# Online and Offline Model for Housekeeping Order Assignment Based on Dynamic Programming Algorithm
## 2 Related Works
The results show that the real-time allocation mode reflects the advantage of the optimal allocation mode when the supply exceeds the demand for users; On the contrary, the fixed time allocation model has the advantage of optimal system resource utilization efficiency. [PERSON] et al. [26] proposed two resource allocation algorithms for multi-satellite systems based on beam-hopping technology. For offline scenarios, a heuristic algorithm was proposed to allocate time and frequency resources, and a successive convex approximation (SCA) algorithm was proposed to allocate power resources. For online scenarios, a DP algorithm is used to maximize the system throughput. [PERSON] et al. [27] established a mixed integer programming (MIP) model to study the joint optimization problem of dynamic bed allocation and patient admission control. Based on biogeography, a dynamic bed and patient admission optimization (BBO-DBPA) algorithm was proposed to obtain the optimal decision plan. [PERSON] et al. [28] proposed a sequential batch processing and allocation algorithm that uses graph-based methods to decompose the original problem into more manageable sub-problems and uses clustering, which effectively solves the problem of the same courier being able to process multiple orders on multiple pickup routes. In 2017, [PERSON] et al. [29] compared the DP and basic block matching (BBM) methods in stereo matching algorithms from three aspects: parallax map accuracy, noise enhancement, and smoothness. The results show that both methods can be used for many stereo vision applications. In 2018, [PERSON] et al. [30] proposed a DP method based on the reduced state space algorithm (RSS-DP), which greatly reduces the state space of the standard dynamic programming (SDP) model by decomposing the number of surplus by-product gases (SBPGs) into references and subsequent allocations, thereby greatly reducing the computational time. [PERSON] et al. [31] aimed at the problem of poor adaptability of traditional control strategies to different driving cycles and adopted a controller based on DP to optimize the power distribution of hybrid energy storage systems (HESSs) offline under several typical working conditions. The offline sample data of DP was processed using a combination of correlation analysis and the mean impact value (MIV) analysis method to obtain the characteristic variables of the extreme learning machine (ELM) model. At the same time, ELM is used to learn the offline data of HESS and to obtain the instantaneous power allocation strategy of HESS. In 2021, [PERSON] et al. [32] proposed an optimal strategy based on DP, which takes the generalized forces and torques as the control and adopts the decoupling position and attitude dynamics calculation, which effectively controls the spacecraft when the thruster fails, and reconfigures the DP strategy and control allocation. Based on the correct answers submitted by students, [PERSON] et al. [33] developed an online semantic error automatic feedback system for programming using a dynamic template matching model. The results show that 80% of the best matching templates for each student are selected by experts using this technology. In 2023, [PERSON] et al. [34] proposed a multi-frame target detection method based on a dynamic programming ring network (DPRN). This method approximates the target trajectory using piecewise linear functions and uses velocity space partitioning DP (VSP-DP) to accumulate the advantage function of the target on each piecewise linear trajectory segment to avoid the diffusion of the advantage function in different velocity spaces. The results indicate that this method is suitable for radar and infrared search and tracking systems. [PERSON] et al. [35] proposed a dynamic allocation mechanism that divides annual allocation plans into monthly scales and dynamically modifies the allocation plan to adapt to the aforementioned fluctuations.