Multi-Agent System for solving Dynamic Operating

Theater Facility Layout Problem Abdelahad CHRAIBI1, 3, Said KHARRAJA1, Ibrahim H. OSMAN2 and Omar ELBEQQALI3

1 University of Lyon, University of Saint-Etienne, Laboratory of Signal and Industrial Process Analysis (LASPI)

Roanne, France

Email: {abdelahad.chraibi, said.kharraja}@univ-st-etienne.fr 2 Suliman S. Olayan’s School of Business, Business Information & Decision Systems, American University of Beirut Beirut,

Lebanon

ibrahim.osman@aub.edu.lb 3 University Sidi Mohamed Ben Abdellah, Faculty of science Dhar El Mahraz, Laboratory of Informatics Image processing and

Numerical Analysis (LIIAN); Fez, Morocco

omarel.beqqali@usmba.ac.ma

Abstract— The Operating Theater (OT) is known to be a fluctuating production system. The unpredictability of populations’ needs has an

impact on the required human and material resources and makes the Operating Theater a dynamic environment. Thus, the use of dynamic

models is getting more realistic to solve OT Layout Problem (OTLP). While solving Dynamic OTLP, Real-life Operating Theater (OT) sizes

are larger than exact methods capacity, this lead to explore other methods as heuristics, metaheuristics or parallel treatment looking for

approximate solutions. In this paper, we developed a novel approach using a Multi-Agent (MA) Decision Making System (DMS) based on a

Quadratic Assignment Problem (QAP) and a Mixed Integer Linear Programming (MILP) for large-sized DOTLP with objective of minimizing

total traveling costs and minimizing the rearrangement costs, by studying an individual layout for each distinctive period based on patients

demand. The DMS generates efficient solutions in reasonable time and gives the final OT layouts in a graphic interface.

Keywords— Dynamic Facility Layout Problem, Multi-Agent Systems; MILP, QAP, Operating Theater

1. INTRODUCTION

The constant and rarely predictable surgical activity progress requiring each time more complex material and technologies, the fight against hospital infections also known as "nosocomial infections" and the continuing growth of population demand for care services are some of the aspects of the evolution of operating theaters in recent years that directly impact on their conception.

The construction of an operating theater is not a frequent process, it may result either from the creation of a new hospital or renovating an existing OT or by the grouping of activities on a common Medical-Technique platform. Thus, Layout planning for Operating Theater is a long-term decision that should be taken carefully, because once the construction is done; it is difficult to change it.

Most hospitals in the world are designed using old techniques and their layouts are planned manually. Looking at real-world projects, Gibson (2007) argues that the planning and design of hospitals is most often based on benchmarks and experiences. Those methods have proven to be inefficient; there is a high cost of maintenance, and poor patient services are usually present.

The actual technological advancement invites hospitals to invest in these intelligent solutions in order to optimize their process and to raise efficiency and performance. This kind of problem is called Facility Layout Planning (FLP).

The main characteristic of today’s health care systems is inconstancy. Under such conditions, some parameters as patients demand is not stable and the facilities must be adaptive

to demand change requirements. From a layout point of view, such problem requires the use of the Dynamic layout planning.

The Dynamic Facility Layout Problem (DFLP) is concerned with the design of multi-period layout plans. We distinguish two type of planning horizon: fixed or rolling one. In planning period of m, rolling horizon consists on replacing the data at the end of period ‘1’, by data for period ‘m+1’, and it continues after finishing each period. In contrast, fixed planning horizon just considers the first m period data without any replacement (Balakrishnan 2009).

Based on the model developed in Chraibi et al. (2014a), this paper present an intelligent DMS using Multi-Agent (MA) architecture to solve DOTLP while respecting the hospitals’ imposed constraints (see FGI). This will allow hospitals to have an interactive tool providing an effective solution to the FLP to design their OT in reduced time while optimizing their expenses.

Multi-agent systems (MAS) have been developed in the context of distributed artificial intelligence and consist of a set of distributed cooperating agents each of which acts autonomously. It provides a novel approach to complex problems in a distributed manner where decisions should be based on processing of information from various sources of diverse nature Woolridge & Jennings (1995).

The agents of MAS communicate with each other, to share results or request resources, which greatly increases the complexity of the system, this is why the role of the coordinator agent is important to ensure the smooth interaction and running of the system. The communication between agents can take two different forms: (a) the negotiation, which is the result of the competition; or (b) the planning, which comes from the

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cooperation between agents. In our case, both cooperation and negotiation are used to solve DOTLP, as it will be explained in section IV.

In the next of this paper, we will present a literature review of the DFLP and works using MAS to solve different industrial problems in section II. The third section will contain the developed model using MILP and MAS, while experiments and results will be shown in section IV. Finally, we will conclude and give a description of future research perspectives.

2. LITERATURE REVIEW

In contrast with the Static FLP, which assumes that the flow data between two departments has no change or is nearly constant over time and solve the plant layout problem for a single period, the DFLP consider varying input data during the planning horizon. DFLP approaches consider a planning horizon generally divided into periods of weeks, months, or years in which the estimated data remains constant for each period. Therefore, it leads to obtain a final robust layout based on the optimal layout of each period.

Two DFLP approaches have been developed to reflect the variability of flow data: (1) developing one optimal layout, which is best over all periods, or (2) a layout plan for multiple periods where rearrangement costs are incurred for layout adaptations (Balakrishnan 2009). Reviews on dynamic layout problems and solution approaches are given in (Kulturel-Konak 2007 & Balakrishnan et al., 1998). In Balakrishnan et al., (1998) authors summarize the different algorithms used to solve the DFLP for equal and unequal department’s size.

A majority of the research in the DFLP assumes equal

department sizes and deterministic material flow. This

formulation is an extension of the well-known quadratic

assignment problem (QAP) used for SFLP (Balakrishnan et

al., 1992) aiming to minimize the traveling and the

rearrangement costs.

FLP is known to be a NP-Hard problem, that’s why it is

difficult to obtain an exact solution for larger-sized instances.

To the best of our knowledge, Chraibi et al. (2014a) increased

the number of facilities to 24 using an exact method (MILP)

based on a symmetric approach.

Moslemipour et al. (2012) give a review of intelligent methods used for designing dynamic and robust layouts in flexible manufacturing systems and present advantages and disadvantages of each one.

Rezazadeh et al. (2009) developed an extended discrete PSO algorithm for solving the Dynamic FLP. They used a local search scheme based on semi-annealing heuristic to find a better solution of gbest (global best).

Madhusudanan et al., (2011) suggest a Simulated Annealing (SA) algorithm to deal with equal size departments DFLP. The application of the proposed model for robust layout has been reinforced by the use of a Total Penalty Cost (TPC) defined as the minimum re-layout cost acceptable to support an agile strategy. Baykasoglu et al., (2006), used an ant colony solution method to solve a DFLP by considering the unconstrained and budget constrained cases.

Jolai et al., (2012) introduce the use of a multi-objective particle swarm optimization (MOPSO) on unequal sized DFLP problem, which aims to minimize the material handling and rearrangement costs and to maximize the total adjacency and distance requests.

McKendall et al., (2010) developed a construction and improvement type heuristic. For construction heuristic, they used a boundary search technique to deal with big-size DFLP which consists on placing departments along the boundaries of already placed departments in the layout. The improvement of the final solution is obtained by the use of a tabu search heuristic.

Even if the research work on FLP seems huge, the number of work on health care especially OT is very unpretentious. The first research work dealing with hospital layout planning using operations research methods was Elshafei (1977). Author developed a construction and an improvement heuristic, and modeled the problem as a QAP to solve it.

Barrett (2008) addressed the designs’ weakness in Clinic of Toronto General Hospital; author used a modified Systematic Layout Planning (SLP) approach to evaluate the clinic’s space usage, operation levels, flow and activity patterns. An improved and aggressive layouts were developed to change and improve current conditions and were evaluated based on a qualitative criteria.

Arnolds et al., (2013) considered the planning of ward layouts over multiple periods using Fixed and Variable wards approach. Different objectives of fixed ward layout models are considered to minimizing either costs for installing fixed patient rooms or the number of demand violations. The variable ward layout considers movable walls that can be rearranged when needed to minimizing costs for a layout plan that satisfies demand in each period. Thus, additional costs for the walls’ movement have to be minimized.

Assem et al. (2012) applied the FLP to the OT. They improved the design of OT by generating a block layout based on a graph theoretic method called SPIRAL which is a qualitative approach to maximize the interdepartmental adjacency of the graph layout. Lin et al. (2013) proposed an approach for designing and optimizing OTFL in hospitals. First, a systematic layout planning (SLP) is applied to design OTFL and they applied fuzzy constraint theory to comprehensively evaluate the layout schemes.

Works on OT still poor and need to be given more attention for its crucial place in hospitals and the major risks of safety and quality of care. Therefore, the designers should consider the facility layout of OT as an essential section in early design phase.

Driven by the real-life problem sizes, works based on approximate approaches are being more and more addressed using either heuristics, metaheuristics or intelligent methods. The choice of method to use is according to the characteristics of the problem such as size, linearity and non-linearity. In this work, we opt for MAS that insure efficient solutions for large-sized problems in a reasonable time.

Today, the interest of using and implementing of MAS no longer needs to be demonstrated. The research on complex agent oriented systems has a wide variety of industrial, business, science and educational application. Design of these

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systems requires adequate methodologies to cope with agent specific characteristics, which result from agent oriented domain analysis.

Even this, the use of MAS in FLP is practically non-existent. Tarkesh et al. (2009) are the first to present an algorithm using a society of virtual intelligent agents to efficiently solve the FLP introducing by this the concepts of emotion for the first time in operational research. They modeled each agent as facility having proprieties such as money and emotions, which are adjusted during the agent’s interactions, defined by market mechanism in which the richer agents can pay extra money to obtain better locations and are less interested in lower ones. To the best of our knowledge it stills the only work dealing with FLP using MA approach.

Otherwise, MAS are used in different domain. Nataraj Urs et al. (2010) presented a distributed MA framework for the VLSI layout design process. They divided the entire floor plan task into many subtasks, and affected each one to an agent to solve it. Finally they make agents interact with each other to negotiate the final placement for the design process.

Cossentino et al. (2011) presented a MA simulation tool for decision making in automatic warehouses management. Their proposed MAS aims to optimize the suitable number of Automated Guided Vehicles used for unloading containers arrived to the warehouse.

Nfaoui et al. (2008) developed an agent-based distributed architecture for collaborative decision-making processes within the global distribution supply chain for a best management of the rush unexpected order for which the quantity of product cannot be delivered partially or completely from the available inventory.

The next section is devoted to our MILP model dealing with the OTLP.

3. FACILITY LAYOUT PROBLEM

Given a set of activities, their areas and the available space, the OTLP seeks to determine the optimal placement of the set of care services’ activities within the available space subject to non-overlapping activities on the floor plan layout while optimizing the value of the objective function. The objective function aims to minimize the Total Traveling Cost (TTC) between activities.

To the best of our knowledge, Hospital layout planning still been addressed as static FLP, in where material handling flows do not change over a long time. As far as we know, hospitals and specifically OT are volatility. Under such conditions, some parameters like patients demand is not stable and the facilities must be adaptive to demand change requirements. For these reasons, a static layout analysis would not be sufficient.

In order to overcome the disadvantages of a static FLP, we provide a Fixed Activity Layout Problem (FALP) which consists to find in only one single decision a robust OT layout which is the best possible layout for all periods. This means that the layout could not be rearranged in later periods.

The FALP aims to minimize the traveling cost for all actors of the OT (doctors, patients, medical and non-medical staff) in each period considering varying input data (number of operation per specialty and frequency of flow for each actor) during the planning horizon. Traditional DFLP approaches

considered a planning horizon, which is generally divided into periods that may be defined in weeks, months, or years. Choosing period length has an impact on the final result. In fact, in short period the flows are fairly constant and there will not have need for layout rearrangement and the use of dynamic layout analysis may not be justified. In contrast, long period will lead to prohibitive rearrangement costs and this goes against the objective of costs’ minimization. This choice should be made according to the studied system based on demand and delivered asset and service.

Finding an optimal OTFL to minimize the various costs requires the following specification of requirements: the number of sections, the land area required by the facility, the number of corridors within the facility, the length, width and orientation of each activity, the activity and corridors allocations to each section and placement of the activities and corridor within each section. In real word, OT contains among others operating rooms, induction rooms, scrub rooms, decontamination, cleaning rooms, arsenals and Post Anesthesia Care Unit (PACU).

In this work, a new three levels approach is introduced (see Fig.1); the first one is to determine the dimensions and orientation of the plant layout or the initial construction site and to divide it into equal size departments corresponding to OT specialties. For each department, the second level is to solve the DFLP for different period of the planning horizon to find the optimal activities’ locations and orientation using the function (1). Finally, after choosing the best layout configuration for each department, the third level consists on assigning each one to a location according to its relationship with other departments. It is anticipated that the department with higher Total Relations Rate (TRR) with others calculated with function (2) is more interested to occupy a location in the middle of the plan in order to decrease its average distance from other departments.

Fig. 1. The three level approach

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This three steps decision making approach can best be handled through an effective and efficient cooperation of multiple agents in the second level to find the best layout and a negotiation protocol in the third one to allow each agent to occupy the best location in the initial plan. In the next section, we provide a detailed framework using MAS to solve the DOTLP using this three level approach.

The model used in this approach is the same introduced in [1] to solve Static OTLP just by considering the period 𝜏𝑡 to all constraints. To solve department layout, we used this MILP formulation while respecting the same assumption:

𝒎𝒊𝒏 𝑭𝟏 = ∑ ∑

𝑵

𝒊=𝟏

∑ ∑ 𝑭𝒕𝒊𝒋𝒌(𝑿𝒑𝒕𝒊𝒋

𝟒

𝒌=𝟏

𝑵

𝒋=𝟏

𝑻

𝒕=𝟏

+ 𝒀𝒑𝒕𝒊𝒋

)(𝝋𝒊𝒋𝒌

∗ 𝝈𝒌)

(1)

While:

𝑭𝒕𝒊𝒋𝒌 is the number of trips between activity ‘ai’ to activity ‘aj’

made by an entity type ‘ek’ in period 𝜏𝑡;

𝝋𝒊𝒋𝒌 is the difficulty of an entity ‘ek’ to move from activity ‘ai’

to activity ‘aj’. It is proportional to the required resources and provided effort;

𝝈𝒌 is the cost factor assigned to entity ‘ek’ which depends on the human resources involved;

𝑿𝒑𝒕𝒊𝒋, 𝒀𝒑𝒕𝒊𝒋 are respectively X-distance and Y-distance between

activity ‘ai’ and ‘aj’ in period 𝜏𝑡. Distances are calculated considering the real token road by corridors according to the departments’ orientation.

T= {𝜏𝑡; t=1, 2,… p } is the set of p periods in the planning horizon;

To calculate the TRR we use this formulation:

𝑇𝑅𝑅ℎ𝑘 = ∑ ∑(𝑟𝑖𝑗ℎ𝑘 + 𝑟𝑗𝑖ℎ𝑘)

𝑁

𝑗=1

𝑁

𝑖=1

ℎ = 1, … , 𝐷; 𝑘 = 1, … , 𝐷

(2)

While:

𝒓𝒊𝒋𝒉𝒌 is the relationship value which expresses the need for

proximity between the activity ‘ai’ in the department ‘h’ and the activity ‘aj’ in the department ‘k’ i.e., if two activities have a strong positive relationship, they are considered adjacent with a rank of A. The AEIOUX rates are equal to 16, 8, 4, 2, 0 and -2, respectively.

Finally, we use the QAP formulation to calculate the placement of each department while minimizing the traveling costs and maximizing the TRR:

min ∑ ∑ ∑ ∑ 𝐶ℎ𝑘𝐷ℎ𝑘𝑋ℎ𝑙𝑋𝑘𝑚

𝐷

𝑙=1

𝐷

𝑚=1

𝐷

𝑘=1

𝐷

ℎ=1

− ∑

𝐷

ℎ=1

∑ 𝑇𝑅𝑅ℎ𝑘𝜇ℎ𝑘

𝐷

𝑘=1

(3)

Subject to:

∑ 𝑋ℎ𝑙

𝐷

ℎ=1

= 1, 𝑙 = 1, … , 𝐷 (4)

∑ 𝑋𝑘𝑚

𝐷

𝑘=1

= 1, 𝑚 = 1, … , 𝐷 (5)

𝑋ℎ𝑙: 1 if department h is assigned to location l, 0 otherwise.

𝜇ℎ𝑘: Adjacency coefficient expresses the desirability of locating adjacent departments next to each other. It will be 1 if two departments are fully adjacent, 0.5 if they belong to the same section or 0 if they are located in different sections.

𝐶ℎ𝑘 : the traveling cost between department ‘h’ and ‘k’.

𝐷ℎ𝑘 : the distance between department ‘h’ and ‘k’.

Constraints (4) and (5) are to insure that each department is assigned to only one location, and each location contains only one department.

4. MULTI-AGENT ARCHITECTURE FOR OTLP

Agents can be categorized into two categories according to their reasoning capacity, namely the cognitive and the reactive agents (Nfaoui [2008]).

Cognitive agents are inspired from the human behavior. Each agent has a partial representation of the environment and other agents. They act in a Perception/Decision/Action cycle. Each agent therefore has the ability to think in terms of its own goals and to manage interactions with other agents and with the environment (Ferber & Perrot [1995]).

On the contrary, reactive agents are not intelligent; they have a reduced capacity protocol and language communication to operate with a Perception/Action cycle so that they react rapidly to asynchronous events without using complex reasoning. Their behavior is then simply dictated by their relationship to their environment without having a representation of other agents or their environment (Drogoul [1993]).

In Our approach, we used cognitive and communicative agents. To communicate, they need a developed language to be able to exchange messages.

However, a simple model of message is not enough to tolerate conversations between agents and to allow language acts take their meaning. For this, we introduced the notion of protocol to support such conversations.

The negotiation strategy is proposed based on the Contract Net protocol implemented using the JADE platform that aims to simplify the development of MAS while providing a complete set of services and agents comply with FIPA specifications (FIPA, A. C. L. [2002]).

To the best of our knowledge, there is only one paper on FLP using MAS and in the few works dealing with OTLP no one is using MAS.

To deal with our problem, we adopt a Master/Slave/Sub-Slave architecture where the Master Processor (MP) is the coordinator of the optimization process, while Slave Processor (SP) is a worker executing tasks coming from MP and the Sub-Slave Processor (Sub_SP) is a worker executing tasks coming from SP. The main task of a MP is to dispatch parameters and orders on generated SPs, which divide the problem according

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to the number of periods in the planning horizon and generate Sub_SPs to solve the sub-problem and send the answer with objective value (see Fig.2).

The developed interaction between agents to solve DOTLP can be described in the following algorithm:

Step 1. Initialization The initiator launches the mainContainer (JADE platform); setup the graphic Interface (GUI); initialize program parameters and register the MP.

Step 2. Divide the initial OT plan Once the MP registered, it divides the OT into equal sized sections according to their specialty and as imposed by hospitals managers. The MP sends each department size and orientation to a SP with the required parameters to solve the department layout problem. Once this, the MP is on standby mode waiting for results coming from SPs.

Step 3. Solve each Department Layout [1] The MP creates and registers a SP for each department; [2] For each period in the planning horizon, each SP generates a Sub_SP to solve for this period. [3] Each Sub_SP first receives the instance of the sub-problem from the SP and starts solving MILP formulation using the equation (1) for the activities and corridors in the department; [4] Once all Sub_SPs finish solving the sub-problems in each period for a department ‘d’, agents start cooperation phase by comparing their results in order to choose the best over all periods. The retained solution is then sends to SP as ’location and orientation to the SP.

Step 4. Solve the whole OT layout Once all SPs receive answer from their Sub_SPs, they start negotiation phase to determine the best assignment for each department using the QAP formulation (3) according to their calculated TRR and send the final solution to the MP. The step stops when the MP collects all solutions.

Step 5. Present the final solution

The result of ’ ’negotiation is a final optimal OT layout. The MP then sends this solution to the GUI that draws it and shows it to the decision makers to validate it.

Step 6 Ag ’ Finally, the MP informs the MainContainer about the end of process and destructs all working agents in the JADE platform.

This study on MAS allowed us to define how the capacity of cognitive agents can be used in DMS, namely their intelligence, cooperation and learning.

In the next section, the implementation of the bellow algorithm will be shown in addition to obtained results compared with previous ones.

5. EXPERIMENTS AND RESULTS

In this section, we validated the proposed MA algorithm based on MILP formulation using a set of previous generated data. We used ILOG CPLEX 12.5 software to solve the model using Windows 7 platform, Intel5® Core ™ i5-3380M CPU@ 2.90GHz and 8Go of RAM.

The algorithm was implemented using JAVA language. We

divide the program into three packages; the first contains all the

required class to model the JADE agents, the second class

models the different OT components (OT, departments,

facilities, activities) while the third one is to design the GUI.

The used data was generated according to our observation

in some OT and some statistics on the number of operation per

day and per specialty, the required doctors and staff number to

do an operation, different actors’ flow in the OT, etc. This

come second after the specifications of the project owners who

decide of the required services, the desired number of activities

in the final OT, their sizes, etc.

Compared to previous obtained results (Chraibi et al,.

[2014a]), this program gives an efficient solution for larger-

sized problems in a shorter time. TABLE I gives an example of

results given by 4, 6 and 8 agents in a planning horizon of 3, 6,

9 and 12 periods. As seen, in less than one minute OTLP with

88 activities can be solved. This offers to architects an

interactive and intelligent tool able to design OT while

respecting international standards.

The number of activities we test here is not a limitation, we

can make the size larger than 88, while it can increase by

increasing the number of agents. Finally, here is an example of

obtained solutions: In Fig.3, we can see an OT of four

departments, resulting from step 2 (Divide the initial OT plan)

while Fig.5 shows the final OT layout after step 5 (Present the

final solution) with 42 activities.

Fig. 2. Master/Slave architecture

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TABLE I. TIME PROCEDING FOR DIFFERENT INSTANCES SIZES

Number

of

agents

Number

of

activities

Number

of

periods

Time (sec)

Iteration

1

Iteration

2

Iteration

3

4 42

3 5,14 4,45 4,10

6 8,50s 8,37s 8,20s

9 12,73s 12,14s 11,80s

12 20,21s 17,79 15,86

6 63

3 7,48s 7,31s 6,84s

6 14,16s 13,48s 13,33s

9 23,56s 20,74s 19,76s

12 28,27s 27,96s 27,24s

8 88

3 10,24s 9,94s 9,51s

6 21,43s 20,38s 18,71s

9 30,16s 29,16s 28,01s

12 44,39s 42,02s 35,48s

6. CONCLUSION

This paper presents a MILP formulation to solve DOTLP

using FALP approach, which consists to find in only one single

decision a robust OT layout for the whole planning horizon.

This paper presents a novel approach based on MAS offering

hospitals an interactive DMS. The method has proved to be

efficient and effective in solving larger sized problems, which

was limited with simple MILP formulation to 24 and can be

used as a decision support tool to planners for efficient OT

layout design.

We do not intend to stop here, future works will be

addressed to increase the performance of each agent to solve

bigger department layout, either by using metaheuristics or by

using intelligent approaches.

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Fig. 3. Final OT Layout

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