The main feature of the model based on the so-called. “ordering point,” also known as an information-level ordering system or continuous review [3], is a condition for placing an order. The decision to place an order is made when the level of disposable inventory[^{1}]falls below a certain specified level, called the information level or reorder point (*ang. ROP – Re-order Point*). The size of the order is determined based on a fixed batch size method. The functioning of the above model is illustrated in Figure 1.

WD – delivery size,

LT- ordering period,

Figure 1. Model of stock level determining the moment of ordering

Source: own elaboration based on [2].

The level of information stock, which determines the moment of ordering, is determined so as to have the ability to meet demand during the replenishment cycle. The amount of demand is determined based on demand forecasts and the average duration of the replenishment cycle. The stock level determined in this way should be increased by the so-called safety stock ^{[2]} [1, 5] . Symbolically, it can be written as follows:

Where:

P_{T} – expected average demand over the assumed replenishment cycle,

ZB – security stock levels.

Determining the first component of the information stock level (P_{T} – expected average demand over the lead time) is relatively straightforward, while determining the second component, which is the safety stock, can cause a bit of trouble. There is a relationship between the size of the safety stock and the level of customer service. It is natural that the larger the safety stock created, the less likely it will be depleted. Keep in mind, however, that maintaining a stockpile entails costs. It therefore seeks to rationalize its size in the context of the level of customer service adopted by the company. The level of customer service determines the company’s probability of immediately meeting demand from its inventory. It thus determines the probability of not depleting the stock during the replenishment cycle. Assuming that demand has a normal distribution, we use tables of the distributions of this distribution to determine the safety factor ω, which is a multiple of the standard error of the forecast, in conjunction with the planned level of customer service. The formula determining the level of information stock takes the form [3]:

Where:

P_{R} – Demand forecast in the adopted forecasting unit of time (e.g., a week),

T – average observed lead time expressed in accepted unit periods,

ω – safety factor,

σ_{PT} – variability of demand during the replenishment cycle, which is determined from the following formula: ,

σ_{T} – variability of replenishment cycle time,

s – The standard error of the demand forecast (if we assume that the forecasting model will be the arithmetic mean model then it can be assumed s=σ_{P}, when σ_{P} – Variability of demand in the adopted unit of time)

The second key parameter of the information-level replenishment model is a fixed delivery lot size. It is usually suggested that the size of the delivery batch should meet the condition of economy and thus ensure that the cost of collecting and maintaining inventory is minimized. If you order a different quantity of goods, the sum of these costs will increase. However, it should be noted that in a situation where the course of the total cost function around the point at which it reaches a minimum is “flat,” then even a few percent deviation from the optimal batch will not cause a significant increase in costs. Thus, there is no need to strictly adhere to a set economic lot size. To calculate the optimal (economic) lot size (*ang. economic order quantity – EOQ*) Wilson’s formula is used [3]:

Where:

P – projected demand over a longer period of time (usually an annual forecast is adopted),

K_{G} – The cost of accumulating inventory – the purchase of one batch, independent of its size,

K_{U} – The cost of keeping one unit of a given commodity in stock for an assumed period of time, usually defined as some fraction of the purchase price, thus:

C – purchase price,

u_{o} – Percentage of maintenance cost in the purchase price.

Currently, there are a number of modifications to the formula presented above that allow it to be applied in various situations. The Sawtooth model, which is a modification of the Wilson model, makes it possible to take into account the cost of inventory on the way. Other modifications make it possible to determine the economic size of a lot assuming inflation or a certain level of shortage in the warehouse [4], or with varying transportation costs depending on the size of the shipment or in cases of large fluctuations in demand. By using economic lot sizing, you can also see which supplier’s offer is more attractive with the discounts they offer. In this case, a calculation should be made for all variants and the most favorable one selected.

**Literature:**

- [1] 20 Cyplik P., Wykorzystanie metod sterowania zapasami – stadium przypadku, Logistyka, 2001, nr 6
- [2] [33] Kiperska-Moroń D., Podstawy podejmowania decyzji logistycznych, wyd. III, Akademia Ekonomiczna, Katowice, 1997
- [3] [38] Krzyżaniak S.: Podstawy zarządzania zapasami w przykładach, Wydanie III, Instytut Logistyki i Magazynowania, Poznań, 2005
- [4] 50 Sarjusz-Wolski Z., O pewnych szczególnych przypadkach sterowania zapasami, Gospodarka Materiałowa i Logistyka 1995, nr 3
- [5] 54 Skowronek Cz., Logistyka w przedsiębiorstwie, PWE, Warszawa, 1995

[1] Disposed (free) stock is understood as the current stock in the warehouse plus the previously placed but not yet fulfilled orders, minus the made reservations of a given assortment intended for execution in a given stock renewal cycle.

[2] A safety (security) stock is understood as a reserve held to achieve an assumed level of customer service in case there is a demand greater than anticipated or the delivery period exceeds the amount observed to date.

*This article was written thanks to the funds from the European Union’s co-financing of the Operational Program Intelligent Development 2014-2020, a project implemented under the competition of the National Center for Research and Development: under the “Fast Track” competition for micro, small and medium-sized entrepreneurs – competition for projects from less developed regions under Measure 1.1: R&D projects of enterprises Sub-measure 1.1.1 Industrial research and development work carried out by enterprises. Project title: “Developing software to improve forecast accuracy and inventory optimization from the perspective of customer and supplier collaborating in the supply chain using fuzzy deep neural networks.*

- #Intelligent Development Operational Program 2014-2020.
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