The Combined Decision Problem: “Pull” vs. “Push” and the Degree of Centralization of Warehousing in the Field of Physical Distribution with a Special Focus on the Polish Market

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This article presents a method for calculating the benefits of using the strategy of replenishing stock in warehouses in the field of distribution (“Pull” or “Push”) in connection with the problem of determining the number of warehouses. The author developed a model to calculate the profitability of different strategies. The use of this model was presented using sample data but based on real cases of companies and processes that the author encountered in Poland in the course of his research.

Abstract

This article concerns the efficiency of the distribution system with different strategies—“Pull” or “Push”—and different sizes of distribution network in terms of when products produced by the manufacturing plant are sent to distribution warehouses. The article hypothesized that the choice of how to replenish stocks in these warehouses—“Pull” or “Push”—and the choice of the degree of centralization of the distribution network (number of warehouses) were two decision problems that should be considered together. This hypothesis was confirmed. A simulation model was developed to conduct simulations for different scenarios (different demand distributions—Gaussian or Gamma different demand fluctuations and the timeliness of replenishing inventories in warehouses). With more expensive goods and greater sales fluctuations, there was a certain tendency towards centralizing storage and using the Pull strategy. The choice of a given strategy had a significant impact on the costs of logistics processes and on the profitability of enterprises. The cost savings ranged from 17% to 54%. The average share of distribution costs in the sales value was 6%. In some cases, it was over 10% (the level of profitability of industrial enterprises In Poland). Choosing the right strategy could, in some cases, change profits by 20%. In most cases, the most cost-effective strategy was a flexible Pull system and centralized storage, which is consistent with real-life business cases.

1. Introduction

The significant decision-making problems which link manufacturing and logistics strategies include determining where the final form of a product is made, where it is stored, and from where it is shipped to the customer. These problems are related to the choice between a Pull or Push strategy.

Pull and Push strategies can be applied at different stages of logistics and production processes, as presented in Figure 1.

The choice of strategy has an impact on the parameters of logistics and production processes and, consequently, on their costs. Since the choice can result in different levels of logistics customer service, it can affect the level of sales.

The aim of this research, the results of which are presented in this article, was to examine the possible impact of a given strategy on economic efficiency and what other factors may affect this efficiency. The problem of choosing between the Pull and Push strategy was combined with the problem of choosing the size of the distribution network (degree of centralization of storage). The aim of these analyses was to show that these two decision-making problems should be considered together rather than separately.

1.1. Pull–Push Strategies and Systems

Pull and Push strategies are the basic production and logistics strategies described by some authors as ‘functional’, that is, according to the classical classification, they are at the lowest level, below competitive strategies, above which are global strategies [1]. At this level, another “functional” strategy is defined—the size of the distribution network (strategy of centralizing or decentralizing the warehouse network). The choice between different strategies is a decision-making problem that should be solved based on a cost-effectiveness calculation.

Strategies at all levels should be consistent with each other, i.e., the strategy at a lower level should stem from the strategy at a higher level. Thus, it seems that the choice of a competitiveness strategy (competing on price or quality) determines the choice of a production or logistics strategy. However, a given production or logistics strategy does not always result in lower costs or better quality. Therefore, it is necessary to carry out calculations to assess the effectiveness of a given strategy.

On the stage of the production process, the strategy “Push” is defined as “Make To Stock” (MTS) and the strategy “Push” is defined as “Make To Order” (MTO) [2,3]. These strategies have an impact both on the costs (production, logistics) and the level of logistics customer service. That means that they can indirectly impact the level of sales (Figure 2). The choice of a given strategy has an impact both on the level of inventories, the capacity for production, the logistics potential, and the technology used (mechanical, automated). They also influence the flow of goods in physical distribution—if the products will be “Pushed” or “Pulled” by the distribution field or directly by customers.

MTS and MTO are two strategies that can be applied in different markets, for different customers and different products. The efficiency of a given production strategy with changing customer requirements depends, among other things, on product characteristics [4]. So, it is not always necessary (and possible) to compare them. The choice of a particular strategy can be influenced by the characteristics of demand (volume of demand, predictability, volatility), the length of lead times, and the nature of cooperation in supply chains [5]. MTO can be chosen for low-volume products, with a wide assortment and low unit volume, manufactured according to individual customer orders. MTS can be used in mass, repetitive production, for high-volume and standard products with a predefined and narrow assortment [2]. In addition to customer demand characteristics, there are also other conditions for the successful implementation of these strategies. In the case of MTO, this condition is a high degree of integration with the suppliers of production materials [6].

There can be combinations and modifications of MTO and MTS strategies. The strategies that combine their advantages are “Postponement” or “Assembly To Order” (ATO). In practice, managers of manufacturing companies usually employ more than one strategy [7]. This includes Engineer-to-Order (ETO). “ETO firms” produce complex, “one of a kind products” and desire shorter lead times as a key factor of the cost competitiveness. Unlike other manufacturing models such as MTO or MTS, the design for an ETO product is not realized until after the engineering process has been completed. Therefore, the problem becomes the determination of an accurate schedule within a complex transactional process for jobs, which have not even been designed yet [8].

For Engineer- and Design-To-Order (ETO and DTO) industrial environments, proper tools are needed. These include, for example, Plan For Every Order (PFEO), which collects information on both suppliers and materials, improving both the management of materials and spaces and communication between the company and suppliers [9]. Another example is tools for the real-time performance evaluation of process measurement based on digital visualization (DV), which use novel technologies to enhance decision-making [10].

The “Push” strategy (as opposed to “Pull”) allows for stable processes throughout the entire production and logistics chain and for a reduction in production costs (lower production capacity required and therefore lower fixed costs, lower production changeover costs, and variable costs). Stable distribution processes, including transportation costs, can also be achieved through, for example, larger delivery batches at times that are convenient for the logistics service provider. Stable production can also be beneficial for the material procurement sector, resulting in lower delivery costs from the supplier. Since the production and distribution of goods is based on forecasts rather than actual demand, this can result in high inventory levels. With the Pull system, inventory can be minimized or eliminated entirely. The effect on customer service is not clear, because in the Push system, products are already ready for delivery. In a Pull system, products are manufactured based on actual demand rather than forecasts. In the MTO system, products still need to be produced, which means that the order fulfillment time may be longer. This strategy can be used when products are produced according to customer requirements (product type, product parameters—“Non-standard products”).

So, in many cases, it is difficult to compare them. For this reason, the comparison presented in this article was made for a specific problem—how to distribute “standard products” to customers. Such products can be sent directly to customers or stored in distribution warehouses. However, even if goods are sent to customers from these warehouses, the question arises as to how stocks are replenished in these warehouses? The production plant can “Push” products to them, or products can be “Pulled” by these warehouses, i.e., the warehouses can place orders according to their actual needs. Each of these strategies has an impact on inventory and warehousing costs in the distribution area, delivery costs, and the level of logistical customer service at the level of these warehouses. So, we are dealing with the problem of “trade-offs”.

As it may seem, the “Pull” strategy can be used when products are made to order and shipped directly to customers. But when goods are distributed through warehouses, the “Push” strategy may be more effective, enabling the stable production and effective delivery of goods to these warehouses and then to customers. However, calculations are needed to prove this.

The choice of a strategy affects at least three basic elements of logistics customer service—availability of inventory in the warehouse, delivery time, and on-time delivery, which are all interrelated. In the “Push” strategy, products available in the warehouse can be shipped instantly to the customer. “Pull” systems are supposed to cope better with the variability of demand processes, but can result in long delivery times if logistics systems are not flexible [11]. However, the delivery time and punctuality of deliveries depend on the distance that the goods are shipped. These factors are taken into account by some authors, as exemplified by the work of Ni [12], who included the cost of order processing delays in the model he developed.

The choice of an appropriate strategy is related to the problem of the uncertainty of demand. Strategies can be reactive (buffering) and proactive (redesign). Angkiriwang et al. [13] made three suggestions based on four case studies. One of the conclusions which was interesting from the point of view of the problems discussed here was that to achieve better flexibility, companies focused more on buffering than on proactive strategies. Inventory therefore allowed the company to adapt to changing customer needs.

The “Push” strategy may be cheaper if it allows for lower production and lower transport costs. This strategy can provide a higher level of logistical customer service as measured by the availability of product stock. However, such security may be illusory, as it may be stocks of products that the customers do not need. A very similar problem is associated with the choice of the degree of centralization of the warehousing network—in a geographically extensive system based on a network of warehouses which are located close to customers, products are ready to be dispatched or collected by the customer. However, again, these may not be the products the customers want. Such a problem arises when the assortment of products is wide, and demand is difficult to predict.

Moreover, it is not obvious that any one strategy is more effective in terms of stock levels. For example, Grosfeld-Nir et al. [14] conclude that:

“Surprisingly, we find that often push out performs pull, i.e., push systems accumulate less WIP than pull systems, while maintaining higher PT”.

Also, a study conducted by Masuchun et al. [15] confirms that a Push strategy can outperform a Pull strategy in terms of customer service levels, but that a Pull strategy can outperform a Push strategy in terms of total inventory. While the latter conclusion is obvious, as that strategy is used to avoid costs but also inventory risks, the former may seem surprising. The occurrence of such seemingly paradoxical situations in terms of both the choice between Pull and Push is confirmed by case studies that can be found in the literature, which justifies continuing research in this field.

1.2. The Economic Efficiency of the “Pull” and “Push” Strategy and Optimization Models

A given strategy does not have to be related to either a competitive strategy or the specifics of a given manufacturing industry, but is an individual choice of a given company, as evidenced by the results of various studies. For example, a study of supply chain strategies used by light vehicle manufacturers in South Africa showed that manufacturers use both Lean and Agile supply chain strategies [16].

The problem is, of course, very complex, because the efficiency of production and logistics systems is not a matter of simply choosing between Pull and Push, or a combination of these systems, but of managing them properly. For example, since the execution of production processes has a large impact on energy consumption, Tan et al. have developed, among other things, a matrix-geometric method of effective Make-to-Order process management to increase energy efficiency [17].

In fact, the Make-to-Order system, if it is to be effective, requires an efficient process management system, also including inventory management. Therefore, research is being conducted on this problem, an example of which is the Cyber-Physical Logistics System (CPLS) developed by Park et al. [18].

Above all, however, it requires proper management of processes throughout the supply chain and appropriate cooperation with suppliers. This problem was addressed by Li et al. [19], who formulated a control model that took into account the dynamic responses of customers to the joint implementation of these strategies in order to minimize the cost of disruption. This model took into account the inventories in this system, which is also worth emphasizing in the context of the considerations carried out in this article, as even if the effect of the Pull system is to reduce the level of inventories, it does not mean their complete elimination.

Pull and Push strategies can be used even in the same company to manage different product groups. Such a view is presented, for example, by D’Alessandro et al. [20], who gave the example of a chemical company that applied the MTS or MTO strategies to specific product groups based on demand volume and variability. However, according to the author of this article, even in the case of standard products, these two strategies can be implemented and are alternatives to each other. It is for such a case that simulations have been carried out, the results of which are presented in this article.

For decision-making purposes and process management in various systems, various models were developed. For example, Schneckenreither et al. [21] presented a flow time estimation procedure for dynamically setting lead times in MTO systems, using an artificial neural network.

The problem of selecting a particular strategy using optimization models is widely described in the literature, which presents both general-purpose models as well as those relating to specific industries [22,23,24,25,26].

Both cost and quality aspects are important in every strategy. A study carried out by Ciechańska and Szwed [27] to compare the effectiveness of the MTS model and the MTA (Make-to-Availability approach) showed that the MTA model can effectively meet customer requirements. Surprisingly, however, the cost resulted from the need to keep inventory at relatively high levels. It is also worth noting that the authors used the category of “opportunity cost”, which was taken into account by Puchkova et al. [28] in their model, which considered various options for inventory control strategies. The optimal solution minimized the total costs (the costs of production, inventory holding and lost sales).

The problem of customer service is particularly important in the MTO (Pull) system, and it is particularly challenging for “Make-to-Order companies” to achieve a high delivery reliability. In order to solve this problem, Mundt and Lödding built a simple model-based procedure to determine delivery times using the throughput diagram with early available information [29]. This problem has been addressed by many authors over the years. For example, Park et al. [30] proposed the delivery date decision support system which integrated the marketing and production planning functions with a consideration of the current capacity and workload smoothing. The system has been implemented in a rotating machinery shop in South Korea.

In the MTO strategy, the accurate estimation of processing time is very important. To solve this problem, tools like workload control (WLC) are developed [31].

Capacity planning is important for efficient production planning in Make-to-Order (MTO) and Assemble-to-Order (ATO). Filho and Marçola [32] proposed a linear programming model to plan the operations using annualized hours (AH). This model has been implemented in a company that produces agricultural implements.

A management system that takes into account possible disruptions in the production system may also be necessary. To solve this problem, Wang et al. (2024) [33] proposed a prediction method based on the spatial and temporal (ST) characteristics of the production process.

The problem of the risk of there being a reduced quality of service in an MTO strategy is highlighted by, for example, Prasetyaningsih et al. [26], who have developed a model to calculate the profitability of this strategy for the case of a company that orders raw material after receiving orders from customers. The lead time is very long, making it impossible for the company to fulfill the customer’s order in time and they have to give a discount of 25–30% of the value of all purchases.

Models have also been developed that take into account the complexity of supply chains or networks. For example, Hammami et al. (2022) [34] have developed a model of a two-stage decentralized supply chain for customized production in a stochastic environment. The model was developed to find the optimal strategy, taking into account the relationship between local delivery times, total delivery times, prices, demand and profits, and the impact of firms’ production capacity.

Fisher [35] developed a model distinguishing between functional and innovative products and between physically efficient and market-responsive supply chains. Products characterized by, among other things, a constant (predictable) demand pattern and long product life cycles require cost minimization and high resource utilization, while innovative products characterized by demand variability and short life cycles should respond to the market with a supply chain that has additional capacity and is more flexible. This model has been empirically tested and has found some validation [36].

There is abundant research concerning the problems of managing and optimizing hybrid systems combining Pull (Make-to-Order) and Push (Make-to-Stock) strategies and models [37]. And also, models have been developed for evaluating hybrid versions of MTO and MTS strategies in specific cases and specific sectors of the economy. For example, Elmehanny et al. developed just such a model for production planning in the garment industry [38]. Specific problems are related to the size of the company, and therefore, Perona et al. [39] developed a model to support inventory management decisions in an MTO–MTS context implemented in small- and medium-sized enterprises (SMEs).

Combining strategies raises new decision-making problems and the need to develop new tools and methods for solving decision-making problems and calculating the profitability of the solutions used. In the case of combined MTS and MTO strategies, in order to optimally position inventories, strategic as well as tactical decoupling points should be identified [40].

To optimize a hybrid “Make-to-Stock–Make-to-Order” environment, Khakdaman et al. [41] developed a novel optimization model for medium-term production scheduling that incorporated three types of uncertainty: suppliers, processes, and customers.

Tsubone and Kobyashi developed the production seat booking system with a combination of Make-to-Order and Make-to-Stock in the production environment [42]. They formulated a production planning model in order to measure the influence on the manufacturing performance, the buffer inventory, and the degree of delivery date satisfaction.

The MTO strategy is characteristic of the Lean Management concept and Just-In-Time strategy. For Lean organizations, the ‘Mapping Tool for Make-to-Order companies’ (2MTO) was developed to analyze and achieve Lean benefits in high-variety–low-volume job shops in an Italian precision mechanic company [43].

Some of the works cited above deal with the very important problem of increasing the efficiency of the systems by proper management. The problem discussed in this article, on the other hand, concerns the issue of the optimization and selection of a given strategy under the unchanged and comparable conditions of using a Pull or Push system.

1.3. Case Studies of Pull and Push Strategies

The literature also contains interesting case studies of companies that have implemented these strategies. Here are some examples:

A company from the plastic packaging sector classified products according to the ABC analysis of the production and used the mixed Pull system, where items in categories A and B should be in supermarkets (Push–MTS) and products in category C should be made according to requests (Pull–MTO) [44]. It is worth noting that this resulted not only in a change in distribution strategy, but also necessitated a reorganization of production processes at the factory.

The need to combine these strategies and use combinations of them for different products postulated by the authors cited above is also supported by case studies from other industries—such as agricultural equipment manufacturing (Köber, Heinecke 2012) [45].

When implementing Pull, there is a need to increase the efficiency of this system so that deliveries to customers can be made efficiently. However, the use of such a strategy can be enabled by the fact that customers are willing to wait for their product. An example of such a strategy is Dell, which was the first company to introduce a Configure-to-Order (CTO) model in which customers can customize computers according to their requirements. The company introduced new products and technologies faster than its competitors. However, shipping times have lengthened (about 7–14 days) because computers are produced after an order is placed [46].

This brings up an aspect that is probably not often mentioned in publications—namely, the logistics aspect. For even if a company actually manages to increase the flexibility of its production system—there remains the question of shipping these goods to customers. In the Push system, the products are already produced; they can be loaded and combined with other products to make the best use of the cargo space of the means of transport. In the Pull/MTO system, such possibilities are already limited. Moreover, in the context of the ever-increasing interest in ecology, it seems that MTS/Push should be the preferred strategy. Similar problems to those in the production field also occur at a later stage, i.e., the physical distribution of goods.

An abundance of research, including models and decision-making tools, demonstrates the complexity of these problems. They also show that there is no single universal optimization model. The model should be adapted to a specific problem.

The question also arises here as to whether the efficiency of a given strategy depends not only on how the stocks in these warehouses are replenished, but also on how many warehouses there are. The level of stock in warehouses, the level of logistics customer service, and the costs of transport to these warehouses are also influenced by the degree of centralization of this network (number of warehouses). Therefore, the question arises as to whether the two decision problems should be considered together. It is difficult to find scientific studies that take these two decision-making problems into account together. For this purpose, a simulation model of such a system was developed to study the impact of different strategies on the efficiency of logistics and, to some extent, production processes.

The literature on the subject and the opinions of company managers and case studies of companies lead to two conclusions. First, the choice of a given production or distribution strategy has a significant impact on the costs of production and logistics processes, and consequently on the financial results of companies that implement given strategies. Secondly, customers expect companies to adapt to their changing requirements, which are difficult to predict. In response, their suppliers tend to use strategies such as “MTO” and “Pull” and avoid building up stocks. This inspired the research presented in this article, which examined the economic efficiency of these strategies.

2. Materials and Methods

The aims of this research were as follows:

• To demonstrate the need to combine decision-making problems concerning the choice between the Pull and Push strategy in the field of goods distribution with the degree of centralization of the distribution network;
• To present the conditions under which given strategies are most effective.

These goals were achieved through simulations conducted with the use of a simulation model developed by the author of the article. The purpose of developing this model and running simulations using it was to see how the size of a distribution network, combined with a given replenishment system (Pull or Push) in that network, affects the efficiency of production and logistics processes. The model can be used to calculate process parameters alone—the level of the inventories, the availability of products (stocked in warehouses) for customers, and the amount of production capacity required. Once the cost elements are taken into account, it can be used to calculate the costs of a given strategy. If this model is expanded to include the costs of logistics processes, it will allow us to calculate the economic efficiency of different strategies or combinations of different strategies. The model can be further expanded by adding production and material procurement costs.

The model uses one measure of the level of logistics service, namely the availability of inventory in a distribution warehouse, which affects the “opportunity cost of sales”. The model calculates how many products could not be sold if the inventory level was insufficient. Thus, it measures the percentage of actual sales versus projected sales.

The tool used to build this model is an Excel spreadsheet with formulae to generate daily demand based on an assumed average daily demand and standard deviation. Simulations are conducted for two types of the demand distribution: Gaussian and Gamma distribution with Excel’s function “IF”, in which the “GAUSS.DIST” or “GAMMA.DIST” function appears, respectively. This is because the model replicates (simulates) the operation of the system throughout the year. The idea is not to use average yearly data, but to reproduce the functioning of a real system as precisely as possible. The demand on each day is generated by a computer “day by day”.

The inventory level on a given day is derived from the inventory level on the previous day, the volume of deliveries on that day, and the sales on that day.

With regard to production, the model works as follows: in the case of the Pull strategy, production volume is adjusted to the current orders of the distribution centers, and in the case of the Push strategy, it is based on the forecasted needs of these centers. In other words, the model adjusts production capacity so that the orders of the warehouses can be 100% fulfilled. This means that in the “Push” system, production should be stable because deliveries to distribution warehouses are made at a constant level. The demand for production capacity should also be lower. In the “Pull” system, in which distribution centers decide when deliveries are to be made, the production system must adapt to current needs. This means that if demand fluctuates, production capacity must be higher and there will be idle production capacity at certain times. This problem will occur especially with seasonal demand. However, to assess whether this will really be the case, calculations must be carried out.

3. Results—Effectiveness of Pull and Push Strategies in Production and Distribution

3.1. The Model and Its Assumptions

The model is a modification of models already developed to evaluate the efficiency and economic effectiveness of the degree of centralization of the warehouse network in the distribution field (Milewski, 2020 [47]; Milewski, Wiśniewski 2022 [48]). The model is applicable to situations where standard products are produced, and the decision problem is whether to “Push” products after production, or whether warehouses should order products based on their needs (“Pull”). So, one could say that warehouses are “customers” for the production. The model presented in this article is a modification of those models because it takes into account not only the number of warehouses but also how stocks are replenished in those warehouses.

The following section presents the results of a simulation conducted to compare the effectiveness of Pull and Push strategies in the field of distributing goods to customers.

The first step was to present the results of a simulation of the impact of the distribution strategy on inventory levels and the availability of stocks (AoS) (Section 3.2).

Subsequently, it was shown how the results of these simulations could be used to calculate the economic efficiency of these strategies (Section 3.3).

The simulations were carried out for two demand distributions: Gaussian and Gamma, and for each of these distributions, for different deviations of demand from the average demand. The model was supposed to take into account different situations in which a given strategy (or a combination of different strategies) would be the most effective. Since the “Push” system is based on forecasts, and “Pull” reacts to actual demand, the effectiveness of these systems was tested with different fluctuations in demand (and therefore different predictability) and different demand characteristics.

Figure 3 shows how strategic decisions affect resource and process parameters and, consequently, economic efficiency.

The functioning of the model is shown in Figure 4.

3.2. Impact on Logistics–Production Potential

The first parameter affected by these strategies was the level of stock availability in warehouses, which can be used as a measure of logistics customer service. The simulation results are presented in Table 1 and Figure 5 and Figure 6.

CDs were replenished in the following three ways:

• “Pull daily” in quantities to meet the actual demand;
• “Push daily”, also in small but fixed amounts, according to forecasts of demand;
• “Push weekly” in fixed amounts corresponding to the average weekly demand.

The third option applies when, e.g., rail transport is used, which is less flexible than road transport, and deliveries are made on schedule.

In the first step, simulations were carried out for a Gaussian distribution and standard deviations of 5% and 30% from the average demand.

For small fluctuations in sales (5% standard deviation of average sales), deliveries in large quantities (“Push weekly”) are the most effective in this regard. A high level of customer service is also ensured by “Pushing” goods daily from the plant to the warehouses. As the number of warehouses increases, the level of customer service drops very sharply in weekly deliveries, while in the “Push daily” method, it remains high.

Daily “Pulled” deliveries result in a lower level of customer service. Only with six distribution centers can they offer a higher level of service than weekly “Push” deliveries. However, in most cases, the best customer service is associated with “Pushing” deliveries in small quantities (daily).

Table 1. Impact of distribution strategies on the availability of stocks in DCs (Gaussian distribution). Yearly sales [items/year] = 40,000.

Strategy	Stand. Dev. of Average Sales	No of DCs
		1	2	3	4	5	6
Pull daily	5%	98.96%	98.95%	98.94%	98.94%	98.93%	98.92%
Push daily	5%	99.62%	99.58%	99.56%	99.56%	99.54%	99.52%
Push weekly	5%	99.67%	99.48%	99.24%	99.07%	98.88%	98.65%
Pull daily	30%	98.83%	98.73%	98.59%	98.68%	98.61%	98.51%
Push daily	30%	99.43%	99.36%	99.07%	99.23%	99.05%	98.97%
Push weekly	30%	97.47%	96.87%	96.41%	96.41%	95.93%	95.61%

Source: own calculations.

Table 1. Impact of distribution strategies on the availability of stocks in DCs (Gaussian distribution). Yearly sales [items/year] = 40,000.

Strategy	Stand. Dev. of Average Sales	No of DCs
		1	2	3	4	5	6
Pull daily	5%	98.96%	98.95%	98.94%	98.94%	98.93%	98.92%
Push daily	5%	99.62%	99.58%	99.56%	99.56%	99.54%	99.52%
Push weekly	5%	99.67%	99.48%	99.24%	99.07%	98.88%	98.65%
Pull daily	30%	98.83%	98.73%	98.59%	98.68%	98.61%	98.51%
Push daily	30%	99.43%	99.36%	99.07%	99.23%	99.05%	98.97%
Push weekly	30%	97.47%	96.87%	96.41%	96.41%	95.93%	95.61%

Source: own calculations.

Figure 5. Availability of stocks in warehouses—5% standard deviation of average sales. Different strategies for distribution (Gaussian distribution).

Figure 5. Availability of stocks in warehouses—5% standard deviation of average sales. Different strategies for distribution (Gaussian distribution).

Figure 6. Availability of stocks in warehouses—30% standard deviation of average sales. Different strategies for distribution (Gaussian distribution).

Figure 6. Availability of stocks in warehouses—30% standard deviation of average sales. Different strategies for distribution (Gaussian distribution).

The situation changes when demand is more volatile (standard deviation of 30% of average demand)—in all strategies and variants, the level of customer service measured by inventory availability is lower, but to varying degrees.

Regardless of the number of CDs in the distribution network, the best inventory availability is again observed for daily “Push” deliveries (Figure 6). This time, a slightly lower but also high level of service is observed for daily “Pull” deliveries. In the case of weekly “Push” deliveries, the level of service is much lower. The results of these simulations are not surprising—as expected, with greater fluctuations in demand and therefore less predictability in demand, a more flexible system that adjusts the volume of deliveries to actual rather than forecast demand is more efficient from a customer service perspective.

The differences between the levels of logistics service appear to be small. But first, they are due to the probability distributions assumed in the simulations and the data generated by the model. Since lower levels of service are observed in practice, there is a need to investigate what the actual probability distributions and sales fluctuations of companies are. The model does not take into account one more service level factor—on-time delivery. This is because it assumes that deliveries arrive on time. Taking into account the delays in deliveries to warehouses would result in either lower service levels or increased inventories.

However, even without considering the above factors, even a small change in the level of logistics customer service can have a big impact on the efficiency of the system. As demonstrated later in the article, the deterioration of service by even a few percent can result in high costs of lost sales. Increasing that service by just a few percent as well can also result in a significant increase in costs—for example, inventory maintenance and warehousing.

Table 2. Impact of distribution strategies on the level of inventories [1000 pcs.] (Gaussian distribution). Yearly sales [items/year] = 40,000.

Strategy	Stand. Dev. of Average Sales	No of DCs
		1	2	3	4	5	6
Pull daily	5%	595	610	620	619	637	657
Push daily	5%	613	680	700	690	716	752
Push weekly	5%	2385	2418	2553	2488	2582	2598
Pull daily	30%	785	905	995	1030	1137	1242
Push daily	30%	925	1267	1608	1383	1728	1894
Push weekly	30%	3329	3658	3986	3807	4366	4816

Source: own calculations.

and Figure 7 and Figure 8 presents results of the simulation of the impact of different strategies on the level of stocks for the levels of service from Table 1.

It is, of course, no surprise that inventory levels increase if there is a shift from a “Pull daily” strategy, which is the most flexible, to a “Push daily” strategy. The largest is in “Push weekly” due to the larger sizes of deliveries to warehouses. In all strategies, inventories increase if sales fluctuations increase from 5% to 30%. In all strategies, too, inventory levels increase as the number of warehouses increases, which confirms (and explains) the existence of the benefits of the strategy of the “centralization of stocks”—better customer service can be achieved with less inventory.

To ensure comparability, calculations were also made for a situation when the level of service in all variants was 100%, which is presented in

Table 3. Impact of distribution strategies on the level of inventories [1000 pcs.] (100% AoS and Gaussian distribution). Yearly sales [items/year] = 40,000.

Strategy	Stand. Dev. of Average Sales	No of DCs
		1	2	3	4	5	6
Pull daily	5%	831	1106	1161	1216	1271	1437
Push daily	5%	944	1164	1438	1713	1987	2262
Push weekly	5%	2390	2923	3472	3746	4569	4843
Pull daily	30%	1390	1667	1944	2221	2498	3330
Push daily	30%	2853	3128	3404	3679	4505	5055
Push weekly	30%	4393	4913	6129	6688	7932	9286

Source: own calculations.

and Figure 9 and Figure 10.

In all variants, there were large increases in stocks, even in the first variant—“Pull daily”/one DC/5% standard deviation. This confirms the relationship between service level, sales, and costs that is known in the logistics literature, and that when the service level is already very high, increasing it even by a small percentage requires a large increase in costs.

The differences were larger in the case of “Pull daily” but smaller in the case of “Push weekly”, which can be explained by the fact that deliveries in larger quantities already resulted in high inventory levels. The differences increased as the number of warehouses increased, once again showing the benefits of centralizing warehousing and confirming the need to combine these two decision problems. In all variants, increasing the number of warehouses resulted in a very high increase in inventory levels. This increase was even greater if sales fluctuations are greater.

The purpose of the next simulation was to examine how these strategies affected the amount of production capacity required in the case in which customer demand was to be 100% satisfied. The impact here was weaker than in the case of inventory (

Table 4. Impact of distribution strategies on the production level and capacity. Yearly sales [items/year] = 40,000.

Strategy	Stand. Dev. of Average Sales	No of DCs
		1	2	3	4	5	6
Pull daily	5%	585	585	585	585	585	585
Push daily	5%	549	549	549	549	549	549
Push weekly	5%	549	549	549	549	549	549
Pull daily	30%	712	712	712	712	712	712
Push daily	30%	554	554	554	554	554	554
Push weekly	30%	551	551	551	551	551	551

Source: own calculations.

). However, given that the cost of maintaining production potential may have been greater than maintaining inventory, there was a need to take this relationship into account as well.

One can see a regularity—the highest required production potential occurred in the “Pull daily” strategy, and the lowest when the products were “Pushed out” in weekly volumes. This also seems easy to interpret—“Pull” requires either a flexible production system or a high potential for the system to adapt to changing needs. Scheduled deliveries, on the other hand, promote production stability.

If demand has a Gamma distribution, service levels are slightly lower than in the case of Gaussian distribution (

Table 5. Impact of distribution strategies on the availability of stocks in DCs (Gamma distribution). Yearly sales [items/year] = 40,000.

Strategy	Stand. Dev. of Average Sales	No of DCs
		1	2	3	4	5	6
Pull daily	3%	98.8%	98.8%	98.7%	98.7%	98.6%	98.5%
Push daily	3%	99.0%	98.9%	98.8%	98.8%	98.7%	98.5%
Push weekly	3%	99.0%	98.8%	98.5%	98.3%	98.1%	97.8%
Pull daily	6%	98.7%	98.5%	98.2%	98.3%	98.2%	98.1%
Push daily	6%	98.8%	98.6%	98.3%	98.2%	98.1%	97.8%
Push weekly	6%	98.8%	98.5%	98.0%	97.8%	97.5%	97.1%

Source: own calculations.

and Figure 11 and Figure 12). The difference, however, is which strategy is more efficient. In the case of Gamma, in almost all cases the level of service was better with daily deliveries than with weekly deliveries. In the strategy “Push weekly “, the level of service was slightly better with a single warehouse. However, it decreased to a large extent with more warehouses. Thus, with weekly deliveries to one warehouse and a standard deviation of 3%, the inventory availability level was 99.0%. When deliveries were made to six DCs, the service level dropped to 97.8%. The situation was similar when the standard deviation was 6%.

Service levels for both Pull and Push daily deliveries also decrease as the number of warehouses increases, but to a much lesser extent than for weekly deliveries.

However, despite not much difference in service levels, the impact of these strategies on stocks is greater. In all cases, stock levels are significantly higher for Gamma than Gaussian distributions (

Table 6. Impact of distribution strategies on the level of inventories [1000 pcs.] (Gamma distribution). Yearly sales [items/year] = 40,000.

Strategy	Stand. Dev. of Average Sales	No of DCs
		1	2	3	4	5	6
Pull daily	3%	1349	1418	1522	1527	1604	1677
Push daily	3%	1443	1550	1732	1727	1856	2071
Push weekly	3%	5229	5927	6166	6515	7222	7736
Pull daily	6%	1507	1784	1872	1910	2069	222
Push daily	6%	2586	2926	3241	3220	3520	3778
Push weekly	6%	7543	9135	9058	9183	9991	10,837

Source: own calculations.

), and in most cases, these differences increase with the number of warehouses. For example, with small standard deviations of demand and one warehouse, the inventory level is 126.85% higher in the case of a Gamma distribution than in the case of a Gaussian distribution. If the goods are distributed over a network of six warehouses, this difference is even greater, at 155.27%. Stocks in the other variants are also significantly higher than under the Gamma distribution. Interestingly, however, these differences would also be very large if customer orders were fully (100%) satisfied. However, in the case of “Pull daily”, inventory levels are very similar (

Table 7. Impact of distribution strategies on the level of inventories [1000 pcs.] (100% AoS and Gamma distribution). Yearly sales [items/year] = 40,000.

Strategy	Stand. Dev. of Average Sales	No of DCs
		1	2	3	4	5	6
Pull daily	3%	843	1114	1170	1225	1283	1447
Push daily	3%	2051	2606	2883	3160	3437	3715
Push weekly	3%	5676	7047	8417	10,062	11,707	12,803
Pull daily	6%	1409	1689	2251	2251	2538	3402
Push daily	6%	4821	5101	5370	5926	6485	7078
Push weekly	6%	8377	10,428	12,736	14,419	16,109	17,833

Source: own calculations.

). This leads to the conclusion that the quick response strategy allows for a high level of customer service without building up high inventory levels.

The effect of the distribution strategy on the production potential for Gamma distribution was also analyzed. The results are similar—first, for each strategy, the amount of required potential is the same for each size of distribution network (number of DCs). Second, the largest production potential is required with the Pull strategy. Thirdly, it is larger with larger sales fluctuations (

Table 8. Impact of distribution strategies on the production level (Gamma distribution). Yearly sales [items/year] = 40,000.

Strategy	Stand. Dev. of Average Sales	No of DCs
		1	2	3	4	5	6
Pull daily	3%	769	769	769	769	769	769
Push daily	3%	554	554	554	554	554	554
Push weekly	3%	548	548	548	548	548	548
Pull daily	6%	955	955	955	955	955	955
Push daily	6%	561	561	561	561	566	566
Push weekly	6%	559	559	559	559	559	559

Source: own calculations.

). However, in the case of Gamma distribution, it is more than 30% larger than in the case of Gaussian distribution.

The simulation results prove that decisions on the choice of replenishment strategy and the size of the warehouse network should be considered together. However, this is obviously not enough to assess the economic effectiveness of a given strategy, as the impact on costs and sales would have to be taken into account.

3.3. Economic Efficiency of Pull and Push Systems

Based on the results obtained from the above simulations, calculations of the economic efficiency of each strategy can be conducted.

The assumptions (data) are shown in

Table 9. Assumptions and input data for calculations of economical effectiveness.

Commodity	Food	Garment	Electronics
No of items [pcs./year]	32,000,000	2,000,000	3,200,000
Weight of a commodity [kg/item]	1.00	2.00	3.00
Weight of a commodity [tons/pellet]	0.80	0.10	0.24
Value of a commodity [EUR/item]	0.6	18	30
Price of a commodity [EUR/item]	1	30	50
Transport costs [EUR/ton/km]—6 CDs
Road transport (Pull)	0.069	0.556	0.232
Road transport (Push)	0.066	0.529	0.221
Rail transport (Push)	0.013	0.106	0.044
Distances [km]	800	800	800
Costs of keeping stocks
Capital costs in inventories	10%	10%	10%
Warehousing [EUR/item/day]	0.001	0.020	0.013

Source: own assumptions.

. When calculating the costs, we made every effort to utilize data on the processes and the costs of these processes occurring in economic practice—e.g., in Poland.

The calculation results for the Gaussian distribution are shown in

Table 10. Costs of distribution of different strategies (Food) [thousands EUR/year].

No of DCs	1	1	6	6	6
Strategy	Pull daily	Push daily	Pull daily	Push daily	Push weekly
Stand. dev. of sales	5%
AoS	98.96%	99.62%	98.92%	99.52%	98.65%
Warehousing and inv.	243	250	268	307	1060
Transport	2380	2267	1779	1694	339
Lost sales	332	121	347	153	432
Total costs	2955	2638	2394	2154	1831
Stand. dev. of sales	30%
AoS	98.8%	99.4%	98.5%	99.0%	95.6%
Warehousing and inv.	320	377	507	773	1965
Transport	2380	2267	1779	1694	339
Lost sales	374	182	476	330	1406
Total costs	3075	2827	2761	2797	3709

Source: own assumptions.

,

Table 11. Costs of distribution of different strategies (Garment) [thousands EUR/year].

No of DCs	1	1	6	6	6
Strategy	Pull daily	Push daily	Pull daily	Push daily	Push weekly
Stand. dev. of sales	5%
AoS	98.96%	99.62%	98.92%	99.52%	98.65%
Warehousing and inv.	268	276	296	338	1169
Transport	2380	2267	1779	1694	339
Lost sales	622	226	651	287	810
Total costs	3270	2769	2725	2320	2318
Stand. dev. of sales	30%
AoS	98.8%	99.4%	98.5%	99.0%	95.6%
Warehousing and inv.	353	416	559	853	2167
Transport	2380	2267	1779	169	339
Lost sales	701	342	892	619	2635
Total costs	3435	3025	3230	3166	5141

Source: own assumptions.

and

Table 12. Costs of distribution of different strategies (Electronic) [thousands EUR/year].

No of DCs	1	1	6	6	6
Strategy	Pull daily	Push daily	Pull daily	Push daily	Push weekly
Stand. dev. of sales	5%
AoS	98.96%	99.62%	98.92%	99.52%	98.65%
Warehousing and inv.	357	368	394	451	1559
Transport	2380	2267	1779	1694	339
Lost sales	1658	603	1735	766	2159
Total costs	4396	3238	3908	2911	4056
Stand. dev. of sales	30%
AoS	98.8%	99.4%	98.5%	99.0%	95.6%
Warehousing and inv.	471	555	745	1137	2889
Transport	2380	2267	1779	1694	339
Lost sales	1870	911	2379	1651	7028
Total costs	4722	3733	4902	4482	10,256

Source: own assumptions.

. They take into account the parameters of shipments; the value of goods; the resulting costs of transportation, inventory maintenance, and storage; and the cost of lost sales. Differences in total costs depend on the delivery strategy used but also on the type of product, because the size and tonnage impact the costs of warehousing and transportation.

The criterion for evaluating the effectiveness of the system is the “total cost”, which includes the costs of inventory, storage, transportation, and the costs of “lost sales”.

The costs of lost sales are derived from the level of inventory availability from previous simulations (Table 1). Thus, if the logistical customer service measured by such a parameter is 98.96% for the “Pull daily”/one DC variant., i.e., the company loses 1.04%. The costs of lost sales are calculating in the following way for “Food”:

No of items × Price of a commodity × 1.04% =
        32,000,000 [pcs./year] × 1 [EUR/item] × 0.04% = 332 EUR/year

which is 11.23% of the “total cost” (Table 10).

For this group of products, the share of these costs increases with the number of warehouses in the distribution network and is obviously higher with larger sales fluctuations. As expected, these costs will be higher for more expensive products (Table 12), which provides a justification for including them in cost calculations.

For “Food” (the cheapest) and with a 5% standard deviation, the lowest total costs occur with regular (“Push every week”) deliveries to six warehouses by rail transport. If sales fluctuations are higher (30%), then deliveries to six warehouses would also be the most efficient, but with the more flexible “Pull daily” delivery system.

Since the value of the goods and the parameters of the shipments are important factors of costs, it can be expected that for more expensive goods (“Electronics”), deliveries with a higher degree of flexibility will be most effective. And this is indeed the case: with small fluctuations in sales (5%), a system of six warehouses is also optimal, yet the cheapest option of rail transport every week should not be used, but rather daily deliveries with road transport, although this is still in the “Push” system. With larger fluctuations in sales (30%) a centralized system is more profitable. This is also the case for “Clothing”.

For similar delivery parameters in the case of Gamma distribution, costs are higher because there is a higher level of inventory, and so the cost of lost sales is higher. For the first variant—deliveries to one warehouse every day in the “Pull” method—total costs increase as the value of goods supplied increases.

As the case of companies that have centralized their distribution systems shows, centralization is effective in the case of large fluctuations in sales; this strategy should therefore be more favorable precisely in the distribution of Gamma demand and more expensive goods. And the results show that it is: only in the case of cheap “Food” is the network of six warehouses still the cheapest.

3.4. Impact of Delivery Times to Warehouses on Economic Efficiency

The model can also be used to simulate the impact of delivery times to warehouses on economic efficiency. The model was modified to include delays after the order was placed by distribution warehouses to the production plant. It was assumed that this delay would be 2 days in all variants, i.e., that warehouses would receive products 3 days after placing an order (in the previous variant, this was after 1 day—Section 3.2. and Section 3.3).

The effect of this factor was significant. As expected, the availability level of stocks was lower and the level of stocks in warehouses increased.

Table 13. Impact of distribution strategies on the availability of stocks in DCs (Gaussian distribution). Three days of delivery to warehouses.

Strategy	Stand. Dev. of Average Sales	No of DCs
		1	2	3	4	5	6
Pull daily	5%	98.34%	98.15%	98.19%	98.16%	98.24%	98.12%
Push daily	5%	98.86%	98.91%	98.87%	98.85%	98.74%	98.82%
Push weekly	5%	99.02%	98.84%	98.63%	98.48%	98.16%	98.03%
Pull daily	30%	98.94%	98.91%	98.52%	98.29%	98.14%	97.29%
Push daily	30%	97.93%	97.83%	97.71%	96.90%	96.58%	96.44%
Push weekly	30%	97.69%	98.27%	96.62%	97.05%	96.74%	96.97%

Source: own calculations.

,

Table 14. Impact of distribution strategies on the level of inventories [1000 pcs.] (Gaussian distribution). Three days of delivery to warehouses.

Strategy	Stand. Dev. of Average Sales	No of DCs
		1	2	3	4	5	6
Pull daily	5%	752	705	845	777	785	885
Push daily	5%	1734	642	689	640	703	705
Push weekly	5%	2301	2333	2453	2392	2351	2457
Pull daily	30%	912	1428	1839	1578	1837	1918
Push daily	30%	1567	1964	2877	1744	1857	2326
Push weekly	30%	2266	4494	2339	2443	2713	3709

Source: own calculations.

,

Table 15. Impact of distribution strategies on the availability of stocks in DCs (Gamma distribution). Three days of delivery to warehouses.

Strategy	Stand. Dev. of Average Sales	No of DCs
		1	2	3	4	5	6
Pull daily	3%	98.50%	98.40%	98.30%	98.30%	98.20%	98.10%
Push daily	3%	98.30%	98.30%	98.10%	98.10%	98.00%	97.90%
Push weekly	3%	98.70%	98.30%	98.10%	97.90%	97.40%	97.00%
Pull daily	6%	98.30%	97.10%	97.80%	98.00%	97.80%	97.60%
Push daily	6%	98.10%	97.90%	97.60%	97.60%	97.40%	97.20%
Push weekly	6%	96.20%	97.90%	94.90%	94.90%	94.30%	93.70%

Source: own calculations.

,

Table 16. Impact of distribution strategies on the level of inventories [1000 pcs.] (Gamma distribution). Three days of delivery to warehouses.

Strategy	Stand. Dev. of Average Sales	No of DCs
		1	2	3	4	5	6
Pull daily	3%	1378	1551	1674	1674	1792	1919
Push daily	3%	1436	1543	1719	1719	1847	2060
Push weekly	3%	6260	6915	7207	7539	8201	8749
Pull daily	6%	1676	2055	2289	2184	2431	2642
Push daily	6%	2567	2914	3231	3203	3507	3765
Push weekly	6%	8668	10,097	10,124	10,285	11,160	12,011

Source: own calculations.

and

Table 17. Comparison of results of simulations (Food).

Time	1 Day		3 Days		1 Day		3 Days
Distribution	Gaussian				Gamma
St. Dev.	5%	30%	5%	30%	3%	6%	3%	6%
No of DCs	6	6	6	1	6	6	6	1
Strategy	Push weekly	Pull daily	Push weekly	Pull daily	Pull daily	Pull daily	Pull daily	Pull daily
Total Costs	1831	2761	2224	3183	2939	3308	3366	3785
Share in Revenue	5.7%	8.6%	7.0%	9.9%	9.2%	10.3%	10.5%	11.8%

Source: own calculations.

summarize the results of the simulations—the level of customer service and the total costs (inventory and storage costs, transportation, lost sales) for three product groups.

The stock availability reached 99% when the demand had a Gaussian distribution in only one case: “Push 1 warehouse” (Table 13). In other cases, it was lower, and in the case of weekly deliveries, “Push weekly”, it was 96–97%. Stock levels were also higher (Table 14).

The distribution of demand was also important here. If the demand had a Gamma distribution, customer service was even lower: in the case of weekly deliveries to six warehouses, the availability was 93.7% (Table 15). The inventory level was also higher (Table 16).

Table 17,

Table 18. Comparison of results of simulations (Garment).

Time	1 Day		3 Days		1 Day		3 Days
Distribution	Gaussian				Gamma
St. Dev.	5%	30%	5%	30%	3%	6%	3%	6%
No of DCs	6	1	6	1	6	1	1	2
Strategy	Push weekly	Push daily	Push daily	Pull daily	Pull daily	Pull daily	Pull daily	Pull daily
Total Costs	2318	3025	3037	3834	3325	3661	4531	4920
Share in Revenue	3.9%	5.0%	5.1%	6.4%	5.5%	6.1%	7.6%	8.2%

Source: own calculations.

and

Table 19. Comparison of results of simulations (Electronics).

Time	1 Day		3 Days		1 Day		3 Days
Distribution	Gaussian				Gamma
St. Dev.	5%		30%		3%	6%	3%	6%
No of DCs	6	6	1	1	1	1	1	2
Strategy	Push daily	Push daily	Push daily	Pull daily	Push daily	Pull daily	Pull daily	Pull daily
Total Costs	2911	3914	3733	4497	4603	5226	5455	5917
Share in Revenue	1.8%	2.4%	2.3%	2.8%	2.9%	3.3%	3.4%	3.7%

Source: own calculations.

show a comparison of the simulation results for all variants (distribution of the change in demand and delivery time to warehouses). They show the supply strategies (combinations of these strategies) with the lowest costs. Extending the lead time of warehouse orders causes a significant increase in costs in every product group.

Extending the delivery time to warehouses for “Food” products results in a 21% increase in costs (Table 17) if the demand has a Gaussian distribution and if the demand fluctuations are small (5%). The increase in costs (28%) for similar parameters is higher in the case of “Electronics” (Table 18), which may seem surprising, taking into account the fact that the value of these goods is higher, so the share of these costs in the sales value should be lower.

The increases are smaller if it is a Gamma distribution, which may lead to the hypothesis that in the case of such a distribution, demand is difficult to satisfy, even with one-day deliveries. In a similar way, one can try to explain the smaller savings in the case when demand fluctuations are greater (6%—Gamma distribution). However, one should be careful in formulating such conclusions. It is surprising that the greatest savings are still seen in the case of medium-value “Clothing” (Table 19). With Gaussian distribution and a 5% demand fluctuation, the costs for this product group are 31% higher, and with a Gamma distribution and a 3% standard deviation, they are 36% higher. However, as with “Food” and “Electronics”, the increases are relatively lower if the sales fluctuations are higher.

Another interesting result of the simulations is that, compared to the “1-day warehouse order fulfillment” variant, if there are 2-day delivery delays, the optimal strategy in almost all cases is “Pull daily” and one central warehouse.

Considering the share of these costs in the sales value, the question arises as to what impact the optimization of delivery processes has on the financial results of companies. This impact depends on the profitability level of companies.

For example, the profitability of the largest Polish companies listed on the Warsaw Stock Exchange are as follows: “Grenevia” (“Electromechanical”)—13% in 2023, but only 3% in 2020. In “Wielton”, from the same industry, it was only 2% and 3% in the same years. The profitability of the tycoons of the Polish Clothing industry in 2023 were as follows: “LPP” was only 9%, and “Vistula Retail Group” 8%. Companies from the food industry also achieved low profitability levels in 2024: “Makarony Polskie”—6%, “Tarczyński”—6%, and “Żywiec”—3%. These profitability levels are therefore similar to the share of distribution costs in the sales value. They were used in individual product groups to simulate the impact of the distribution strategy on profits. The results are shown in Table 17, Table 18 and Table 19.

Delivery delays to distribution centers result in a more than 20% reduction in profits in the “Food” sector, both in the case of the Gaussian and Gamma distributions for both low and high sales fluctuations, and in the “Clothing” sector, for the Gamma distribution and for both low and high sales fluctuations. The profit losses in “Electronics” are lower (3.6–5.3%).

4. Discussion and Conclusions

The results of the calculations support the hypothesis that the choice of distribution strategy—Pull or Push—and the choice of the degree of centralization of the distribution network should be considered together. With more expensive goods and higher sales fluctuations, there is tendency to centralize warehousing and use “Pull” strategies and with cheaper goods and smaller sales fluctuations, there is a tendency rather to “Push” in larger quantities to a larger distribution network.

The simulation results, especially taking into account the extension of the delivery time (Section 3.4), further confirm the views found in scientific publications and case studies that the answer to uncertainty on both the sales and procurement sides is not to expand the distribution network, but on the contrary, to centralize it.

The above calculations are only examples. They are based on the assumptions made regarding storage and transportation costs primarily. For example, it is assumed that the rates for transportation services by rail are 40% lower than by road. However, they may explain why the centralization of distribution systems is quite a common strategy but also why rail transportation has a small share in the transportation market.

However, rail transportation requires a sufficient scale of operations to be profitable. This confirms the view that an important factor in choosing the Pull strategy is the level of production and sales [2]—in the case of low levels and small quantities of deliveries, MTO production and direct delivery to the customer seem to be the optimal solution.

There are other assumptions as well. The model assumes that the company loses revenue in proportion to the availability of products in the warehouse. The impact, however, can be broader—the customer may abandon cooperation with the supplier entirely. Logistical customer service can also be measured by other parameters—the speed and timeliness of deliveries to customers. The effects of the deterioration of these parameters are even more difficult to estimate. A company that wants to use this model should take into account its individual circumstances and possible customer reactions. Most likely, the level of logistics customer service will be based on customer requirements and this level will be the benchmark. The strategy chosen will be the one that allows the customer to be served at the assumed level and will be the cheapest.

It cannot be said that a given logistics or production strategy results from a given competitive strategy of a company (low costs or good customer service). Simulation results also show that each of these strategies—Pull or Push—may be cheaper or result in better customer service, so it is necessary to calculate their economical efficiency using, for example, a model such as the one presented in this article.

In addition, one should consider the impact of choosing a particular strategy not only on distribution costs but also on production costs and material procurement costs. Applying a Pull strategy and maintaining a high level of logistical customer service requires an efficient production and material procurement system. Using the model presented in this article, simulations are carried out to determine the impact of the choice of distribution strategy on the level of required production capacity. As with profitability levels, the share of production costs can be taken from financial reports. The costs include all expenses from the procurement of materials to the production of finished products. The share of these costs in many industries and many Polish companies is very high and often reaches up to 80%.

Any company that would like to use this model would have to use its own demand data, which may have its own characteristics in a given company. Inventory availability is very high, ranging from 90% to 100%. The case studies of companies that have implemented this strategy show that these levels may be lower in practice. This leads to the conclusion that demand fluctuations are actually greater and demand is in fact less predictable. There is therefore a need for research in this area.

Products are sold and distributed to intermediaries who also have their own purchasing strategy, which will have a significant impact on the characteristics and predictability of demand.

The approach used here is economic; it only compares costs and does not assume process improvements. The efficiency of a strategy can be improved by optimizing the management system. For example, a Pull system and centralized storage can be profitable for a company if supply chains are effectively managed and work well together. The processes in these supply chains can be optimized by using a management concept such as Lean Management or an Agile strategy. The “Pull” system and centralized warehousing can be profitable for a company if the supply chains are managed effectively and the partners in these chains work well together.

The simulations carried out show that the type of product and the characteristics of its demand are of significant importance, which is in line with, for example, the concept presented in Fisher’s model [35]. However, the conclusions that can be drawn from it seem to be different. For products with greater demand fluctuations, Fisher proposes an Agile strategy and the creation of potential reserves, including inventory, while in the model presented in this article, the response to demand fluctuations is a Pull strategy and inventory reduction. However, the model presented in this article assumes that demand is predictable, even if there are large fluctuations in demand. It therefore applies more to functional (typical) products rather than innovative ones.

However, the main conclusion of the study is that although certain regularities can be observed regarding the choice of strategy combinations, calculations are necessary to assess in which cases (e.g., type of products) a given strategy is profitable. The article does not show which strategies are used by individual companies, but rather which strategies could be used and how economically efficient these strategies would be.