Intelligent storage carbon dioxide emission evaluation method based on queuing theory

Abstract

The invention relates to an intelligent warehouse carbon dioxide emission evaluation method based on a queuing theory. The method comprises the following steps: S1, establishing a carbon emission estimation model of a self-climbing robot warehouse; s2, establishing a travel time expression; s3, calculating carbon dioxide emission and charging energy consumption; s4, analyzing the semi-open type queuing network model with the priority and calculating the battery charging probability; s5, performing simulation verification on the model; and S6, comparing the influence and profit generation of different priority strategies and different distribution strategies on the self-climbing robot warehouse, and selecting an optimal operation strategy. According to the invention, a warehouse manager can be helped to select a greener warehouse operation strategy, a decision tool is provided for the warehouse manager to find an optimal dynamic priority parameter, the maximum tolerable throughput time of two order types is ensured, the system profit is maximized, and the consumption is reduced.

Description

Technical Field

[0001] The present invention relates to the field of management science and engineering technology, and in particular to an intelligent warehousing carbon dioxide emission assessment method based on queuing theory. Background Art

[0002] In the field of modern warehousing and logistics, automated and intelligent robotic systems are gradually becoming key technologies for improving efficiency and reducing costs. However, with the popularity of these systems in practical applications, the environmental impact and energy consumption problems they generate during operation are gradually emerging. In previous studies, the carbon dioxide emissions from self-climbing robotic warehousing are often ignored. To address this defect, we developed a priority-based semi-open queuing network model, which not only considers the energy consumption of the robotic warehouse in different operation steps, but also considers the impact of robot congestion and robot battery charging on warehousing performance. The model can evaluate the impact of various operation strategies such as shared allocation strategy, dedicated allocation strategy, static priority strategy and dynamic priority strategy on carbon dioxide emissions and throughput time according to the needs of different order types (expedited orders and standard orders), providing a flexible tool for warehouse managers to help them choose the optimal strategy that can reduce carbon emissions and optimize throughput time while meeting the maximum tolerable throughput time requirements of different types of orders. Summary of the invention

[0003] In view of the defects of the prior art, the purpose of the present invention is to provide a method for evaluating carbon dioxide emissions in intelligent warehousing based on queuing theory. By evaluating the carbon dioxide emissions and throughput time of self-climbing robot warehousing, an improved iterative approximate average algorithm is used to solve a semi-open queuing network model that takes priority into account. Taking into account robot congestion and battery charging, a quantitative analysis is performed on each operating link in the warehouse, and the carbon dioxide emissions and throughput time under different priority strategies and different allocation strategies are compared. Finally, a strategy model that can meet the different lead time requirements of different order categories is obtained. 1. In order to achieve the above-mentioned purpose, the technical solution adopted by the present invention is: a method for evaluating carbon dioxide emissions from intelligent warehousing based on queuing theory, comprising the following steps: S1: Establish a carbon emission estimation model for self-climbing robot warehouses. S2: Establish travel time expression; S3: Calculate carbon dioxide emissions and charging energy consumption; S4: Analysis of the semi-open queueing network model with priorities and calculation of battery charging probability; S5: Conduct simulation verification on the above model; S6: Compare the impact of different priority strategies and different allocation strategies on the self-climbing robot warehouse and profit generation, and select the optimal operation strategy.

[0004] Furthermore, establishing the travel time expression in step S2 includes: Calculate the travel time to the destination lane entrance using the following formula: Where: G S Indicates lane, C l Indicates the length of the storage location, M l Indicates the length of the shelf, A a A represents the safe distance between the shelf and the robot's walking route. b Indicates the safe distance between two shelves, C b Indicates the width of the storage location, V g represents the ground speed of the robot, s represents the number of lanes; Calculate the time from the destination lane entrance to the bottom of the destination storage column using the following formula: Where: α represents the lane, C l Indicates the length of the storage location, M l Indicates the length of the shelf, V g represents the ground speed of the robot; Calculate the travel time between the bottom of the target storage / picking column and the target storage / retrieval level using the following formula: Where: β,l represents the lane, C h Indicates the height of the storage location, M h Indicates the height of the shelf, M l Indicates the length of the shelf, V v Indicates the vertical speed of the robot; Calculate the time for loading and unloading pallets using the following formula: Where: l represents the lane, t l Indicates the time when the robot loads / unloads a pallet; Calculate the robot's travel time from the bottom of the target storage column to the bottom of the target retrieval column using the following formula: Where: γ represents the lane, C l Indicates the length of the storage location, M l Indicates the length of the shelf, V g represents the ground speed of the robot; Calculate the travel time of the robot from the bottom of the destination retrieval column to the lane exit using the following formula: Where: o represents lane, C l Indicates the length of the storage location, M l Indicates the length of the shelf, V g Indicates the ground speed of the robot.

[0005] Furthermore, the calculation process of step S3 is as follows: S31: Calculate the carbon dioxide emissions generated by the robot's vertical operation. The calculation formula is as follows: Where: E v,l and E v,d Respectively represent the energy consumption of the robot when it moves vertically with load and without load; E l represents the energy consumed by the robot to load and unload pallets; ω refers to the carbon dioxide emissions converted from gas per kilowatt-hour; S32: Calculate the carbon dioxide emissions generated by the robot's horizontal operation. The calculation formula is as follows: E h,l and E h,d They represent the energy consumption of the robot's horizontal movement with and without load, respectively. ω refers to the carbon dioxide emissions converted from gas per kilowatt-hour, and W represents the time the robot waits for orders at the workstation. S33: The carbon dioxide emissions generated by each operation of the robot can be calculated as: E=E a +E C In the formula, E represents the carbon dioxide emissions of each robot operation; S34: The charging energy consumption of each robot activity can be calculated as: Where C represents the energy consumption of each robot activity; C l Indicates energy consumption per kilowatt-hour.

[0006] Further, step S4 includes the following steps: S41: According to the charging energy consumption in step S3, the energy consumed by the robot to complete one charge is E W *W+E i *(TH-W), using D to represent the energy of a fully charged robot, confirm the maximum number of cycles of a fully charged robot; S42: Confirm the number of cycles per second that a fully charged robot can perform; S43: confirming the operating time of the fully-charged robot; S45: Calculate the probability that the robot needs to be charged.

[0007] Further, in step S6, comparing the impact of different priority strategies and different allocation strategies on the self-climbing robot warehouse and the profit generation includes the following steps: S61: Comparison of the throughput time and CO2 emissions of a self-climbing robot warehouse using a dynamic priority strategy and a static priority strategy; S62: Compare the differences in throughput time and CO2 emissions between the shared allocation strategy and the dedicated allocation strategy in a self-climbing robot warehouse.

[0008] The beneficial effects of the present application are: 1. The present invention provides an optimal warehouse operation management strategy by calculating carbon dioxide emissions. The present invention applies a semi-open priority queuing network that takes into account priorities to study the impact of different priority strategies on the throughput time of different types of orders, and calculates the carbon dioxide emissions of self-climbing robot warehousing under different operation strategies. For the expected system performance, the shared allocation strategy is superior to the dedicated allocation strategy in terms of throughput time and carbon dioxide emissions. If the warehouse manager wants to balance the throughput time between expedited orders and standard orders in the self-climbing robot warehouse, a dynamic priority strategy is applied. Because the dynamic priority strategy can meet the lead time requirements of different orders without increasing carbon dioxide emissions.

[0009] 2. This application can help warehouse managers select appropriate dynamic priority parameters to maximize system profits while considering carbon emissions and ensure satisfactory system performance for different order categories. BRIEF DESCRIPTION OF THE DRAWINGS

[0011] Figure 1 It is a top view of the self-climbing robot system;

[0012] Figure 2 A carbon emission estimation model for a self-climbing robot system for two order types;

[0013] Figure 3 Comparison of static and dynamic priority strategies in terms of throughput time and CO2 emissions;

[0014] Figure 4 Comparison of shared allocation and dedicated allocation strategies in terms of throughput time and CO2 emissions;

[0015] Figure 5 Figure 1 shows the impact of dynamic priorities on throughput time and profit considering energy consumption. DETAILED DESCRIPTION

[0017] The present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0018] This embodiment provides a method for evaluating carbon dioxide emissions from intelligent warehousing based on queuing theory, comprising the following steps: S1: Establish a carbon emission estimation model for self-climbing robot warehouses; S2: Establish travel time expression; S3: Calculate carbon dioxide emissions and charging energy consumption; S4: Analysis of the semi-open queueing network model with priorities and calculation of battery charging probability; S5: Conduct simulation verification on the above model; S6: Compare the impact of different priority strategies and different allocation strategies on the self-climbing robot warehouse and profit generation, and select the priority strategy.

[0019] Furthermore, in step S1, the modeling and solving process is as follows:

[0020] 1. Scenario description:

[0021] Priority strategy and allocation strategy.

[0022] In this invention, we use P O represents the priority parameter, different categories of orders (S, E∈O, P S Indicates the priority parameter of the standard order. E The priority parameter of the expedited order is higher than the priority parameter of the standard order. E >P S For the same category, the priority is the same. When a robot is available, the decision maker can calculate the instantaneous priority by using the following equation,

[0023] S O (t) = P O -(tt O ) (1) Where S O (t) represents the priority of order O at time t, t O is the time when order O arrives at the system. t represents the current time.

[0024] The present invention also evaluates a dedicated allocation strategy and a shared allocation strategy.

[0025] Based on the dedicated allocation strategy, some robots are assigned to serve expedited orders and the rest are assigned to serve standard orders. Robots can only serve the orders they are assigned to.

[0026] Under the shared allocation strategy, robots are shared by different order types (expedited orders and standard orders) and pallets are randomly stored on the shelves.

[0027] In addition, the racks are divided into two groups: racks dedicated to expedited orders and racks dedicated to standard orders. The racks dedicated to expedited orders are located near the workstations. The racks dedicated to standard orders are located away from the workstations.

[0028] 2. Carbon emission estimation model:

[0029] (1) We use synchronization station J to simulate the synchronization of orders and robots. For a system with static priorities, at synchronization station J, the available robot will serve the first expedited order that arrives. If there are no expedited orders waiting in the queue, the available robot will serve the first standard order that arrives. For a system with a dynamic priority policy, at synchronization station J, the available robot will serve the order S with the highest instantaneous priority. O (t). If there is no order waiting in the queue, the robot will wait for the order. Otherwise, the order will wait for the robot.

[0030] (2) The robot enters the entrance of the destination lane (G S We use a single server to simulate the robot's movement from the destination lane entrance to the bottom of the destination storage column.

[0031] (3) In the target storage column, the robot with the load first navigates to the specified layer To unload the tray It then descends to the bottom without any load.

[0032] (4) The unloaded robot moves to the target picking column bottom.

[0033] (5) When the robot completes the operation in the target storage column, it moves to the lane exit

[0034] (6) When the probability is P c , the battery charge has dropped below the safe threshold, so the robot needs to be charged

[0035] Further, determining the travel time in step S2 includes: Calculate the travel time to the destination lane entrance using the following formula: Where: G S Indicates lane, Cl Indicates the length of the storage location, M l Indicates the length of the shelf, A a A represents the safe distance between the shelf and the robot's walking route. b Indicates the safe distance between two shelves, C b Indicates the width of the storage location, V g represents the ground speed of the robot and s represents the number of lanes.

[0036] Calculate the time from the destination lane entrance to the bottom of the destination storage column using the following formula: Where: α represents the lane, C l Indicates the length of the storage location, M l Indicates the length of the shelf, V g Indicates the ground speed of the robot.

[0037] Calculate the travel time between the bottom of the target storage / picking column and the target storage / retrieval level using the following formula:

[0038] Where: β,l represents the lane, C h Indicates the height of the storage location, M h Indicates the height of the shelf, M l Indicates the length of the shelf, V v Indicates the vertical speed of the robot.

[0039] Calculate the time for loading and unloading pallets using the following formula: Where: l represents the lane, t l Indicates the time when the robot loads / unloads a pallet.

[0040] The robot's travel time from the bottom of the target storage column to the bottom of the target retrieval column is calculated as follows: Where: γ represents the lane, C l Indicates the length of the storage location, M l Indicates the length of the shelf, V g Indicates the ground speed of the robot.

[0041] The robot travel time from the bottom of the destination column to the lane exit Where: o represents lane, C l Indicates the length of the storage location, M l Indicates the length of the shelf, Vg Indicates the ground speed of the robot.

[0042] In the further step S3, the calculation process of carbon dioxide emissions and charging energy consumption is as follows:

[0043] The CO2 emissions generated by a robotic warehouse depend on the movement mode – horizontal or vertical – and the loaded state – whether the robot is loaded or unloaded. We therefore differentiate between the robot’s operating states and calculate the associated CO2 emissions.

[0044] 1. Carbon dioxide emissions generated by vertical operations of robots.

[0045]

[0046] In the formula, E v,l and E v,d Represents the energy consumption of the robot when it moves vertically with load and without load. E l is the energy consumed by the robot to load and unload the pallet. ω is the CO2 emissions per kilowatt-hour converted from the gas. We assume that the electricity comes from natural gas, which emits 460 g of CO2 per kilowatt-hour.

[0047] 2. Carbon dioxide emissions generated by horizontal operations of robots.

[0048] In the formula, E h,l and E h,d They represent the energy consumption of the robot's horizontal movement with and without load, respectively. ω refers to the carbon dioxide emissions converted from gas per kilowatt-hour, and W represents the time the robot waits for orders at the workstation.

[0049] 3. The carbon dioxide emissions generated by each operation of the robot can be calculated as

[0050] E=E a +E C (10)

[0051] Where E represents the carbon dioxide emissions of each robot operation.

[0052] 4. The charging energy consumption of each robot activity can be calculated as

[0053]

[0054] Where C represents the energy consumed by the robot for each activity. l It represents the energy consumption per kilowatt-hour. The electricity price is defined as 0.25 USD / hour.

[0055] Step S4 includes the following steps:

[0056] S41: According to the charging energy consumption in step S3, the energy consumed by the robot to complete one charge is E W *W+E i *(TH-W), using D to represent the energy of a fully charged robot, confirm the maximum number of cycles of a fully charged robot;

[0057] S42: Confirm the number of cycles per second that a fully charged robot can perform;

[0058] S43: confirming the operating time of the fully-charged robot;

[0059] S45: Calculate the probability that the robot needs to be charged.

[0060] In step S4, the semi-open queueing network with priority is analyzed and the battery charging probability is calculated. The analysis process is as follows:

[0061] 1. The solution to the semi-open queuing network with priority is as follows:

[0062] For a semi-open queueing network with two dynamic priority orders, we use P E and P S To indicate the priority parameter (P E >P S ),λ E represents the arrival rate of expedited orders, λ S represents the arrival rate of standard orders. TH(R) represents the maximum throughput of the closed queueing network transformed from the original model consisting of all service stations except the synchronization station. M E ,M S represent the average remaining service time for expedited orders and standard orders respectively. n is the probability that n available robots are at the synchronization station. We define

[0063]

[0064] Step 1: For SOQN with dynamic priority policy, the expected waiting time for expedited orders is: The estimated waiting time for standard orders is

[0065] For the solution method of semi-open queueing network with static priority, the priority parameter P of the expedited order can be E Set to a maximum value, the priority parameter P of the standard order S Set to a minimum value to calculate the robot storage throughput time, and the calculation of TH(R) can be analyzed using an iterative approximate mean.

[0066] 2. Solution method for semi-open queueing network with unknown probability of reaching service node:

[0067] In our model, the battery charging probability is unknown in advance. We use step 2 to calculate the battery charging probability, which is also the access probability to the battery charging service node. We use W(current) and TH(current) to represent the waiting time and throughput time calculated after the algorithm iterates the current number of times, respectively. W(last) and TH(last) are the values ​​of the waiting time and throughput time calculated after the algorithm takes the last iteration, respectively. ∈ is a very small value.

[0068] Step 2: The probability of the robot battery being charged after the current operation can be calculated as

[0069] When |TH(current)-TH(last)|<ε and |W(current)-W(last)|<ε.

[0070] Proof: According to formula (11), the energy consumed to complete a picking operation is E W *W+E i *(TH-W). D represents the energy of a fully charged robot. A fully charged robot can run up to In addition, a fully charged robot can cycle within one second (λ S +λ E ) / R times, where R represents the number of robots. Therefore, the duration that a fully charged robot can run is Therefore, the probability that the robot needs to be charged is

[0071] Since the values ​​of throughput time and waiting time are unknown at the beginning, we set the initial value of the battery charging probability between 0 and 1, and then we can use steps 1 and 2 to calculate the value of the battery charging probability.

[0072] Furthermore, in step S5, simulation data results are obtained.

[0073] Comparing the throughput time of expedited and standard orders and the utilization rate (ρ) of the robot between the analytical and simulation models, we fixed the priority parameter of standard orders to 1 and varied the priority parameter of expedited orders from 1.1 to 1.9. The arrival rate of expedited orders was fixed to 0.09 (pallets / second) and the standard arrival rate varied from 0.08 to 0.10 (pallets / second). We ran the simulation model 10 times for 20 hours and calculated the 95% credible interval.

[0074] Further, in step S6, the process is as follows:

[0075] We also compared the throughput time and CO2 emissions of the self-climbing robot warehouse using the dynamic priority strategy and the static priority strategy. Figure 3 A comparative analysis of static and dynamic priority strategies in terms of throughput time and CO2 emissions is illustrated.

[0076] It is concluded that the dynamic priority strategy has a considerable impact on the throughput time of the self-climbing robot warehouse, while having no significant impact on its CO2 emissions. Warehouse managers can flexibly choose appropriate dynamic priority parameters to meet the maximum tolerable throughput time required for standard orders and expedited orders.

[0077] Again, the differences in throughput time and carbon dioxide emissions between the shared allocation strategy and the dedicated allocation strategy in the self-climbing robot warehouse are compared. Figure 4 As shown in Figures 4a and 4b, (1) for expedited orders, the dedicated allocation strategy can shorten the throughput time and reduce carbon dioxide emissions compared with the shared allocation strategy. (2) for standard orders, the shared allocation strategy can shorten the throughput time and reduce carbon dioxide emissions compared with the dedicated allocation strategy. (3) for the expected performance of the system, in most cases, the shared allocation strategy has a shorter throughput time and less carbon dioxide emissions than the dedicated allocation strategy.

[0078] Next, we calculate the impact of dynamic priority on the throughput time and profit of a robotic warehouse:

[0079] We use equations (12) and (13) to calculate the system profit, considering the electricity costs of expedited orders and standard orders, respectively.

[0080] I E =M E *λ E -C E *λ E (12)

[0081] I S =M S *λ S -C S *λ S (13)

[0082] Among them I E and I S Represents the net profit of expedited orders and standard orders respectively. E and C S represents the electricity cost required to complete a picking operation. We can use formula (11) to calculate C E and C S The value of .

[0083] Figure 5 The impact of dynamic priority on the throughput time and profit of a robotic warehouse considering electricity costs is shown.

[0084] Profit margin of expedited orders vs. standard orders The same level of profit margins for expedited orders and standard orders Arrival rates for expedited orders and standard orders The higher it is, the higher the profit.

[0085] Based on our model, warehouse managers can determine appropriate priority parameters based on profit margins to maximize system performance, such as profit, while considering the power cost of meeting the throughput time requirements of all order categories. Since self-climbing robot warehouses are widely used in e-commerce, the system contains multiple order categories with similar operating costs, and maximizing system profit is the primary goal of warehouse managers, we choose system profit as the objective function in the optimization model. The optimization model is as follows:

[0086] maxI(P E ,P S )=I E +I S (14)

[0087] in, and Respectively represent the maximum allowable throughput time for expedited orders and standard orders. E ) indicates that it has a priority parameter P E The throughput time of the expedited order. S ) indicates that it has a priority parameter P S The throughput time of a standard order. E ,P S ) represents the system profit.

[0088] In summary, this paper proposes a model to evaluate the impact of different priority strategies and allocation strategies on the throughput time and CO2 emissions of expedited and standard orders in a self-climbing robot warehouse, and considers battery management. To address the challenge of unknown battery charging probability of the robot, an iterative approximation analytical algorithm is proposed to solve the model. Our model can meet the maximum tolerable throughput time requirements of different types of orders while considering CO2 emissions.

[0089] The above description is only a preferred embodiment of the present invention and does not limit the present invention in any form. Although the present invention has been disclosed as a preferred embodiment as above, it is not used to limit the present invention. Any technician familiar with this profession can make some changes or modify the technical contents disclosed above into equivalent embodiments without departing from the scope of the technical solution of the present invention. However, any simple modification, equivalent change and modification made to the above embodiments according to the technical essence of the present invention without departing from the content of the technical solution of the present invention still fall within the scope of the technical solution of the present invention.

Claims

1. A method for evaluating carbon dioxide emissions from intelligent warehousing based on queuing theory, characterized in that: The following steps are involved: S1: Establish a carbon emission estimation model for self-climbing robot warehouses. S2: Establish travel time expression; S3: Calculate carbon dioxide emissions and charging energy consumption; S4: Analysis of the semi-open queueing network model with priorities and calculation of battery charging probability; S5: Simulate and verify the model; S6: Compare the impact of different priority strategies and different allocation strategies on the self-climbing robot warehouse and profit generation, and select the optimal operation strategy.

2. According to claim 1, a method for evaluating carbon dioxide emissions from intelligent storage based on queuing theory is characterized in that: The travel time expression established in step S2 includes: Calculate the travel time to the destination lane entrance using the following formula: Where: G S Indicates lane, C l Indicates the length of the storage location, M l Indicates the length of the shelf, A a A represents the safe distance between the shelf and the robot's walking route. b Indicates the safe distance between two shelves, C b Indicates the width of the storage location, V g represents the ground speed of the robot, s represents the number of lanes; Calculate the time from the destination lane entrance to the bottom of the destination storage column using the following formula: Where: α represents the lane, C l Indicates the length of the storage location, M l Indicates the length of the shelf, V g represents the ground speed of the robot; Calculate the travel time between the bottom of the target storage / picking column and the target storage / retrieval level using the following formula: Where: β,l represents the lane, C h Indicates the height of the storage location, M h Indicates the height of the shelf, M l Indicates the length of the shelf, V v Indicates the vertical speed of the robot; Calculate the time for loading and unloading pallets using the following formula: Where: l represents the lane, t l Indicates the time when the robot loads / unloads a pallet; Calculate the robot's travel time from the bottom of the target storage column to the bottom of the target retrieval column using the following formula: Where: γ represents the lane, C l Indicates the length of the storage location, M l Indicates the length of the shelf, V g represents the ground speed of the robot; Calculate the travel time of the robot from the bottom of the destination retrieval column to the lane exit using the following formula: Where: o represents lane, C l Indicates the length of the storage location, M l Indicates the length of the shelf, V g Indicates the ground speed of the robot.

3. The method for evaluating carbon dioxide emissions from intelligent warehousing based on queuing theory according to claim 2 is characterized in that: The calculation process of step S3 is as follows: S31: Calculate the carbon dioxide emissions generated by the robot's vertical operation. The calculation formula is as follows: Where: E v,l and E v,d Respectively represent the energy consumption of the robot when it moves vertically with load and without load; E l represents the energy consumed by the robot to load and unload pallets; ω refers to the carbon dioxide emissions converted from gas per kilowatt-hour; S32: Calculate the carbon dioxide emissions generated by the robot's horizontal operation. The calculation formula is as follows: E h,l and E h,d They represent the energy consumption of the robot's horizontal movement with and without load, respectively. ω refers to the carbon dioxide emissions converted from gas per kilowatt-hour, and W represents the time the robot waits for orders at the workstation. S33: The carbon dioxide emissions generated by each operation of the robot can be calculated as: E=E a +E C In the formula, E represents the carbon dioxide emissions of each robot operation; S34: The charging energy consumption of each robot activity can be calculated as: Where C represents the energy consumption of each robot activity; C l Indicates energy consumption per kilowatt-hour.

4. The method for evaluating carbon dioxide emissions from intelligent warehousing based on queuing theory according to claim 2 is characterized in that: Step S4 includes the following steps: S41: According to the charging energy consumption in step S3, the energy consumed by the robot to complete one charge is E W *W+E i *(TH-W), using D to represent the energy of a fully charged robot, confirm the maximum number of cycles of a fully charged robot; S42: Confirm the number of cycles per second that a fully charged robot can perform; S43: confirming the operating time of the fully-charged robot; S45: Calculate the probability that the robot needs to be charged.

5. The method for evaluating carbon dioxide emissions from intelligent warehousing based on queuing theory according to claim 2 is characterized in that: In step S6, comparing the impact of different priority strategies and different allocation strategies on the self-climbing robot warehouse and the profit generation includes the following steps: S61: Comparison of the throughput time and CO2 emissions of a self-climbing robot warehouse using a dynamic priority strategy and a static priority strategy; S62: Compare the differences in throughput time and CO2 emissions between the shared allocation strategy and the dedicated allocation strategy in a self-climbing robot warehouse.

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