Bu çalışmanın amacı, bir dağıtım ağı için çok dönemli sipariş büyüklüğü belirleme problemi için bir stok yönetim modeli oluşturulması ve oluşturulan bu modelin benzetim ile doğrulanmasıdır. Çalışmada, merkezi bir depo ve N adet bayi ile çalışan iki aşamalı bir dağıtım ağında tüm yönetimin tek bir merkezden gerçekleştirildiği bir stokastik stok yönetim sistemi ele alınmıştır. Bayiler malları doğrudan ve yalnızca bir dağıtıcıdan karşılarken, dağıtıcı stoklarını dış bir tedarikçiden yenilemektedir. Ulaştırma kaynakları kısıtlardan dolayı tüm üyelerin dönemsel stok takibi yaptığı ve planlama süresinin tüm üyeler için aynı olduğu kabul edilmiştir. Stok bulundurma maliyetleri zamana bağlı olarak hesaplanmaktadır. Karşılanamayan tüm talepler daha sonra karşılanmak üzere bir bekleme listesine alınmakta ve hem zamana, hem de karşılanamayan talep sayısına bağlı olarak maliyetlendirilmektedir. Bayilerde ve depoda bulundurulan stok miktarı bir üst sınır seviyesi ile kısıtlanmıştır. Bayiler aynı maliyet yapılarına ve stok yenilenme dönemlerine sahiptirler fakat farklı talep ve maliyet parametrelerine bağlı olarak benzer olmadıkları düşünülmüştür. Varsayılan bu sistemin modellenmesi, sistemin bayi, dağıtıcı ve ulaştırma olarak belirlenen üç ayrı bileşeninin önce ayrı olarak ele alınması ve ardından ortak kısıtlar ve değişkenler aracılığıyla merkezi sistem için bütünleştirilmesi yoluyla yapılmıştır. Daha sonra geliştirilen bu modelin doğruluğu deneylerle gösterilmiş ve sunulan modelin varsayımların önerdiği sistem için geçerliliği kesikli benzetim kullanılarak incelenmiştir. İstatistiki testler modelin varsayılan sistemi yansıtma başarımının yüksek olduğu ve varsayılan sistemin iyileştirilmesi için kullanılabileceğini göstermiştir.

We focus on a multi period stochastic lot sizing problem in a two-echelon distribution network which operates under a Push Control System (PCS). The PCS is an integrated inventory control system for the supply chain, in which the supplier decides on the appropriate inventory levels of each product and on the inventory policies to maintain these levels. The main assumption of the push control system is centralized control and availability of enditem demand information. Suppliers monitor retailers’ inventory levels in order to decide order quantities, shipping and timing of replenishment orders. A push control system allows chain members directly benefit from minimization of distortion of demand information (known as the bullwhip effect) which is transferred from downstream supply network members to upstream members (Çetinkaya and Lee, 2000). As a result, it becomes possible to reduce the stock out situations and inventory carrying costs, while increasing the customer service levels. Moreover, centralization of inventory decisions provides a reduction in the variability of system parameters, so makes it possible to deal with time varying demand without much complexity. Existing methods for the evaluation of periodic review, two-echelon policies are usually developed for systems with lead times of integer multiples of periods. This study is concerned with a system where review periods are longer than the replenishment lead times, in other words lead times are multiples (not necessarily integer) of period lengths. In such a case, determination of the order-up-to levels is not only dependent on demand distribution over lead times but also expected inventory levels through the period. Also, inventory carrying costs are charged not on the ending inventory levels of periods but on the average inventory levels of the periods. We assume two types of backorder costs: (1) per unit short, and (2) per unit short per time. When considering the two-echelon situation, we include transportation costs in terms of unit variable transportation costs and fixed batch costs for flow of the products from warehouse to retailers. We study a two-echelon distribution inventory system with a single central warehouse and N retailers. Retailers directly order from the warehouse to replenish their stocks where warehouse replenishes its stock from an outside supplier. All facilities follow a periodic inventory order policy where the length of planning periods are the same for all retailers as well as at the warehouse. We analyzed the retailer, warehouse and transportation components and combined them in to a total system model by system constraints and use of common variables. We developed a simulation model to test the mathematical model. The statistics of interest are determined as: retailer(s)’ average inventory level, warehouse’s average inventory level, retailer(s)’ average backorder level, average number of backorders, and total system cost. The simulation is run 80 times for 20 periods for each experiment and mean and standard variation values of the selected statistics are collected. These values are then compared to the values determined by the mathematical model. The results show that the representation of given periodic review system by mathematical model is acceptable, since mathematically obtained values of most of the given variables are in acceptance region with a 5% type I error, which corresponds to a 95% confidence interval. This model can be used for estimation of cost figures and effects of changes in system parameters by a “what-if analysis” in similar practical situations. Moreover, it can be used in an inventory control optimization problem to determine the optimal lot sizes under given assumptions. The contribution of the study is the novel mathematical model structure which is suitable for handling systems with both longer and shorter lead times than the period length. The model captures the complex cost structures like piecewise linear transportation costs, fixed costs, inventory holding costs, and two types of shortage costs. We present different formulations for obtaining expected values of the parameters depending on the parameter characteristics and assumptions. For example, the expected number of back-orders is evaluated by the distribution of the demand during lead times of retailers and distributor plus the period length. Also, developed model is comprehensive in means of cost parameters handled and it can be easily simplified according to the needs of the business environment.