider a stochastic single-item inventory problem. A retailer keeps a single product on stock to satisfy customers stochastic demand. The retailer is replenished periodically from a supplier with ample stock. For the delivery of the product, trucks with finite capacity are available and a fixed shipping cost is charged whenever a truck is dispatched regardless of its load. Furthermore, linear holding and backorder costs are considered at the end of a review period. A replenishment policy is proposed to determine order quantities taking into account transportation capacity and aiming at minimizing total average cost. Every period an order quantity is determined based on an order-up-to logic. If the order quantity is smaller than a given threshold then the shipment is delayed. On the other hand, if the order quantity is larger than a second threshold then the initial order size is enlarged and a full truckload is shipped. An order size between these two thresholds results in no adaption of the order quantity and the order is shipped as it is. We illustrate that this proposed policy is close to the optimal policy and much better than an order-up-to policy without adaptations. Moreover, we show how to compute the cost optimal policy parameters exactly and how to compute them by relying on approximations. In a detailed numerical study, we compare the results obtained by the heuristics with those given by the exact analysis. A very good cost performance of the proposed heuristics can be observed

Efficient optimization of the dual-index policy using Markov chains

3We consider the inventory control of a single product in one location with two supply sources facing stochastic demand. A premium is paid for each product ordered from the faster `emergency' supply source. Unsatistfied emand is backordered and ordering decisions are made periodically. The optimal control policy for this system is known to be complex. For this reason we study a type of base-stock policy known as the dual-index policy (DIP) as control mechanism for this inventory system. Under this policy ordering decisions are based on a regular and an emergency inventory position and their corresponding order-up-to-levels. Previous work on this policy assumes deterministic lead times and uses simulation to and their optimal order-up-to levels. We provide an alternate proof for the result that separates the optimization of the DIP in two one-dimensional problems. An insight from this proof allows us to generalize the model to accommodate stochastic regular lead times and provide an approximate evaluation method based on limiting results so that optimization can be done without simulation. An extensive numerical study shows that this approach yields excellent results for deterministic lead times and good results for stochastic lead times

A Mixed-Integer Linear Programming Model for Transportation Planning in the Full Truck Load Strategy to Supply Products with Unbalanced Demand in the Just in Time Context: A Case Study

[EN] Growing awareness in cutting transport costs and minimizing the environmental impact means that companies are increasingly interested in using the full truck load strategy in their supply tasks. This strategy consists of filling trucks completely with one product type or a mixture of products from the same supplier. This paper aims to propose a mixed-integer linear programming model and procedure to fill trucks which considers limitations of stocks, stock levels and unbalanced demand and minimization of the total number of trucks used in the full truck load strategy. The results obtained from a case study are presented and are exported in a conventional spreadsheet available for a company in the automotive industry.Maheut ., JP.; García Sabater, JP. (2013). A Mixed-Integer Linear Programming Model for Transportation Planning in the Full Truck Load Strategy to Supply Products with Unbalanced Demand in the Just in Time Context: A Case Study. IFIP Advances in Information and Communication Technology. 397:576-583. doi:10.1007/978-3-642-40361-3_73S576583397Bitran, G.R., Haas, E.A., Hax, A.C.: Hierarchical production planning: a single stage system. Operations Research 29, 717–743 (1981)Sun, H., Ding, F.Y.: Extended data envelopment models and a practical tool to analyse product complexity related to product variety for an automobile assembly plant. International Journal of Logistics Systems and Management 6, 99–112 (2010)Boysen, N., Fliedner, M.: Cross dock scheduling: Classification, literature review and research agenda. Omega 38, 413–422 (2010)Garcia-Sabater, J.P., Maheut, J., Garcia-Sabater, J.J.: A two-stage sequential planning scheme for integrated operations planning and scheduling system using MILP: the case of an engine assembler. Flexible Services and Manufacturing Journal 24, 171–209 (2012)Ben-Khedher, N., Yano, C.A.: The Multi-Item Replenishment Problem with Transportation and Container Effects. Transportation Science 28, 37–54 (1994)Cousins, P.D.: Supply base rationalisation: myth or reality? European Journal of Purchasing Supply Management 5, 143–155 (1999)Kiesmüller, G.P.: A multi-item periodic replenishment policy with full truckloads. International Journal of Production Economics 118, 275–281 (2009)Goetschalckx, M.: Transportation Systems Supply Chain Engineering, vol. 161, pp. 127–154. Springer, US (2011)Liu, R., Jiang, Z., Fung, R.Y.K., Chen, F., Liu, X.: Two-phase heuristic algorithms for full truckloads multi-depot capacitated vehicle routing problem in carrier collaboration. Computers Operations Research 37, 950–959 (2010)Arunapuram, S., Mathur, K., Solow, D.: Vehicle Routing and Scheduling with Full Truckloads. Transportation Science 37, 170–182 (2003

Controlling a process with three different states

This paper is concerned with a process model which combines two fields: reliability theory and statistical process control. We consider three possible states of a production process: working on high quality, working on low quality and not working. Three different control strategies are presented and investigated. An economic approach is used in order to compare them and to determine the optimal control policy

A multi-item periodic replenishment policy with full truckloads

In this paper we consider a stochastic multi-item inventory problem. A retailer sells multiple products with stochastic demand and is replenished periodically from a supplier with ample stock. At each order instant it is decided which product to order and how much to order. For the delivery of the products trucks with a finite capacity are available. The dispatched trucks arrive at the retailer after a constant leadtime and with each truck fixed shipping costs are charged independent on the number of units shipped. Additionally, linear holding and backorder costs at the end of a review period are considered. Since fixed transportation costs are high coordination of orders and full truckload shipments can benefit from economies of scale. We propose a dynamic order-up-to policy where initial ordersizes can be reduced as well as enlarged to create full truckloads. We show how to compute the policy parameters and in a detailed numerical study we compare our policy with a lower bound and an uncoordinated periodic replenishment policy. An excellent cost performance of the proposed policy can be observed when average time between two shipments is not too large and fixed shipping costs are high.Inventory Stochastic modelling Coordinated replenishments Joint setup costs

A new approach for controlling a hybrid stochastic manufacturing / remanufacturing system with inventories and different leadtimes

This paper addresses the control problem of a stochastic recovery system with two stocking points and different leadtimes for production and remanufacturing. For such systems the optimal control policy for a linear cost model is not known. Therefore, in the literature several heuristic policies are investigated and analyzed. In this paper a new approach is provided which differs substantially from the existing ones. Instead of using one inventory position for the production and remanufacturing decisions we base the decisions on two aggregate variables which are defined different for different leadtime relations. By means of numerical examples we illustrate that system performance, measured in average costs per time unit, can be improved substantially by our new approach, especially for large leadtime differences