Multi-item inventory control with full truckloads : a comparison of aggregate and individual order triggering

In this paper we consider the stochastic joint-replenishment problem in an environment where transportation costs are dominant and full truckloads or full container loads are required. One replenishment policy, taking into account capacity restrictions of the total order volume, is the so-called QS policy, where replenishment orders are placed to raise the individual inventory positions of all items to their order-up-to levels, whenever the aggregate inventory position drops below the reorder level. We first provide a method to compute the policy parameters of an QS policy such that item target service levels can be met, under the assumption that demand can be modeled as a compound renewal process. The approximate formulas are based on renewal theoretic results and are tested in a simulation study, revealing a good performance. Second, we compare the QS policy with a simple allocation policy, where replenishment orders are triggered by the individual inventory positions of the items. At the moment when an individual inventory position drops below its item reorder level a replenishment order is triggered and the total vehicle capacity is allocated among all items such that the expected elapsed time before the next replenishment order is maximized. In an extensive simulation study it is illustrated that the QS policy outperforms this allocation policy, standing for lower inventory levels to obtain the same service level. While for identical items the difference between the performance of both policies is negligible, differences can be large for different item characteristics

The Can-Order Policy for One-Warehouse N-Retailer Inventory System: A Heuristic Approach

We study an application of the can-order policy in one-warehouse n-retailer inventory system, and propose a heuristic approach for setting the appropriate inventory policy. On the can-order policy, an order is triggered when a retailer's inventory position reaches its must-order level. Then other retailers are examined whether their inventory reaches their can-order level, and if so they are filled by this order as well. Warehouse fulfills all involved retailers' inventory to their order-up-to levels. The can-order policy is not only able to save the total system-wide cost from joint replenishment, but it is also simple to use. Computer simulation is utilized to preliminarily study and to determine the best-known solution. We propose a heuristic approach utilizing decomposition technique, iterative procedure, and golden section search to obtain the satisfying total system-wide cost. This can save our computational time to find the appropriate inventory policy setting. We found that the proposed heuristic approach performs very well with the average cost gap less than 2% comparing to the best-known solution. It also provides satisfactory computational time from the reduced search space. Thus, the can-order policy can be very useful for such system

The Q(s,S) control policy for the joint replenishment problem extended to the case of correlation among item-demands

We develop an algorithm to compute an optimal Q(s,S) policy for the joint replenishment problem when demands follow a compound correlated Poisson process. It is a non-trivial generalization of the work by Nielsen and Larsen (2005). We make some numerical analyses on two-item problems where we compare the optimal Q(s,S) policy to the optimal uncoordinated (s,S) policies. The results indicate that the more negative the correlation the less advantageous it is to coordinate. Therefore, in some cases the degree of correlation determines whether to apply the coordinated Q(s,S) policy or the uncoordinated (s,S) policies. Finally, we compare the Q(s,S) policy and the closely connected P(s,S) policy. Here we explain why the Q(s,S) policy is a better choice if item-demands are correlated.joint replenishment problem; compound correlated Poisson process

A Stochastic Process Study of Two-Echelon Supply Chain with Bulky Demand Process Incorporating cost Sharing Coordination Strategies

This research considers a single-item two-echelon supply chain facing a sequence of stochastic bulky customer demand with random order inter-arrival time and random demand size. The demand process is a general renewal process and the cost functions for both parties involve the renewal function and its integral. The complexity of the general renewal function causes the computational intractability in deciding the optimal order quantities, so approximations for the renewal function and its integral are introduced to address the computational complexity. Asymptotic expansions are commonly used in the literature to approximate the renewal function and its integral when the optimal decisions are relatively large compared to the mean of the inter-renewal time. However, the optimal policies do not necessarily fall in the asymptotic region. So the use of asymptotic expansions to approximate the renewal function and its integral in the cost functions may cause significant errors in decision making. To overcome the inaccuracy of the asymptotic approximation, this research proposes a modified approximation. The proposed approximation provides closed form functions for the renewal function and its integral which could be applied to various optimization problems such as inventory planning, supply chain management, reliability and maintenance. The proposed approximations are tested with commonly used distributions and applied to an application in the literature, yielding good performance. By applying the proposed approximation method to the supply chain cost functions, this research obtains the optimal policies for the decentralized and the centralized cases. The numerical results provide insights into the cost savings realized by the centralization of the supply chain compared to the decentralized case. Furthermore, this research investigates coordination schemes for the decentralized case to improve the utilities of parties. A cost sharing mechanism in which the vendor offers the retailer a contract as a compensation of implementing vendordesired inventory policy is investigated. The sharing could be realized by bearing part of the retailer’s inventory holding cost or fixed cost. The contract is designed to minimize the vendors cost while satisfying the individual rationality of the retailer. Other forms of coordination mechanisms, such as the side payment and delayed payment, are also discussed

Tactical design of production-distribution networks : safety stocks, shipment consolidation and production planning

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Joint replenishment problem in two echelon inventory systems with transportation capacity

Cataloged from PDF version of article.In this study, we examine the stochastic joint replenishment problem in the presence of a transportation capacity. We first study the multi-retailer and singleechelon setting under a quantity based joint replenishment policy. A limited fleet of capacitated trucks is used for the transportation of the orders from the ample supplier in our setting. We model the shipment operations of the trucks as a queueing system, where the customers are the orders and trucks are the servers. Consequently, different transportation limitation scenarios and methods of approach for these scenarios are discussed. We then extend our model to a two-echelon inventory system, where the warehouse also holds inventory. We characterize the departure process of the warehouse inventory system, which becomes the arrival process of the queueing system that models the shipment operations between the warehouse and the retailers. This arrival process is then approximated to an Erlang Process. Several numerical studies are conducted in order to assess the sensitivity of the total cost rate to system and cost parameters as well as the performance of the approximation.Büyükkaramıklı, Nasuh ÇağdaşM.S

Multi-item inventory systems with joint ordering and transportation decisions

Inventory Models;inkoop

The Value of Information in an (R,s,Q) Inventory Model

In this paper we compare three methods for the determination of the reorder point s in an (R; s; Q) inventory model subject to a service level constraint. The three methods di er in the modelling assumptions of the demand process which in turn leads to three di erent approximations for the distribution function of the demand during the lead time.The rst model is most common in the literature, and assumes that the time axis is divided in time units (e.g. days).It is assumed that the demands per time unit are independent and identically distributed random variables.The second model monitors the customers individually.In this model it is assumed that the demand process is a compound renewal process, and that the distribution function of the interarrival times as well as that of the demand per customer are approximated by the rst two moments of the associated random variable.The third method directly collects information about the demand during the lead time plus undershoot, avoiding convolutions of stochastic random variables and residual lifetime distributions.Consequently, the three methods require di erent types of information for the calculation of the reorder point in an operational setting.The purpose of this paper is to derive insights into the value of information; therefore it compares the target service level with the actual service level associated with the calculated reorder point.It will be shown that the performance of the rst model (discrete time model) depends on the coe cient ofvariation of the interarrival times. Furthermore, because we use asymptotic relations in the compound renewal model, we derive some bounds for the input parameters within which this model applies. Finally we show that the aggregated information model is superior to the other two models.

Coordinated inventory replenishment and outsourced transportation operatoins

Cataloged from PDF version of article.We consider a one-warehouse N retailers supply chain with stochastic demand. Inventory is managed in-house whereas transportation is outsourced to a 3PL provider. We develop analytical expressions for the operating characteristics under both periodic and continuous joint replenishment policies. We identify the settings where a periodic review policy is comparable to a continuous review one. In our numerical test-bed, the periodic policy performed best in larger supply chains operating with larger trucks. We also observed that if the excess utilization charge is less than 25%, outsourcing becomes beneficial even if outsourcing cost is 25% more than the in-house fleet costs