# Optimizing Inventory Replenishment for Seasonal Demand with Discrete Delivery Times
## 3 Methodology  
Figure 1 shows the general scheme of the study steps. This section starts with defining the unique characteristics of the problem. Then, other steps are discussed later in more detail. The assumptions are very close to the real situation on the ground. The DP model reaches the optimal solution much faster than MIP. The last step shows that the plan must be updated every week depending on the available information about demand and current inventory size. After this step, the discussion of the results is presented. The basic calculations of EOQ, which assume that the demand is stable all the year, are insufficient to take into consideration the trend in demand. In this study, the consideration is for the end products. It is worth mentioning that material requirements planning (MRP) is developed specifically to help manufacturers manage dependent demand inventory, while in this study, the concentration is on independent demand (finished products). Dependent demand is such as the needed number of chair legs, depending on the forecasted number of chairs. The natures of demand for both types are different, and planning time horizon for independent demand is usually longer. The dependent demand is lumpy and occurs once every several weeks. However, independent demand is continuous and can occur every day. The reader might refer to [PERSON] et al. [51] for more information about MRPand its basic possible lot sizing rules, such as fixed order quantity (FQQ), periodic order quantity (POQ), and lot-for-lot (L4L). There are, however, other types of MRP, such as fixed period requirements (FPR), least unit cost (LUC), least total cost (LTC), and part-period balancing (PPB). Optimality can be found in MRP by the Wagner-Whitin Algorithm (WW). However, WW replaces EOQ for the case of lumpy demand (dependent demand), and it usually assumes that demand is known without any variability [52]. The MRP lot sizing rules, however, can be useful for replenishment planning of materials or semi-finished products needed to produce the drinks. Figure 2 shows the first-tier suppliers and customers of the company. There are two stages of supplying drinks: from suppliers or factory to the warehouse, and from the warehouse to small retailers. The company has its own factory beside the warehouse, where drinks can be produced in the factory or bought from suppliers. Different rules of replenishment can be applied between the company and the retailers. This study focuses on the replenishment system from suppliers to the warehouse. Different items can have different calculations. In the literature, economic production quantity (EPQ) was investigated differently, because the assumption was that the production process of the lot needs several days. Usually, a production lot can be produced in few hours in the day. That means that products coming to the warehouse arrive on the same day. Therefore, the economic order quantity and economic production quantity can be investigated in the same way, but with different considerations for lead time. Figure 1: Study general steps. Suppliers are informed about the demand before the items are delivered to the warehouse. These suppliers can be very distant from the retailers and therefore, this warehouse can play the role of a consolidation center to reduce transportation costs. Bigger trucks can be used from the suppliers to the warehouse, and then smaller trucks can be assigned from the warehouse to each customers' area. This supply chain can use the make-to-stock method. The demand rate during a short period can be relatively stable. However, different seasons can have different consumption rates. Therefore, accurate forecasting is necessary. The deviations of the demand are not only in the average demand rate but also in the standard deviation of it. The lot size should be able to adjust the safety stock. Because of the long distance and because of the different types and sizes of drinks, suppliers prefer to send goods every few days (for example one week) instead of every day.