DOPSG: Distributed Optimized Patient Scheduling

• The paper demonstrates a decentralized algorithm (DOPSG) that reduces waiting times and resource idle times through group-based patient migrations.
• The methodology uses local agent data and a group-based migration protocol to efficiently balance loads in multi-agent hospital settings.
• Experimental results reveal significant reductions in completion time and tardiness compared to FCFS, WSPT, and non-grouped scheduling methods.

Distributed Optimized Patient Scheduling with Grouping (DOPSG) is a decentralized scheduling algorithm designed for multi-agent hospital environments subject to dynamic workloads and resource constraints. DOPSG operates strictly with partial, local information, requires no global patient or resource knowledge, and employs a group-based migration protocol to redistribute patient agents when hospital resource contention occurs. Its principal objectives are to reduce patient waiting times and resource idle times by dynamically optimizing patient-to-resource assignments through localized decision processes and minimal inter-agent communication (Mageshwari et al., 2012).

1. System Structure and Assumptions

DOPSG models the hospital workflow as a Multi-Agent System (MAS) comprising two key agent types: Patient Agents (PA) and Resource Agents (RA). Each patient agent $P_i$ encapsulates a unique identifier, a priority weight $w_i \in \mathbb{R}^+$, an arrival time $t^{\mathrm{arr}}_i$, and an ordered task queue $\{r_{i,1}, r_{i,2}, ...\}$ corresponding to the resources needed for the patient's care episode. Each resource agent $R_j$ (representing departments or examination rooms) maintains a fixed capacity $T_j$, current load $C_j$, and a neighbor set $\mathcal{N}_j$ of adjacent resources.

No agent—neither RA nor PA—possesses global state knowledge. RAs know only their own and their neighbors’ instantaneous loads ($C_k$ for $k \in \mathcal{N}_j$); PAs know only their local patient parameters and required task sequence. This strict locality forms the core assumption of DOPSG and necessitates a communication protocol for load balancing: whenever $C_j > T_j$, indicating overcrowding, $R_j$ initiates a migration protocol based on the computed overflow $E_j = \max\{0, C_j - T_j\}$.

2. Overflow Grouping and Migration Protocol

When a resource agent detects overcrowding ($C_j > T_j$), it solicits neighboring resources via Request$(j, E_j)$ messages. Each neighbor $R_k$ computes available capacity ($F_k = T_k - C_k$) and responds with either an acceptance—including available free slots—or a rejection.

If capacity exists at a neighbor, $R_j$ forms a group $G$ of overflow PAs for migration, selecting exactly $\min(E_j, F_k)$ patients. The grouping criteria prioritize:

• Higher patient priority $w_i$
• Earlier arrival time $t^{\mathrm{arr}}_i$
• The most common next task $r_{i,1}$ within the overflow cohort

The similarity metric for grouping is

$$S(a,b) = \gamma\,\mathbf{1}_{r_{a,1}=r_{b,1}}\ -\ \alpha\,\frac{|w_a-w_b|}{\max_i w_i}\ -\ \beta\,\frac{|t^{\mathrm{arr}}_a-t^{\mathrm{arr}}_b|}{\max_i t^{\mathrm{arr}}_i}$$

with weights $\alpha, \beta, \gamma > 0$. Patients are ranked by the key

$$\mathrm{Key}(P_i) = w_i - \eta\,t^{\mathrm{arr}}_i + \delta\,\mathbf{1}_{r_{i,1}=\bar r}$$

where $\bar r$ is the most common required next task in the overflow population. The top $m$ patients are selected for transfer.

After migration, both source and target resource agents update their load states, and, if overcrowding persists, the grouping protocol repeats iteratively until local stability is achieved.

3. Scheduling Algorithm and Computational Analysis

DOPSG’s assignment problem is formalized with binary variables $x_{i,j}$, where $x_{i,j}=1$ iff patient $i$ is assigned to resource $j$. Each patient must be assigned for every task ($\sum_j x_{i,j}=1$) while enforcing capacity constraints ($\sum_i x_{i,j} \le T_j$).

Patient waiting time is $w_i = C^{\mathrm{end}}_i - t^{\mathrm{arr}}_i$. Resource idle time is $u_j = T_j - \sum_i p_{i,j}$, where $p_{i,j}$ denotes the processing time. DOPSG seeks to minimize the multi-objective cost

$$\min\,\{W + \lambda U\},\quad W = \sum_i w_i,\ U = \sum_j u_j,\ \lambda \ge 0$$

The dominant computational step per overflow event is sorting the overflow pool, yielding an event complexity of $O(N\log N + |\mathcal{N}_j|)$, where $N$ is the overflow cohort size and $|\mathcal{N}_j|$ is the neighbor count.

4. Operation Under Partial Information

DOPSG is designed for environments lacking a centralized scheduler or global database. Each resource agent acts on its own and direct neighbors’ load information only; patient agents never broadcast outside their own control context. Communications are localized—Request/Accept and Migrate messages involve only overflow sizes and free slot counts. Migration occurs for groups and not for individual agents, reducing message passing and synchrony overhead.

Convergence is ensured, as each migration strictly reduces local overload, terminating when all resources operate within capacity. While some patients may be migrated to nonoptimal resources (in the absence of global knowledge), the local grouping strategy—by priority and arrival—partially mitigates such inefficiencies. Empirically, DOPSG outperforms both ungrouped distributed algorithms and conventional resource scheduling heuristics.

5. Experimental Performance and Comparative Results

Experiments were conducted in JADE on a scenario with 3 resource agents and 50 patient agents, each with randomized processing times and priorities in 1–5. Baseline comparators were:

• FCFS (First-Come-First-Serve)
• WSPT (Weighted Shortest Processing Time)
• DOPS (Distributed Optimized Patient Scheduling without grouping)
• DOPSG

The primary metrics included total completion time, total tardiness, weighted completion and tardiness:

Metric	FCFS	WSPT	DOPS	DOPSG
Total completion time	3240	3180	3130	3080
Total tardiness	640	600	570	520
Weighted comp. time	3500	3450	3420	3340
Weighted tardiness	710	670	650	590

DOPSG achieved:

• A 1.7% reduction in total completion time over FCFS/WSPT, 1.6% versus DOPS
• An 18.8% reduction in total tardiness over FCFS, 13.3% over WSPT, and 8.8% over DOPS
• Weighted tardiness decreased by 41% vs FCFS, 37% vs WSPT, and 9.2% vs DOPS

Statistical analysis averaging 20 randomized runs showed standard deviation less than 2%, indicating robustness.

6. Findings, Limitations, and Directions

Key findings indicate that DOPSG achieves comparable or superior performance to both classical heuristics and distributed scheduling without grouping, using only local and nearest-neighbor information. Group-based migrations reduce communication overhead and improve convergence.

Limitations include the heuristic nature of the patient grouping metric; more advanced clustering (e.g., k-means, hierarchical) could enhance group selection. Neighbor selection is static; adaptive or learned strategies (e.g., Q-learning) are proposed for future work. Further extensions include heterogeneous resource speeds, differentiated handling of emergency vs. elective patients, online task streams, and validation against broader, real-world datasets comprising hundreds of resources and thousands of patients (Mageshwari et al., 2012).