An integer planning-based model for ordering and transporting raw materials for manufacturing companies

. With the development of building materials manufacturing enterprises, the ordering, transportation and storage of raw materials have become important factors affecting the production of manufacturing enterprises. In order to ensure the normal production and operation activities and reduce the production cost as much as possible, enterprises need to reasonably adjust the relevant raw material ordering scheme and transportation scheme to ensure both the considerable production efficiency and the healthy and sustainable production. In this paper, a mathematical model based on sequential heuristic algorithm and integer programming is established to develop the most economical ordering scheme and the least lossy transportation scheme for raw materials in the process of production operation.


Introduction
In this paper, we first use the normal distribution test method [1,2] combined with the sequential heuristic algorithm [3,4] to refer to the 50 important suppliers that have been selected, and finally arrive at the result that the enterprise can satisfy the production requirements by selecting the top 22 suppliers among them. The integer programming method [5~7] is used to develop the most economical ordering scheme for raw materials. According to the ordering scheme and the loss rate of forwarders using 0-1 planning to develop the least amount of loss forwarding scheme.

Model assumptions and notation 2.1 Basic assumptions
(1) Assume that in the first week of the first year, the firm has just enough raw materials in stock to meet two weeks of production.
(2) Assume that the statement in the title that "the enterprise shall maintain, as far as possible, a stock of raw materials that is not less than sufficient to meet its two-week production requirements" means that this week's stock meets this week's and next week's production capacity.
(3) Assume that there are no production accidents in the production process of the enterprise.

Variable Description
The symbols appearing in this paper are specified in Table 1.

Model construction and solving
First we identified the 50 most important suppliers and the results are shown in Table 2. The supply volume basically tends to be stable, except for some large fluctuations. Analyzing the reasons for individual fluctuations, we found that, considering the actual situation, there may be a situation where the higher the order quantity, the higher the supply quantity, i.e., the supply quantity and the order quantity are changing in an approximate trend [8] . Therefore, the ranking is not only related to the supply quantity, that is, the order quantity, but also affected by the out-of-stock rate and the number of weeks out of stock, so there are individual fluctuations.

Selection of suppliers
The conversion rate of converting A, B and C raw materials to capacity is.
where L is the unit capacity. First we use the above conversion formula to convert the order quantity and supply quantity for each week in Annex 1 to capacity respectively, and draw two line statistical graphs, as in Figure 1 and   From the above chart, we can see that the capacity of each week's order quantity is above 28.2 thousand cubic meters, and most of them are less than 30.0 thousand cubic meters, and a few data of order quantity are on the large side. Comparing the capacity of each week's supply quantity, we find that the capacity of supply quantity most of the time does not meet the capacity of 28.2 thousand cubic meters, which may make the inventory decrease after accumulating for many weeks, so we think the data of large order quantity is to make the supply quantity increase in order to increase the inventory, and do not treat it as abnormal data. At the same time, according to the order quantity of each week from the first week is slightly more than 28,200 cubic meters can be inferred, the data of the last five years is only the data of the enterprise for a certain period of time, so we assume that the first week has inventory to meet the capacity of 56,400 cubic meters for two weeks, after each week only to meet the order quantity greater than 28,200 cubic meters can be. According to the supplier ranking, firstly, the supplier's weekly supply is converted to capacity, and then the total weekly supply of all suppliers for 240 weeks is tested for normal distribution, and the histogram and normal distribution curve are drawn as in Figure 3.
From Figure 3, we can see that the total weekly supply of all suppliers is normally distributed, and we take the confidence interval as 0.95. The weekly supply outside the confidence interval is not considered, and then the capacity of each week is accumulated from the first ranked supplier using the sequential heuristic algorithm for the remaining weeks until there is one week in 240 weeks with a capacity greater than or equal to 28,200,000 m3. The number of suppliers that appear at this moment as the selected suppliers is the minimum number of suppliers. Finally, the minimum number of suppliers is 22, which are the top 22 suppliers in question 1, as shown in Table 3.

Ordering program development
Assuming that the unit price of raw materials of category C is a, the raw materials of category A and B are 1.1a and 1.2a, respectively, and considering that the capacity generated by units of raw materials of category A, B and C is different, the consumption of each unit of raw materials of A, B and C are.
Considering that in addition to raw material purchase costs, there are raw material transportation and storage costs, and the unit costs of these two costs are the same. The size of these two costs is mainly reflected in the amount of raw materials required per unit of product, the more raw materials of a certain type required per unit of product, it means that the more transportation and storage costs per unit of this type of raw materials required. The question gives a unit of product consumption A material 0.6m³ , consumption B material 0.66m³ , consumption C material 0.72m³ , therefore, the unit A, B, C material required for the transport costs in the order of A < B < C.
From the actual situation, the cost of purchasing materials must be much larger than the material transportation cost and storage cost, so first consider the material cost: A = C < B, it can be concluded that A and B materials are superior to C materials. Then consider the transportation and savings fees: A < B < C, you can conclude that A material is better than B material is better than C material. Considering the three costs together, the order of priority for ordering raw materials A, B and C is.

GAGBM 2022
Volume 27 (2022) 192 Therefore, when developing the ordering scheme, the priority should be given to purchasing material A, then material C, and finally material B. The objective function of the most economical ordering scheme is given according to the order of purchase priority.
Where G(A) represents the purchase of material A, and G(B) and G(C) are the same. The total weekly supply of 22 suppliers is plotted in Figure 4. Different color dots in the graph indicate the supply quantity corresponding to the same week in each of the 5 years, and the graph is randomly selected to mark the 5 weeks of each year. From the figure can be seen in the same week of each year has a certain periodicity of supply, therefore, for each supplier in the next 24 weeks of weekly supply capacity, we take the maximum value of the previous 5 years of the week's orders for its supply ceiling, for each supplier in the next 24 weeks of arrival rate, take the average of the previous 5 years of the week's arrival rate as the supply rate of this week in the program. Fig. 4 Line graph of total supply from selected suppliers According to the arrival and capacity of the first 240 weeks to calculate the last week of inventory is 0.94 million cubic meters, that is, the future before the first week of inventory is 0.94 million cubic meters, according to the title conditions of the first week of orders should meet.
Where D1 denotes the order quantity in the first week and K0 denotes the inventory quantity before the first week, which is 0.94 million cubic meters. Then the inventory for any week should satisfy.
According to each supplier's weekly supply ceiling for the next 24 weeks can generate a matrix of suppliers' weekly supply capacity, where each element is each supplier's weekly supply ceiling, set to aij (i is the supplier ranked 1-22, j is the number of weeks), then.
Processing the matrix yields the constraint as [9] .

Transit program development
At this point we already know the ordering scheme for the next 24 weeks and how much raw material to order from which suppliers for each week is known, so we develop a specific transit scheme for each week. As with solving for the future weekly supply ceiling, we take the average of the loss rates for the same week each year as the loss rate for this week in the next 24 weeks for each future supplier's weekly supply [10] .
Establish the objective function.
Using the above model to find the transit solution for each future week. Finally, the matrix of the resulting ordering scheme is column summed to obtain the order quantity for each week, which is compared with the order quantity for the first 24 weeks of each of the previous 5 years to obtain Figure 5. The graph above shows that the next 24 weeks have roughly the same ebb and flow trend as the first 24 weeks of ordering in each of the previous five years, so the ordering program is working relatively well.

Conclusion
The main raw materials required for the production of a building materials manufacturer are wood fibers and other fiber materials, etc. The types available are A, B, and C. The enterprise schedules production on a 48-week basis in a year and needs to determine suppliers, order quantities, forwarders, and supply quantities 24 weeks in advance based on capacity requirements. This paper solves the problem of choosing at least a few suppliers to meet the production needs of this enterprise. The paper also develops the most economical weekly ordering plan for raw materials and the least costly transportation plan for the next 24 weeks for these suppliers. Finally, we analyze the effectiveness of the implementation of the ordering and transfer schemes. In this paper, a combination of sequential heuristic algorithm and normal distribution rejection data is flexibly used for least supplier selection; integer programming and iteration are combined to find the most economical ordering scheme. However, uncertainties such as backlog of goods are not considered when building the model.