JP2020013261A - Yard waiting demurrage time prediction device, method and program - Google Patents

Abstract

To enable the prediction of an expectation value of a yard waiting demurrage time in landing articles transported by using a transport ship at an unloading point.SOLUTION: In the case where the amount obtained by adding a prediction object period start total stock in a yard of an unloading point and an unloading amount total (hereafter, the unloading amount total is called as an arrival amount) of a transport ship that arrives during a prediction object period exceeds the capacity of the yard, a yard waiting demurrage time prediction device 100 calculates an expectation value of a yard waiting demurrage time by integrating a function obtained by multiplying a formula of a prediction model by the occurrence probability of the arrival amount per predetermined unit time with respect to the arrival amount by using the prediction model that yard waiting demurrage occurs as much as a time obtained by dividing an excess by a used amount of the prediction object period.SELECTED DRAWING: Figure 1

Description

  The present invention relates to a yard waiting time estimation device, method, and program for estimating a yard waiting time at the time of unloading goods transported using a transport ship at a landing site.

In the steel industry, electric power companies, etc., unload raw materials, fuels, materials, products, etc., transported by ships (transportation vessels) from overseas production bases, etc., at landing sites such as factories and inventory bases. Store as inventory in receiving area called yard.
Here, when the transport ship arrives at the landing site, the capacity of the yard is insufficient, and the ship cannot be unloaded. Such a vessel is called a yard waiting vessel, and a large percentage of the causes of transport vessels staying at sea is large, and there is a demand for a drastic technological development to reduce the yard waiting vessel. In order to reduce the number of yards in the yard, it is necessary to reduce the amount of stock held in the yard.However, the lower the amount of inventory, the greater the risk of shutdown due to out of stock. It can be said that it is important to identify trade-offs in inventory levels. Until now, theoretical analysis has not been performed sufficiently on yards in yards, and there is a problem that it is not clear how much yards in yards will decrease in order to reduce inventory.

  Patent Literature 1 discloses a raw material handling management method for loading and unloading raw materials with a plurality of ships at a port having a plurality of berths. From the scale, unloading capacity, and repair information, automatically set a cargo handling plan including the berth of the ship, the date of berthing, and the date of departure, and calculate the early departure / demurrage fee for the ship, so that the entire port A raw material handling management method is disclosed in which a cargo handling plan and an early leaving / shipping fee are output, and if there is a modification of the vessel assignment plan, the aforementioned procedure is executed again based on the modified vessel assignment plan. I have.

  Non-Patent Document 1 discloses that a product arriving according to a Poisson process is temporarily stored in a buffer, and a warehouse system is modeled by a queuing network theory for a warehouse that ships a product when group constraints are satisfied. A method for analytically calculating a warehouse capacity is disclosed.

JP-A-11-100127

Noriyuki Ozaki, Toshimitsu Higashi, Tatsunori Hara, Jun Ota: Layout Design Method for Automatic Warehouse Considering Operational Constraints, Proc. 29-30, 2014

However, Patent Literature 1 is a technique for precisely calculating the early leaving / berthing fee for a fixed plan, and when a condition such as a fleet configuration or facility capacity is given, the yard waiting time is given. It does not predict the expected value.
Non-Patent Document 1 discloses a method of determining a warehouse capacity based on the current equipment configuration and the arrival frequency of products. When the warehouse capacity is exceeded, the time during which products cannot enter the warehouse (a yard waiting ship of a transport ship). Time).

  The present invention has been made in view of such circumstances, and an object of the present invention is to be able to predict an expected value of a yard waiting time when given conditions such as a fleet configuration and facility capacity. I do.

The gist of the present invention for solving the above problems is as follows.
[1] A yard waiting time prediction device for predicting a yard waiting time at the time of unloading an article transported using a transport ship at a landing site,
The sum of the stock quantity at the beginning of the forecast period in the landing yard and the total unloading amount of the transport ship arriving during the forecast period (hereinafter, the total unloading amount is referred to as the receiving amount) is the amount of the yard. If the capacity was exceeded, using the prediction model that the yard waiting vessel occurs only the time divided by the amount of use in the prediction target period, the excess,
Means for calculating the expected value of the yard waiting time by integrating a function obtained by multiplying the calculation formula of the prediction model by the probability of occurrence of the amount of arrival per unit time with respect to the amount of arrival. A yard waiting time prediction device.
[2] Based on actual data, the number of transport ships arriving per the predetermined unit time and the unloading amount of each transport ship are represented by probability distributions, respectively.
The arrival amount per predetermined unit time is represented by a probability distribution that combines a probability distribution of the number of transport ships arriving per predetermined unit time and a probability distribution of unloading amount of each transport ship. A yard waiting time prediction device according to [1].
[3] Based on actual data, the number of transport ships arriving per the predetermined unit time is represented by a Poisson distribution, and the unloading amount of each transport ship is represented by a gamma distribution,
The yard waiting time estimation device according to [2], wherein the arrival amount per predetermined unit time is represented by a Tweedie distribution.
[4] The yard according to any one of [1] to [3], wherein the forecast stock at the start of the forecast period, the capacity of the yard, and the usage amount in the forecast period are given as fixed values. Waiting vessel time prediction device.
[5] The yard waiting time estimation device according to [4], wherein the integration section is set to ∞ from a value obtained by subtracting the stock amount at the start of the prediction period from the capacity of the yard.
[6] A yard waiting time prediction method for predicting a yard waiting time when unloading goods transported by using a transport ship at a landing site,
The sum of the stock quantity at the beginning of the forecast period in the landing yard and the total unloading amount of the transport ship arriving during the forecast period (hereinafter, the total unloading amount is referred to as the receiving amount) is the amount of the yard. If the capacity was exceeded, using the prediction model that the yard waiting vessel will occur for the time obtained by dividing the excess by the amount used in the prediction target period,
An expected value of the yard waiting time is calculated by integrating a function obtained by multiplying the calculation formula of the prediction model by the occurrence probability of the amount of arrival per unit time with respect to the amount of arrival. Yard waiting time prediction method.
[7] A program for predicting the yard waiting time when unloading goods transported using a transport ship at a landing site,
The sum of the stock quantity at the beginning of the forecast period in the landing yard and the total unloading amount of the transport ship arriving during the forecast period (hereinafter, the total unloading amount is referred to as the receiving amount) is the amount of the yard. If the capacity was exceeded, using the prediction model that the yard waiting vessel will occur for the time obtained by dividing the excess by the amount used in the prediction target period,
A computer calculates the expected value of the yard waiting time by integrating a function obtained by multiplying the calculation formula of the prediction model by the probability of occurrence of the arrival amount per unit time with respect to the arrival amount. Program to let you.

  ADVANTAGE OF THE INVENTION According to this invention, when conditions, such as a fleet composition and equipment capacity, are given, the expected value of yard waiting time can be predicted.

1 is a diagram illustrating a schematic configuration of an entire system including a yard waiting time estimation device according to an embodiment. 5 is a flowchart illustrating a yard waiting time calculation method by the yard waiting time prediction apparatus according to the embodiment. It is a figure for explaining a way of thinking of yard waiting time. It is a graph which shows the example of distribution of the arrival interval of the transport ship of a steelworks. It is a graph which shows the example of distribution of the unloading amount for every transport ship which arrived at the steelworks. It is a graph which shows the result of having expressed the amount of arrival per day by Tweedie distribution. It is a graph which shows the expected value of the yard waiting time with respect to yard surplus.

Hereinafter, preferred embodiments of the present invention will be described with reference to the accompanying drawings.
In the present embodiment, as an example of the steel industry, in a situation where raw materials such as ore and coal transported using a transport ship are unloaded at steelworks from mountains located around the world, An example of predicting an expected value of time (hereinafter, also simply referred to as yard waiting time) will be described. The raw material corresponds to the article referred to in the present invention, and the steelworks corresponds to the landing in the present invention.

  The forecast of yard waiting time shall be made on a daily basis. Because the operation data is updated on a daily basis, it is desirable to predict the yard waiting time on a daily basis. The present invention is not limited to the day unit, but is also applicable to the case where the yard waiting time is predicted at different unit times. For example, if a plurality of days is set as a unit time, an average yard waiting time in a plurality of days can be predicted.

FIG. 1 is a diagram illustrating a schematic configuration of an entire system including a yard waiting time estimation device according to an embodiment.
The yard waiting vessel time prediction device 100 predicts the yard waiting vessel time occurring in the prediction target period. The database 200 stores various data including actual data used by the yard waiting time prediction device 100 and data of calculation results by the yard waiting time prediction device 100. The host computer 300 is also referred to as a business computer or the like, and refers to data stored in the database 200, and stores and updates data in the database 200.

  In the yard waiting time estimation device 100, the data capturing unit 101 reads, from the database 200, the arrival date and time of each transport ship, the unloading amount of each transport ship, and the daily amount of raw materials during the data analysis period at the target steelworks. Data such as average usage, daily average inventory of yards, and yard capacity are captured. As the data analysis period, for example, the user may be allowed to specify an arbitrary period.

The prediction model construction unit 102 constructs a prediction model for predicting the yard waiting time based on the data acquired by the data acquisition unit 101.
In the present embodiment, it is assumed that the yard waiting time per unit time in a certain prediction target period is predicted, and both the prediction target period and the unit time are one day. If the prediction target period extends over a plurality of unit times such as one month, the following calculation is performed for each unit time. The day on which this calculation is performed is hereinafter also referred to as the current day. As shown in FIG. 3, the inventory amount of the previous day, which is the forecasted inventory amount at the yard of the steelworks, and the total unloading amount of the transport ship arriving on the day (hereinafter, the total unloading amount is referred to as the receiving amount). If the combined amount exceeds the capacity of the yard, it is considered that a yard waiting vessel will occur only for the time obtained by dividing the excess by the usage on the day. That is, the yard waiting time [day (day)] is represented by the calculation formula of Expression (1). In the present embodiment, the stock amount [ton (t)] of the previous day, the yard capacity [ton], and the usage amount [ton] of the day are given as fixed values. The stock quantity of the previous day may be, for example, a daily average stock quantity of the yard. Further, the usage amount on the day may be, for example, a daily average usage amount of the raw materials. In this manner, in equation (1), the incoming quantity [ton] of the day becomes a probability variable, and the expected value of the yard waiting time can be calculated by calculating the probability distribution of the incoming quantity of the day.

  The most influential factor on the yard waiting time is the amount of goods received on the day, and the calculation accuracy does not significantly deteriorate even if other items are set to definite values. Note that the inventory amount, yard capacity, and usage amount on the previous day are not limited to fixed values, and may be given as functions. For example, if daily performance data is given to the usage amount of the previous day, the stock amount of the previous day, and the capacity of the yard, the yard waiting time expected on that day can be predicted.

Assuming that the set of transport ships arriving on the day is i = 1, 2, 3,..., N, and the unloading amount of each transport ship is X _i , the incoming amount y of the day is expressed as shown in Expression (2). , it is given as the sum of unloading amount of X _i of the transport ship to arrive on the day.
Here, the number N of transport ships arriving per day is a random variable that varies from day to day. Moreover, unloading amount X _i for each transport ship is also a random variable which varies by transport ship. Therefore, to represent the stock amount y of the day with a probability distribution, it may be obtained and the probability distribution of the number N of the transport ship to arrive per day, and the probability distribution of the unloading amount X _i of each transport ship.

The prediction model construction unit 102 includes a ship number modeling unit 102a, an unloading amount modeling unit 102b, and a receiving amount modeling unit 102c. Although the details will be described later, the ship number modeling unit 102a represents the number N of transport ships arriving per day by a probability distribution. Moreover, unloading amount modeling unit 102b will be described in detail later, it represents the unloading amount X _i for each transport ship in a probability distribution. Then, the arrival amount modeling unit 102c calculates the amount of arrival per day by the probability distribution of the number N of transport ships arriving per day obtained by the number of ships modeling unit 102a and the unloading amount modeling unit 102b. represented by a probability distribution obtained by combining the probability distributions of the landing amount X _i for each determined transport ship.
It should be noted that the construction of the prediction model here does not mean that the calculation formula of equation (1) itself is created, but the prediction model is set by reflecting the given information in the framework of the calculation formula set in advance. To do.

  The calculation unit 103 integrates a function obtained by multiplying the calculation formula (formula (1)) of the prediction model constructed by the prediction model construction unit 102 by the probability of occurrence of the amount of arrival per day for the amount of arrival. Calculate the expected value of the yard waiting time.

  The calculation result output unit 104 outputs the expected value of the yard waiting time, which is the calculation result of the calculation unit 103. Outputting the calculation result means, for example, displaying it on a display device (not shown) or sending it to an external device such as the database 200.

FIG. 2 is a flowchart illustrating a yard waiting time estimation method by the yard waiting time estimation device 100 according to the embodiment.
In step S1, the data capturing unit 101 reads, from the database 200, the date and time of arrival of each transport ship, the amount of unloading of each transport ship, the average daily usage of raw materials, and the yardage during the data analysis period at the target steelworks. Import data such as daily average inventory and yard capacity.

In steps S2 to S4, the prediction model construction unit 102 constructs a prediction model for predicting the yard waiting time on the basis of the data captured in step S1.
As described above, the yard waiting time is expressed by the equation (1), and the expected value of the yard waiting time can be calculated by calculating the probability distribution of the arrival amount on the day.

In step S2, the number-of-ships modeling unit 102a represents the number N of transport ships arriving per day in a probability distribution based on the data captured in step S1.
FIG. 4 shows an example of the distribution of arrival intervals of transport ships at a steelworks. The horizontal axis in FIG. 4 represents the arrival interval [days] of the transport ship, and the vertical axis represents the frequency [times]. The distribution in FIG. 4 is obtained based on the arrival date and time of each transport ship during the data analysis period captured in step S1. From FIG. 4, it can be seen that the arrival intervals of the transport vessels follow an exponential distribution. The exponential distribution is a distribution representing random arrival, and is a distribution characterized by a parameter λ as shown in equation (3). λ represents the average number of transport ships arriving at the steelworks per unit time. In the present embodiment, λ is the average number of transport ships arriving at the steelworks per day. As a result of fitting by non-linear regression analysis to the distribution of the arrival intervals of the transport ship in FIG. 4, a value of λ = 0.25 was obtained.

  Here, a process in which the intervals of events follow an exponential distribution is called a stationary Poisson process, and it is known that the number of arrivals per unit time in an arrival process in which the arrival intervals follow an exponential distribution follows a Poisson distribution. Therefore, if the probability that the number of transport ships arriving on the day is N is P [N], the probability distribution is represented by Expression (4).

  In the present embodiment, the arrival interval of the transport ship is represented by an exponential distribution, but is not limited to the exponential distribution. For example, when a transport ship is accommodated in a plurality of ports, the arrival intervals of the transport ships may follow a gamma distribution. In this case, the arrival interval of the transport ship may be represented by a gamma distribution. When the arrival interval of the transport ship changes depending on the season, the parameter λ of the exponential distribution can be a function λ (t) that changes with time t. In this case, the number N of transport ships arriving per day can be represented by a probability distribution called a non-stationary Poisson distribution.

In step S3, the unloading amount modeling unit 102b, based on the acquired data in step S1, represents the unloading amount X _i for each transport ship in a probability distribution.
FIG. 5 shows an example of the distribution of the unloading amount of each transport ship arriving at the steelworks. The horizontal axis in FIG. 5 represents the unloading amount [ton] for each transport ship, and the vertical axis represents the frequency [times]. The distribution in FIG. 5 is obtained based on the unloading amount of each transport ship during the data analysis period, which is taken in step S1. From FIG. 5, it can be seen that the unloading amount of each transport ship has a peak at about 40,000 to 60,000 tons, and has a long tail on the right side. In the present embodiment, the unloading amount X _i for each transport ship, represented by gamma distribution. The gamma distribution is known to be suitable as a modeling method for a distribution having a long tail on the right side, and is a distribution characterized by a scale parameter α and a shape parameter θ as shown in Expression (5). As a result of performing a non-linear regression analysis by a gamma distribution on the distribution of the unloading amount of each transport ship in FIG. 5, values of α = 4.2 × 10 ⁻⁵ and θ = 3.24 were obtained.

In the present embodiment, the unloading amount X _i for each transport ship expressed in gamma distribution, it is not limited to a gamma distribution. For example, if the unloading amount of each transport ship has a uniform variation centered on a certain average lot size, the unloading amount of each transport ship may follow a normal distribution. In this case, the unloaded quantity X _i for each transport ship may be represented by a normal distribution.

In step S4, the arrival amount modeling unit 102c calculates the arrival amount per day based on the probability distribution of the number N of transport ships arriving per day obtained in step S2 and the probability distribution of each transportation ship obtained in step S3. represented by a probability distribution obtained by combining the probability distributions of the landing amount X _i.
In the present embodiment, as described above, represents the number N of transport vessels arriving per day at Poisson distribution, it expressed the landing amount X _i for each transport ship in gamma distribution. Here, it is known that a distribution in which the number of event occurrences follows a Poisson distribution and a processing (loading amount) for each event follows a gamma distribution can be modeled as a distribution called a Tweedie distribution. The Tweedie distribution is a kind of exponential distribution family, and the cumulative distribution function follows Expression (6).

6, the probability distribution of the number N of transport vessels arriving per day based on FIG. 4, the arrival of the daily by using the probability distribution of the landing amount X _i for each transport ship according to FIG. 5 The result represented by the Tweedie distribution is shown. The horizontal axis in FIG. 6 represents the amount of incoming cargo [ton] per day, the left vertical axis represents the probability, and the right vertical axis represents the cumulative probability. The solid line in FIG. 6 represents the probability distribution, and the dotted line represents the cumulative probability distribution. It can be seen that the probability of arrival per day is most likely to be 0, and when there is an arrival, the probability becomes maximum around 50,000 to 60,000 tons. The Tweedie distribution has the advantage that a distribution having a high probability near 0 can be well represented, and the amount of stock per day can be accurately modeled.

In this embodiment, represents the number N of transport vessels arriving per day in a Poisson distribution, the unloading amount X _i for each transport ship expressed as a gamma distribution, but represents the arrival of the daily in Tweedie distribution, It is not limited to the Tweedie distribution. For example, according to the number N is Poisson distribution freighter arriving per day, if the unloaded quantity X _i for each transport ship has to follow a log-normal distribution, the stock amount per day, using a log-normal compound Poisson process May be calculated. Alternatively, the actual data of the amount received per day may be approximated by a non-linear function, and the approximated function may be used as a probability distribution of the amount received per day. For example, an approximate function may be created by excluding the zero value from the actual data of the amount received per day and then applying a gamma distribution as a nonlinear function.

In step S5, the calculation unit 103 integrates a function obtained by multiplying the calculation formula (formula (1)) of the prediction model constructed in steps S2 to S4 by the probability of occurrence of the amount of arrival per day for the amount of arrival. Then, the expected value of the yard waiting time is calculated.
Assuming that the previous day's inventory amount is s, the day's arrival amount is y, the yard capacity is W, and the day's usage amount is u, the yard waiting time expressed by the equation (1) is (s + y-W) / u. is there. The expected value of the yard waiting time is calculated by integrating a function obtained by multiplying the yard waiting time (s + y-W) / u by the probability of occurrence p of the incoming quantity y per day. Here, as shown in FIG. 3, if a value obtained by subtracting the inventory amount s of the previous day from the yard capacity W is defined as the yard surplus, a yard waiting vessel occurs when the arrival amount y of the day reaches the yard surplus. The integration interval is from the yard surplus (W-s) at which a yard waiting vessel occurs to the arrival amount y on the day to ∞. Note that the upper limit of the integration section is not limited to ∞, and the value may be set as long as the maximum time during which a wreck occurs is known from the operation results. Assuming that the probability of occurrence of the arrival quantity per day is p (y | λ, α, θ), the expected value E [T] of the yard waiting time T is expressed by equation (7).

  In the present embodiment, the stock amount s, the yard capacity W, and the usage amount u of the current day are given as fixed values on the previous day, but are not limited thereto. If the forecast target period extends over multiple days, that is, if the expected value of the yard waiting time is calculated over multiple days, the initial inventory is given on the first day, and the actual The inventory amount may be calculated according to the amount of raw materials received or used by the transport ship, and the expected value of the yard waiting time may be calculated using the inventory amount given by the calculation as inventory on the day. Alternatively, an expected value of the yard waiting time may be calculated by giving a substantially constant value to all of the stock amounts in the prediction target period. If all or part of the inventory amount s, the yard capacity W, and the usage amount u on the previous day are values that change stochastically, the value that changes stochastically is multiplied by the occurrence probability. By integrating the combined functions, the expected value of the yard waiting time can be calculated.

In step S6, the calculation result output unit 104 outputs the expected value of the yard waiting time as the calculation result in step S5.
FIG. 7 is a graph showing an expected value of the yard waiting time with respect to the yard surplus. The horizontal axis in FIG. 7 represents the yard reserve, and the vertical axis represents the expected value of the yard waiting time. The crosshairs in the figure show the average yard surplus of the steelworks and the expected value of the corresponding yard stay time. From FIG. 7, it can be seen that the yard waiting time estimated based on the actual data during the data analysis period is an average of 4.5 hours per day. The actual yard detention time in the same period was 10.1 [h / day], which was slightly lower than the actual value.
The yard waiting time calculated in the present embodiment is a result calculated only in consideration of the equipment capacity, excluding the effects of equipment and operation trouble, etc., and therefore, it is assumed that a lower value is calculated compared to the actual result. . In the case where there is a restriction on how to handle yards and brands, if the present invention is applied to each yard for managing brands, it is expected that the calculation accuracy will be further improved. By the way, it is important to estimate the lower limit of the yard waiting time in consideration of the equipment capacity in determining capital investment and estimating the effect of introduction.In considering these, the present invention is a sufficiently useful index. I can say.

  As described above, the expected value of the yard waiting time can be predicted based on the theoretical analysis of the yard staying vessel. This makes it possible to determine the trade-off between the yard waiting vessels and the stock quantity necessary for stable operation, thereby suppressing the yard waiting vessels and securing an appropriate stock quantity.

As described above, the present invention has been described with the embodiment. However, the above embodiment is merely an example of the embodiment in carrying out the present invention, and the technical scope of the present invention is interpreted in a limited manner. It must not be. That is, the present invention can be implemented in various forms without departing from the technical idea or the main features.
Although the flowchart of FIG. 2 illustrates that the prediction models in steps S2 to S4 are constructed each time, the present invention is not limited to this. For example, a prediction model may be constructed in advance based on the actual data during the data analysis period, and the result may be stored in the yard waiting time prediction device 100 or the database 200 in advance.

The yard waiting time estimation device to which the present invention is applied is realized by a computer device having, for example, a CPU, a ROM, a RAM, and the like. Although the yard waiting time prediction device 100 is shown as one device in FIG. 1, for example, a configuration constituted by a plurality of devices may be used.
The present invention can also be realized by supplying software (program) for realizing the functions of the present invention to a system or apparatus via a network or various storage media, and a computer of the system or apparatus reads and executes the program. It is feasible.

  100: yard waiting time prediction device, 101: data capture unit, 102: vessel prediction model construction unit, 102a: number of ships modeling unit, 102b: unloading amount modeling unit, 102c: receiving amount modeling unit, 103 : Calculation unit, 104: calculation result output unit

Claims (7)

A yard waiting time prediction device that predicts a yard waiting time when unloading goods transported using a transport ship at a landing site,
The sum of the stock quantity at the beginning of the forecast period in the landing yard and the total unloading amount of the transport ship arriving during the forecast period (hereinafter, the total unloading amount is referred to as the receiving amount) is the amount of the yard. If the capacity was exceeded, using the prediction model that the yard waiting vessel occurs only the time divided by the amount of use in the prediction target period, the excess,
Means for calculating the expected value of the yard waiting time by integrating a function obtained by multiplying the calculation formula of the prediction model by the probability of occurrence of the amount of arrival per unit time with respect to the amount of arrival. A yard waiting time prediction device. Based on actual data, the number of transport ships arriving per the predetermined unit time and the unloading amount of each transport ship are represented by probability distributions, respectively.
The arrival amount per predetermined unit time is represented by a probability distribution that combines a probability distribution of the number of transport ships arriving per predetermined unit time and a probability distribution of unloading amount of each transport ship. The yard waiting time estimation device according to claim 1, wherein Based on actual data, the number of transport ships arriving per the predetermined unit time is represented by a Poisson distribution, and the unloading amount of each transport ship is represented by a gamma distribution,
The yard waiting time estimation device according to claim 2, wherein the amount of arrival per predetermined unit time is represented by a Tweedie distribution.   The yard waiting time estimation according to any one of claims 1 to 3, wherein the prediction target period start stock amount, the yard capacity, and the usage amount of the prediction target period are given as fixed values. apparatus.   5. The yard waiting time prediction device according to claim 4, wherein the integration section is set to a value obtained by subtracting the forecast stock at the start of the target period from the capacity of the yard to ∞. A yard waiting time prediction method for predicting a yard waiting time when unloading goods transported using a transport ship at a landing site,
The sum of the stock quantity at the beginning of the forecast period in the landing yard and the total unloading amount of the transport ship arriving during the forecast period (hereinafter, the total unloading amount is referred to as the receiving amount) is the amount of the yard. If the capacity was exceeded, using the prediction model that the yard waiting vessel occurs only the time divided by the amount of use in the prediction target period, the excess,
An expected value of the yard waiting time is calculated by integrating a function obtained by multiplying the calculation formula of the prediction model by the probability of occurrence of the amount of arrival per unit time with respect to the amount of arrival. Yard waiting time prediction method. A program for predicting a yard waiting time when unloading goods transported using a transport ship at a landing site,
The sum of the stock quantity at the beginning of the forecast period in the landing yard and the total unloading amount of the transport ship arriving during the forecast period (hereinafter, the total unloading amount is referred to as the receiving amount) is the amount of the yard. If the capacity was exceeded, using the prediction model that the yard waiting vessel occurs only the time divided by the amount of use in the prediction target period, the excess,
A computer calculates the expected value of the yard waiting time by executing a function of integrating the function obtained by multiplying the calculation formula of the prediction model by the probability of occurrence of the arrival amount per unit time with respect to the arrival amount. Program to let you.

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