# A Conceptual Framework for Logistics Management and Project Planning in the Clinical Trials Industry

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## Abstract

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## 1. Introduction

## 2. Literature Review

#### 2.1. Clinical Trial Industry Background

#### 2.2. Challenges and Requirements in Managing Clinical Trials

#### 2.3. Service Industry and Servitization

#### 2.4. Project Management

#### 2.5. Contemporary Software Tools

#### 2.6. Visualization and Collaboration Tools

- There is no reported conceptual framework based on contemporary software tools and architectures, all interacting with specialized software applications for accounting, inventory, and label or kit design software.
- There is no reported project planning tool or methodology for resource management. In particular, this paper will look at different managerial strategies to plan and execute logistics tasks.

## 3. Project Management Challenges in Clinical Trials

- Participant recruitment and management include recruiting eligible patients and managing their health and safety.
- Budget management includes managing the allocated money for each activity of the protocol and amendments.
- Logistics and supply chain include coordination of shipping supplies and treatments from the manufacturer to the sites and collected samples from the sites to the assay laboratories.
- Inventory management includes maintaining the appropriate level of unexpired supplies and treatments at each site.
- Production and Assembly includes designing and producing the desired supplies (sample collection kits) and treatments for clinical trials.
- Data management includes tracking the logistical data such as data about patients, supplies, samples, sample shipments, and clinical data such as laboratory results.
- Compliance management includes meeting regulatory compliance practices while conducting clinical trials. Examples of regulators are the Institutional Review Board (IRB), and Ethical Review Board (ERB) or Research Ethics Board (REB) regulations.

#### 3.1. Protocol Amendments

#### 3.2. Demand for Patients

#### 3.3. Data Management

- Enrollment log that includes the list of enrolled patients in a site.
- Supplies or kits that are produced by the CRO for the sites.
- Shipments schedule to ship collected samples from the site to the central laboratory for analysis.
- Sample shipments that the site ships to the central laboratory.
- Sample Inventory Log (SIL) is the manifest of samples being shipped in a shipment. Electronic SIL (eSIL) is the electronic format of the SIL.
- Notifications that are in the form of emails that are sent to inform the laboratory of incoming samples shipments.

#### 3.4. Diverse Software Applications and Data Sources

## 4. Development of a Streamlined Integrative Conceptual Framework

- Web portal and its interactions with human users.
- Auto-monitoring tools implemented using intelligent software agents.
- Clinical trials BPMS to execute and orchestrate the tasks amongst resources and stakeholders.
- Project card to host data regarding all project activities in one place.
- External applications (for specialized tasks).
- Document repository.
- Data repository.
- Analytics module to capture key performance indicators through the layers.
- Security.

#### 4.1. Web Portal and Its Interactions with Human Users

#### 4.2. Intelligent Agents

#### 4.3. Clinical Trials BPMS Requirements

- A platform for documenting the budget requirements such as type and number of supplies, sample shipment frequencies, and contacts.
- A platform to design labels, kits, manuals and share the drafts with sponsors for comments and approvals. Templates for designing labels, jigs, and manuals should be populated automatically by the available data in the budget.
- A platform to train site staff about the testing plans.
- Change the management functionality to update the affected data.

- Patient’s enrollment and kit inventory databases should be shared between the sites and CRO.
- The CRO should be notified by the system to produce and ship the required kits.
- If the kits need to be modified, the sponsor should identify in the system in which time point data should be changed and an automatic notification should be sent to the stakeholders.
- There should be a collaborative platform for changing the design of the kits between CRO and sponsor due to frequent changes in the protocols. Conversation systems can be incorporated in the platform.
- Shipments from CRO to sites can be tracked by the system; shipment notification should be sent to the sites automatically.
- The approved site orders should be sent to the production department to plan inventory and production.
- Sites can track their requests on the platform.

- SILs should be filled out electronically at sites either manually or using barcodes with data integrity checks on forms. A similar approach to [51] can be applied here.
- A conversation platform is available as a hyperlink on the form to contact other team members for questions.
- The user can view the list of samples collected for each patient and schedule sample shipment either manually or automatically. The site staff will be notified when they should ship the samples.
- This system can be linked to the courier database to track the shipments.
- Automatic shipment notification along with the list of samples in the shipment and tracking number should be sent to the assay laboratory.
- Labs need to confirm receipt of samples on the platform. Follow-ups will be sent in case of no response.
- The platform should be able to handle sample discrepancies by contacting responsible parties.

#### 4.4. Project Card

- The progress in the entire project or a specific area.
- The resources that have been involved in any tasks.
- The link to documents that have been collected during the project.
- The history of tasks and changes.
- The list of supplies used in the clinical trials.
- The list of contacts.
- The list of patients and their collected samples.
- The link to conversations and notifications.

#### 4.5. External Applications

#### 4.6. Document Repository

#### 4.7. Data Repository

#### 4.8. Analytics (As Shown Spanning the Entire Architecture in Figure 7)

- Which sites are making errors that require training? Which suppliers and partner companies are making errors and reasons?
- What are the common errors?
- What are the bottlenecks?
- Identify the common trends for supplies and kits in all clinical trials. SKU wise, size wise, design wise, quantity wise.
- Identify the historical demand for supplies and services and forecast future demand.

#### 4.9. Security (As Shown Spanning the Entire Architecture in Figure 7)

#### 4.10. Implementation

#### 4.10.1. Database System (Project Card)

#### 4.10.2. Application Design in BPM Software

#### 4.10.3. Integration of BPM Software with External Software

#### 4.10.4. Intelligent Agents

#### 4.10.5. Reports and Dashboards for Every Protocol

## 5. Resource and Project Planning in the Clinical Trial Logistics Management

#### 5.1. Description of the Project Tasks and Resources

#### 5.2. Task Flow

#### 5.3. Conceptual Solution for Planning the Tasks and Resources

- Assign tasks of any project (protocol) to people in a group according to their qualifications. For example, in the QC group, some people can only use QC labels, while some are qualified to QC budgets as well as labels.
- Include familiarity factors for resources.
- Assign similar projects to one project manager for more efficiency.
- Assign urgent or high-priority tasks to more experienced people to process them faster.
- Assign tasks according to the resource’s workload.
- Transfer resources from one resource group to the other for cross training and when work demand moves from one department to the other.
- Project tasks stay with the same person or group who started the first task of that job within that process to increase the familiarity factor.
- Assign simpler tasks to new employees.

#### 5.4. Model 1—Task Scheduling LP

#### 5.4.1. Scenario I—Fixed Shared Resources among All Projects

#### 5.4.2. Scenario II—Fixed Dedicated Resources for Each Project

#### 5.4.3. Scenario III—Fixed Dedicated Resources in Project Work Groups

#### 5.5. Model 2—Resource Planning LP

#### 5.5.1. Scenario IV—Variable Shared Resources

#### 5.5.2. Scenario V—Variable Dedicated Resources

#### 5.5.3. Scenario VI—Variable Dedicated Work Groups

#### 5.6. Background Research on RCMPSP

#### 5.7. Task Planning Model (Scenarios I and II)

#### 5.7.1. Sets and Indices

- $V\mathrm{s}\mathrm{e}\mathrm{t}\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{j}\mathrm{e}\mathrm{c}\mathrm{t}\mathrm{s},v\in V$
- ${P}_{v}\mathrm{s}\mathrm{e}\mathrm{t}\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{c}\mathrm{e}\mathrm{s}\mathrm{s}\mathrm{e}\mathrm{s}\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{j}\mathrm{e}\mathrm{c}\mathrm{t}v,p\in {P}_{v}$
- ${J}_{vp}\mathrm{s}\mathrm{e}\mathrm{t}\mathrm{o}\mathrm{f}\mathrm{t}\mathrm{a}\mathrm{s}\mathrm{k}\mathrm{s}\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{c}\mathrm{e}\mathrm{s}\mathrm{s}p\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{j}\mathrm{e}\mathrm{c}\mathrm{t}v,j\in {J}_{vp}$
- ${p}_{vN}\mathrm{l}\mathrm{a}\mathrm{s}\mathrm{t}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{c}\mathrm{e}\mathrm{s}\mathrm{s}\left(\mathrm{i}\mathrm{n}\mathrm{d}\mathrm{e}\mathrm{x}\mathrm{e}\mathrm{d}\mathrm{w}\mathrm{i}\mathrm{t}\mathrm{h}N\right)\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{j}\mathrm{e}\mathrm{c}\mathrm{t}v$
- ${j}_{vpL}\mathrm{l}\mathrm{a}\mathrm{s}\mathrm{t}\mathrm{t}\mathrm{a}\mathrm{s}\mathrm{k}\left(\mathrm{i}\mathrm{n}\mathrm{d}\mathrm{e}\mathrm{x}\mathrm{e}\mathrm{d}\mathrm{w}\mathrm{i}\mathrm{t}\mathrm{h}L\right)\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{c}\mathrm{e}\mathrm{s}\mathrm{s}p\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{j}\mathrm{e}\mathrm{c}\mathrm{t}v$
- ${j}_{vpF}\mathrm{f}\mathrm{i}\mathrm{r}\mathrm{s}\mathrm{t}\mathrm{t}\mathrm{a}\mathrm{s}\mathrm{k}\left(\mathrm{i}\mathrm{n}\mathrm{d}\mathrm{e}\mathrm{x}\mathrm{e}\mathrm{d}\mathrm{w}\mathrm{i}\mathrm{t}\mathrm{h}F\right)\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{c}\mathrm{e}\mathrm{s}\mathrm{s}p\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{j}\mathrm{e}\mathrm{c}\mathrm{t}v$
- ${S}_{v}\mathrm{s}\mathrm{e}\mathrm{t}\mathrm{o}\mathrm{f}\mathrm{a}\mathrm{l}\mathrm{l}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{c}\mathrm{e}\mathrm{s}\mathrm{s}\mathrm{p}\mathrm{r}\mathrm{e}\mathrm{c}\mathrm{e}\mathrm{d}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{e}\mathrm{r}\mathrm{e}\mathrm{l}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{s}\mathrm{h}\mathrm{i}\mathrm{p}\mathrm{s}\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{j}\mathrm{e}\mathrm{c}\mathrm{t}v$
- ${Q}_{vp}\mathrm{s}\mathrm{e}\mathrm{t}\mathrm{o}\mathrm{f}\mathrm{a}\mathrm{l}\mathrm{l}\mathrm{t}\mathrm{a}\mathrm{s}\mathrm{k}\mathrm{p}\mathrm{r}\mathrm{e}\mathrm{c}\mathrm{e}\mathrm{d}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{e}\mathrm{r}\mathrm{e}\mathrm{l}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{s}\mathrm{h}\mathrm{i}\mathrm{p}\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{c}\mathrm{e}\mathrm{s}\mathrm{s}p\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{j}\mathrm{e}\mathrm{c}\mathrm{t}v$
- ${M}_{vpj}\mathrm{s}\mathrm{e}\mathrm{t}\mathrm{o}\mathrm{f}\mathrm{m}\mathrm{o}\mathrm{d}\mathrm{e}\mathrm{s}\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{t}\mathrm{a}\mathrm{s}\mathrm{k}j\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{c}\mathrm{e}\mathrm{s}\mathrm{s}p\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{j}\mathrm{e}\mathrm{c}\mathrm{t}v$
- $G\mathrm{s}\mathrm{e}\mathrm{t}\mathrm{o}\mathrm{f}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{o}\mathrm{u}\mathrm{r}\mathrm{c}\mathrm{e}\mathrm{g}\mathrm{r}\mathrm{o}\mathrm{u}\mathrm{p}\mathrm{s},g\in G$
- ${K}_{g}\mathrm{s}\mathrm{e}\mathrm{t}\mathrm{o}\mathrm{f}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{e}\mathrm{w}\mathrm{a}\mathrm{l}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{o}\mathrm{u}\mathrm{r}\mathrm{c}\mathrm{e}\mathrm{s}\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{g}\mathrm{r}\mathrm{o}\mathrm{u}\mathrm{p}g,k\in {K}_{g}$
- $T\mathrm{s}\mathrm{e}\mathrm{t}\mathrm{o}\mathrm{f}\mathrm{t}\mathrm{i}\mathrm{m}\mathrm{e}\mathrm{p}\mathrm{e}\mathrm{r}\mathrm{i}\mathrm{o}\mathrm{d}\mathrm{s}\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{j}\mathrm{e}\mathrm{c}\mathrm{t},t\in T$

#### 5.7.2. Parameters

- ${EE}_{vpj}\mathrm{e}\mathrm{a}\mathrm{r}\mathrm{l}\mathrm{i}\mathrm{e}\mathrm{s}\mathrm{t}\mathrm{f}\mathrm{i}\mathrm{n}\mathrm{i}\mathrm{s}\mathrm{h}\mathrm{t}\mathrm{i}\mathrm{m}\mathrm{e}\mathrm{o}\mathrm{f}\mathrm{t}\mathrm{a}\mathrm{s}\mathrm{k}j\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{c}\mathrm{e}\mathrm{s}\mathrm{s}p\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{j}\mathrm{e}\mathrm{c}\mathrm{t}v$
- ${LL}_{vpj}\mathrm{l}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{s}\mathrm{t}\mathrm{f}\mathrm{i}\mathrm{n}\mathrm{i}\mathrm{s}\mathrm{h}\mathrm{t}\mathrm{i}\mathrm{m}\mathrm{e}\mathrm{o}\mathrm{f}\mathrm{t}\mathrm{a}\mathrm{s}\mathrm{k}j\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{c}\mathrm{e}\mathrm{s}\mathrm{s}p\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{j}\mathrm{e}\mathrm{c}\mathrm{t}v$
- ${E}_{vp}\mathrm{e}\mathrm{a}\mathrm{r}\mathrm{l}\mathrm{i}\mathrm{e}\mathrm{s}\mathrm{t}\mathrm{f}\mathrm{i}\mathrm{n}\mathrm{i}\mathrm{s}\mathrm{h}\mathrm{t}\mathrm{i}\mathrm{m}\mathrm{e}\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{c}\mathrm{e}\mathrm{s}\mathrm{s}p\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{j}\mathrm{e}\mathrm{c}\mathrm{t}v$
- ${L}_{vp}\mathrm{l}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{s}\mathrm{t}\mathrm{f}\mathrm{i}\mathrm{n}\mathrm{i}\mathrm{s}\mathrm{h}\mathrm{t}\mathrm{i}\mathrm{m}\mathrm{e}\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{c}\mathrm{e}\mathrm{s}\mathrm{s}p\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{j}\mathrm{e}\mathrm{c}\mathrm{t}v$
- ${d}_{vpjm}\mathrm{d}\mathrm{u}\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{o}\mathrm{f}\mathrm{t}\mathrm{a}\mathrm{s}\mathrm{k}\mathrm{s}j\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{c}\mathrm{e}\mathrm{s}\mathrm{s}p\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{j}\mathrm{e}\mathrm{c}\mathrm{t}v,\mathrm{o}\mathrm{p}\mathrm{e}\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{n}\mathrm{g}\mathrm{o}\mathrm{n}\mathrm{m}\mathrm{o}\mathrm{d}\mathrm{e}m$
- ${r}_{vpjgkm}\mathrm{u}\mathrm{s}\mathrm{a}\mathrm{g}\mathrm{e}\mathrm{o}\mathrm{f}\mathrm{t}\mathrm{a}\mathrm{s}\mathrm{k}\mathrm{s}j\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{c}\mathrm{e}\mathrm{s}\mathrm{s}p\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{j}\mathrm{e}\mathrm{c}\mathrm{t}v,$
- $\mathrm{o}\mathrm{p}\mathrm{e}\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{n}\mathrm{g}\mathrm{o}\mathrm{n}\mathrm{m}\mathrm{o}\mathrm{d}\mathrm{e}m\mathrm{from}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{e}\mathrm{w}\mathrm{a}\mathrm{b}\mathrm{l}\mathrm{e}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{o}\mathrm{u}\mathrm{r}\mathrm{c}\mathrm{e}k\mathrm{o}\mathrm{f}\mathrm{g}\mathrm{r}\mathrm{o}\mathrm{u}\mathrm{p}g$
- ${dd}_{v}\mathrm{a}\mathrm{s}\mathrm{s}\mathrm{i}\mathrm{g}\mathrm{n}\mathrm{e}\mathrm{d}\mathrm{d}\mathrm{u}\mathrm{e}\mathrm{d}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{j}\mathrm{e}\mathrm{c}\mathrm{t}v$
- ${ddd}_{vp}\mathrm{d}\mathrm{u}\mathrm{e}\mathrm{d}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{c}\mathrm{e}\mathrm{s}\mathrm{s}p\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{j}\mathrm{e}\mathrm{c}\mathrm{t}v$
- ${c}_{v}\mathrm{r}\mathrm{e}\mathrm{l}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{v}\mathrm{e}\mathrm{w}\mathrm{e}\mathrm{i}\mathrm{g}\mathrm{h}\mathrm{t}\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{j}\mathrm{e}\mathrm{c}\mathrm{t}v$
- ${c}_{vp}\mathrm{r}\mathrm{e}\mathrm{l}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{v}\mathrm{e}\mathrm{w}\mathrm{e}\mathrm{i}\mathrm{g}\mathrm{h}\mathrm{t}\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{c}\mathrm{e}\mathrm{s}\mathrm{s}p\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{j}\mathrm{e}\mathrm{c}\mathrm{t}v$
- ${b}_{gk}\mathrm{u}\mathrm{n}\mathrm{i}\mathrm{t}\mathrm{c}\mathrm{o}\mathrm{s}\mathrm{t}\mathrm{o}\mathrm{f}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{e}\mathrm{w}\mathrm{a}\mathrm{b}\mathrm{l}\mathrm{e}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{o}\mathrm{u}\mathrm{r}\mathrm{c}\mathrm{e}k\mathrm{b}\mathrm{e}\mathrm{l}\mathrm{o}\mathrm{n}\mathrm{g}\mathrm{i}\mathrm{n}\mathrm{g}\mathrm{t}\mathrm{o}\mathrm{g}\mathrm{r}\mathrm{o}\mathrm{u}\mathrm{p}g$
- ${BR}_{g}\mathrm{n}\mathrm{u}\mathrm{m}\mathrm{b}\mathrm{e}\mathrm{r}\mathrm{o}\mathrm{f}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{e}\mathrm{w}\mathrm{a}\mathrm{b}\mathrm{l}\mathrm{e}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{o}\mathrm{u}\mathrm{r}\mathrm{c}\mathrm{e}\mathrm{s}\mathrm{i}\mathrm{n}\mathrm{g}\mathrm{r}\mathrm{o}\mathrm{u}\mathrm{p}g\mathrm{p}\mathrm{e}\mathrm{r}\mathrm{p}\mathrm{e}\mathrm{r}\mathrm{i}\mathrm{o}\mathrm{d}t$
- or
- ${BR}_{vg}\mathrm{n}\mathrm{u}\mathrm{m}\mathrm{b}\mathrm{e}\mathrm{r}\mathrm{o}\mathrm{f}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{e}\mathrm{w}\mathrm{a}\mathrm{b}\mathrm{l}\mathrm{e}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{o}\mathrm{u}\mathrm{r}\mathrm{c}\mathrm{e}\mathrm{s}\mathrm{i}\mathrm{n}\mathrm{g}\mathrm{r}\mathrm{o}\mathrm{u}\mathrm{p}g\mathrm{p}\mathrm{e}\mathrm{r}\mathrm{p}\mathrm{e}\mathrm{r}\mathrm{i}\mathrm{o}\mathrm{d}t\mathrm{d}\mathrm{e}\mathrm{d}\mathrm{i}\mathrm{c}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{d}\mathrm{t}\mathrm{o}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{j}\mathrm{e}\mathrm{c}\mathrm{t}v$

#### 5.7.3. Decision Variables

- ${x}_{vpjmt}=\left\{\right)separators="|">\begin{array}{c}1,\mathrm{i}\mathrm{f}\mathrm{t}\mathrm{a}\mathrm{s}\mathrm{k}j\mathrm{o}\mathrm{f}\mathrm{}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{c}\mathrm{e}\mathrm{s}\mathrm{s}p\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{j}\mathrm{e}\mathrm{c}\mathrm{t}v\mathrm{o}\mathrm{p}\mathrm{e}\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{n}\mathrm{g}\mathrm{o}\mathrm{n}\mathrm{m}\mathrm{o}\mathrm{d}\mathrm{e}\mathrm{m}\mathrm{i}\mathrm{s}\mathrm{f}\mathrm{i}\mathrm{n}\mathrm{i}\mathrm{s}\mathrm{h}\mathrm{e}\mathrm{d}\mathrm{a}\mathrm{t}\mathrm{p}\mathrm{e}\mathrm{r}\mathrm{i}\mathrm{o}\mathrm{d}t\\ 0,otherwise\end{array}$
- ${TC}_{v}=\mathrm{W}\mathrm{e}\mathrm{i}\mathrm{g}\mathrm{h}\mathrm{t}\mathrm{e}\mathrm{d}\mathrm{t}\mathrm{a}\mathrm{r}\mathrm{d}\mathrm{i}\mathrm{n}\mathrm{e}\mathrm{s}\mathrm{s}\mathrm{c}\mathrm{o}\mathrm{s}\mathrm{t}\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{j}\mathrm{e}\mathrm{c}\mathrm{t}v$
- ${TC}_{vp}=\mathrm{W}\mathrm{e}\mathrm{i}\mathrm{g}\mathrm{h}\mathrm{t}\mathrm{e}\mathrm{d}\mathrm{t}\mathrm{a}\mathrm{r}\mathrm{d}\mathrm{i}\mathrm{n}\mathrm{e}\mathrm{s}\mathrm{s}\mathrm{c}\mathrm{o}\mathrm{s}\mathrm{t}\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{c}\mathrm{e}\mathrm{s}\mathrm{s}p\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{j}\mathrm{e}\mathrm{c}\mathrm{t}v$

#### 5.7.4. Mathematical Model

#### 5.8. Task Planning (Scenario III)

#### 5.8.1. Sets and Indices

- $V\mathrm{s}\mathrm{e}\mathrm{t}\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{j}\mathrm{e}\mathrm{c}\mathrm{t}\mathrm{s},v\in V$
- $W\mathrm{s}\mathrm{e}\mathrm{t}\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{j}\mathrm{e}\mathrm{c}\mathrm{t}\mathrm{w}\mathrm{o}\mathrm{r}\mathrm{k}\mathrm{g}\mathrm{r}\mathrm{o}\mathrm{u}\mathrm{p}\mathrm{s},w\in W$
- ${P}_{v}\mathrm{s}\mathrm{e}\mathrm{t}\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{c}\mathrm{e}\mathrm{s}\mathrm{s}\mathrm{e}\mathrm{s}\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{j}\mathrm{e}\mathrm{c}\mathrm{t}v,p\in {P}_{v}$
- ${J}_{vp}\mathrm{s}\mathrm{e}\mathrm{t}\mathrm{o}\mathrm{f}\mathrm{t}\mathrm{a}\mathrm{s}\mathrm{k}\mathrm{s}\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{c}\mathrm{e}\mathrm{s}\mathrm{s}p\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{j}\mathrm{e}\mathrm{c}\mathrm{t}v,j\in {J}_{vp}$
- ${p}_{vN}\mathrm{l}\mathrm{a}\mathrm{s}\mathrm{t}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{c}\mathrm{e}\mathrm{s}\mathrm{s}\left(\mathrm{i}\mathrm{n}\mathrm{d}\mathrm{e}\mathrm{x}\mathrm{e}\mathrm{d}\mathrm{w}\mathrm{i}\mathrm{t}\mathrm{h}N\right)\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{j}\mathrm{e}\mathrm{c}\mathrm{t}v$
- ${j}_{vpL}\mathrm{l}\mathrm{a}\mathrm{s}\mathrm{t}\mathrm{t}\mathrm{a}\mathrm{s}\mathrm{k}\left(\mathrm{i}\mathrm{n}\mathrm{d}\mathrm{e}\mathrm{x}\mathrm{e}\mathrm{d}\mathrm{w}\mathrm{i}\mathrm{t}\mathrm{h}L\right)\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{c}\mathrm{e}\mathrm{s}\mathrm{s}p\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{j}\mathrm{e}\mathrm{c}\mathrm{t}v$
- ${j}_{vpF}\mathrm{f}\mathrm{i}\mathrm{r}\mathrm{s}\mathrm{t}\mathrm{t}\mathrm{a}\mathrm{s}\mathrm{k}\left(\mathrm{i}\mathrm{n}\mathrm{d}\mathrm{e}\mathrm{x}\mathrm{e}\mathrm{d}\mathrm{w}\mathrm{i}\mathrm{t}\mathrm{h}F\right)\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{c}\mathrm{e}\mathrm{s}\mathrm{s}p\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{j}\mathrm{e}\mathrm{c}\mathrm{t}v$
- ${S}_{v}\mathrm{s}\mathrm{e}\mathrm{t}\mathrm{o}\mathrm{f}\mathrm{a}\mathrm{l}\mathrm{l}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{c}\mathrm{e}\mathrm{s}\mathrm{s}\mathrm{p}\mathrm{r}\mathrm{e}\mathrm{c}\mathrm{e}\mathrm{d}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{e}\mathrm{r}\mathrm{e}\mathrm{l}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{s}\mathrm{h}\mathrm{i}\mathrm{p}\mathrm{s}\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{j}\mathrm{e}\mathrm{c}\mathrm{t}v$
- ${Q}_{vp}\mathrm{s}\mathrm{e}\mathrm{t}\mathrm{o}\mathrm{f}\mathrm{a}\mathrm{l}\mathrm{l}\mathrm{t}\mathrm{a}\mathrm{s}\mathrm{k}\mathrm{p}\mathrm{r}\mathrm{e}\mathrm{c}\mathrm{e}\mathrm{d}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{e}\mathrm{r}\mathrm{e}\mathrm{l}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{s}\mathrm{h}\mathrm{i}\mathrm{p}\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{c}\mathrm{e}\mathrm{s}\mathrm{s}p\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{j}\mathrm{e}\mathrm{c}\mathrm{t}v$
- ${M}_{vpj}\mathrm{s}\mathrm{e}\mathrm{t}\mathrm{o}\mathrm{f}\mathrm{m}\mathrm{o}\mathrm{d}\mathrm{e}\mathrm{s}\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{t}\mathrm{a}\mathrm{s}\mathrm{k}j\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{c}\mathrm{e}\mathrm{s}\mathrm{s}p\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{j}\mathrm{e}\mathrm{c}\mathrm{t}v$
- ${M}_{w}\mathrm{s}\mathrm{e}\mathrm{t}\mathrm{o}\mathrm{f}\mathrm{m}\mathrm{o}\mathrm{d}\mathrm{e}\mathrm{s}\mathrm{i}\mathrm{n}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{j}\mathrm{e}\mathrm{c}\mathrm{t}\mathrm{w}\mathrm{o}\mathrm{r}\mathrm{k}\mathrm{g}\mathrm{r}\mathrm{o}\mathrm{u}\mathrm{p}w$
- $G\mathrm{s}\mathrm{e}\mathrm{t}\mathrm{o}\mathrm{f}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{o}\mathrm{u}\mathrm{r}\mathrm{c}\mathrm{e}\mathrm{g}\mathrm{r}\mathrm{o}\mathrm{u}\mathrm{p}\mathrm{s},g\in G$
- ${K}_{g}\mathrm{s}\mathrm{e}\mathrm{t}\mathrm{o}\mathrm{f}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{e}\mathrm{w}\mathrm{a}\mathrm{l}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{o}\mathrm{u}\mathrm{r}\mathrm{c}\mathrm{e}\mathrm{s}\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{g}\mathrm{r}\mathrm{o}\mathrm{u}\mathrm{p}g,k\in {K}_{g}$
- $T\mathrm{s}\mathrm{e}\mathrm{t}\mathrm{o}\mathrm{f}\mathrm{t}\mathrm{i}\mathrm{m}\mathrm{e}\mathrm{p}\mathrm{e}\mathrm{r}\mathrm{i}\mathrm{o}\mathrm{d}\mathrm{s}\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{j}\mathrm{e}\mathrm{c}\mathrm{t},t\in T$

#### 5.8.2. Parameters

- ${EE}_{vpj}\mathrm{e}\mathrm{a}\mathrm{r}\mathrm{l}\mathrm{i}\mathrm{e}\mathrm{s}\mathrm{t}\mathrm{f}\mathrm{i}\mathrm{n}\mathrm{i}\mathrm{s}\mathrm{h}\mathrm{t}\mathrm{i}\mathrm{m}\mathrm{e}\mathrm{o}\mathrm{f}\mathrm{t}\mathrm{a}\mathrm{s}\mathrm{k}j\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{c}\mathrm{e}\mathrm{s}\mathrm{s}p\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{j}\mathrm{e}\mathrm{c}\mathrm{t}v$
- ${LL}_{vpj}\mathrm{l}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{s}\mathrm{t}\mathrm{f}\mathrm{i}\mathrm{n}\mathrm{i}\mathrm{s}\mathrm{h}\mathrm{t}\mathrm{i}\mathrm{m}\mathrm{e}\mathrm{o}\mathrm{f}\mathrm{t}\mathrm{a}\mathrm{s}\mathrm{k}j\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{c}\mathrm{e}\mathrm{s}\mathrm{s}p\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{j}\mathrm{e}\mathrm{c}\mathrm{t}v$
- ${E}_{vp}\mathrm{e}\mathrm{a}\mathrm{r}\mathrm{l}\mathrm{i}\mathrm{e}\mathrm{s}\mathrm{t}\mathrm{f}\mathrm{i}\mathrm{n}\mathrm{i}\mathrm{s}\mathrm{h}\mathrm{t}\mathrm{i}\mathrm{m}\mathrm{e}\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{c}\mathrm{e}\mathrm{s}\mathrm{s}p\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{j}\mathrm{e}\mathrm{c}\mathrm{t}v$
- ${L}_{vp}\mathrm{l}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{s}\mathrm{t}\mathrm{f}\mathrm{i}\mathrm{n}\mathrm{i}\mathrm{s}\mathrm{h}\mathrm{t}\mathrm{i}\mathrm{m}\mathrm{e}\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{c}\mathrm{e}\mathrm{s}\mathrm{s}p\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{j}\mathrm{e}\mathrm{c}\mathrm{t}v$
- ${d}_{vpjm}\mathrm{d}\mathrm{u}\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{o}\mathrm{f}\mathrm{t}\mathrm{a}\mathrm{s}\mathrm{k}\mathrm{s}j\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{c}\mathrm{e}\mathrm{s}\mathrm{s}p\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{j}\mathrm{e}\mathrm{c}\mathrm{t}v,\mathrm{o}\mathrm{p}\mathrm{e}\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{n}\mathrm{g}\mathrm{o}\mathrm{n}\mathrm{m}\mathrm{o}\mathrm{d}\mathrm{e}m$
- ${r}_{vpjgkm}\mathrm{u}\mathrm{s}\mathrm{a}\mathrm{g}\mathrm{e}\mathrm{o}\mathrm{f}\mathrm{t}\mathrm{a}\mathrm{s}\mathrm{k}\mathrm{s}j\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{c}\mathrm{e}\mathrm{s}\mathrm{s}p\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{j}\mathrm{e}\mathrm{c}\mathrm{t}v,$
- $\mathrm{o}\mathrm{p}\mathrm{e}\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{n}\mathrm{g}\mathrm{o}\mathrm{n}\mathrm{m}\mathrm{o}\mathrm{d}\mathrm{e}m\mathrm{from}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{e}\mathrm{w}\mathrm{a}\mathrm{b}\mathrm{l}\mathrm{e}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{o}\mathrm{u}\mathrm{r}\mathrm{c}\mathrm{e}k\mathrm{o}\mathrm{f}\mathrm{g}\mathrm{r}\mathrm{o}\mathrm{u}\mathrm{p}g$
- ${dd}_{v}\mathrm{a}\mathrm{s}\mathrm{s}\mathrm{i}\mathrm{g}\mathrm{n}\mathrm{e}\mathrm{d}\mathrm{d}\mathrm{u}\mathrm{e}\mathrm{d}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{j}\mathrm{e}\mathrm{c}\mathrm{t}v$
- ${ddd}_{vp}\mathrm{d}\mathrm{u}\mathrm{e}\mathrm{d}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{c}\mathrm{e}\mathrm{s}\mathrm{s}p\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{j}\mathrm{e}\mathrm{c}\mathrm{t}v$
- ${c}_{v}\mathrm{r}\mathrm{e}\mathrm{l}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{v}\mathrm{e}\mathrm{w}\mathrm{e}\mathrm{i}\mathrm{g}\mathrm{h}\mathrm{t}\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{j}\mathrm{e}\mathrm{c}\mathrm{t}v$
- ${c}_{vp}\mathrm{r}\mathrm{e}\mathrm{l}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{v}\mathrm{e}\mathrm{w}\mathrm{e}\mathrm{i}\mathrm{g}\mathrm{h}\mathrm{t}\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{c}\mathrm{e}\mathrm{s}\mathrm{s}p\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{j}\mathrm{e}\mathrm{c}\mathrm{t}v$
- ${b}_{gk}\mathrm{u}\mathrm{n}\mathrm{i}\mathrm{t}\mathrm{c}\mathrm{o}\mathrm{s}\mathrm{t}\mathrm{o}\mathrm{f}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{e}\mathrm{w}\mathrm{a}\mathrm{b}\mathrm{l}\mathrm{e}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{o}\mathrm{u}\mathrm{r}\mathrm{c}\mathrm{e}k\mathrm{b}\mathrm{e}\mathrm{l}\mathrm{o}\mathrm{n}\mathrm{g}\mathrm{i}\mathrm{n}\mathrm{g}\mathrm{t}\mathrm{o}\mathrm{g}\mathrm{r}\mathrm{o}\mathrm{u}\mathrm{p}g$
- ${BR}_{gk}\mathrm{n}\mathrm{u}\mathrm{m}\mathrm{b}\mathrm{e}\mathrm{r}\mathrm{o}\mathrm{f}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{e}\mathrm{w}\mathrm{a}\mathrm{b}\mathrm{l}\mathrm{e}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{o}\mathrm{u}\mathrm{r}\mathrm{c}\mathrm{e}\mathrm{s}k\mathrm{i}\mathrm{n}\mathrm{g}\mathrm{r}\mathrm{o}\mathrm{u}\mathrm{p}g\mathrm{p}\mathrm{e}\mathrm{r}\mathrm{p}\mathrm{e}\mathrm{r}\mathrm{i}\mathrm{o}\mathrm{d}t$

#### 5.8.3. Decision Variables

- ${x}_{vpjmt}=\left\{\right)separators="|">\begin{array}{c}1,\mathrm{i}\mathrm{f}\mathrm{t}\mathrm{a}\mathrm{s}\mathrm{k}j\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{c}\mathrm{e}\mathrm{s}\mathrm{s}p\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{j}\mathrm{e}\mathrm{c}\mathrm{t}v\mathrm{o}\mathrm{p}\mathrm{e}\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{n}\mathrm{g}\mathrm{o}\mathrm{n}\mathrm{m}\mathrm{o}\mathrm{d}\mathrm{e}\mathrm{m}\mathrm{i}\mathrm{s}\mathrm{f}\mathrm{i}\mathrm{n}\mathrm{i}\mathrm{s}\mathrm{h}\mathrm{e}\mathrm{d}\mathrm{a}\mathrm{t}\mathrm{p}\mathrm{e}\mathrm{r}\mathrm{i}\mathrm{o}\mathrm{d}t\\ 0,\mathrm{o}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{r}\mathrm{w}\mathrm{i}\mathrm{s}\mathrm{e}\end{array}$
- ${TC}_{v}=\mathrm{W}\mathrm{e}\mathrm{i}\mathrm{g}\mathrm{h}\mathrm{t}\mathrm{e}\mathrm{d}\mathrm{t}\mathrm{a}\mathrm{r}\mathrm{d}\mathrm{i}\mathrm{n}\mathrm{e}\mathrm{s}\mathrm{s}\mathrm{c}\mathrm{o}\mathrm{s}\mathrm{t}\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{j}\mathrm{e}\mathrm{c}\mathrm{t}v$
- ${TC}_{vp}=\mathrm{W}\mathrm{e}\mathrm{i}\mathrm{g}\mathrm{h}\mathrm{t}\mathrm{e}\mathrm{d}\mathrm{t}\mathrm{a}\mathrm{r}\mathrm{d}\mathrm{i}\mathrm{n}\mathrm{e}\mathrm{s}\mathrm{s}\mathrm{c}\mathrm{o}\mathrm{s}\mathrm{t}\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{c}\mathrm{e}\mathrm{s}\mathrm{s}p\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{j}\mathrm{e}\mathrm{c}\mathrm{t}v$
- ${y}_{vw}=\left\{\right)separators="|">\begin{array}{c}1,\mathrm{i}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{j}\mathrm{e}\mathrm{c}\mathrm{t}v\mathrm{i}\mathrm{s}\mathrm{i}\mathrm{n}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{w}\mathrm{o}\mathrm{r}\mathrm{k}\mathrm{g}\mathrm{r}\mathrm{o}\mathrm{u}\mathrm{p}w\\ 0,\mathrm{o}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{r}\mathrm{w}\mathrm{i}\mathrm{s}\mathrm{e}\end{array}$

#### 5.8.4. Mathematical Model

#### 5.9. Resource Planning Model (Scenario IV and V)

#### 5.9.1. Sets and Indices

- $V\mathrm{s}\mathrm{e}\mathrm{t}\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{j}\mathrm{e}\mathrm{c}\mathrm{t}\mathrm{s},v\in V$
- ${P}_{v}\mathrm{s}\mathrm{e}\mathrm{t}\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{c}\mathrm{e}\mathrm{s}\mathrm{s}\mathrm{e}\mathrm{s}\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{j}\mathrm{e}\mathrm{c}\mathrm{t}v,p\in {P}_{v}$
- ${J}_{vp}\mathrm{s}\mathrm{e}\mathrm{t}\mathrm{o}\mathrm{f}\mathrm{t}\mathrm{a}\mathrm{s}\mathrm{k}\mathrm{s}\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{c}\mathrm{e}\mathrm{s}\mathrm{s}p\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{j}\mathrm{e}\mathrm{c}\mathrm{t}v,j\in {J}_{vp}$
- ${p}_{vN}\mathrm{l}\mathrm{a}\mathrm{s}\mathrm{t}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{c}\mathrm{e}\mathrm{s}\mathrm{s}\left(\mathrm{i}\mathrm{n}\mathrm{d}\mathrm{e}\mathrm{x}\mathrm{e}\mathrm{d}\mathrm{w}\mathrm{i}\mathrm{t}\mathrm{h}N\right)\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{j}\mathrm{e}\mathrm{c}\mathrm{t}v$
- ${j}_{vpL}\mathrm{l}\mathrm{a}\mathrm{s}\mathrm{t}\mathrm{t}\mathrm{a}\mathrm{s}\mathrm{k}\left(\mathrm{i}\mathrm{n}\mathrm{d}\mathrm{e}\mathrm{x}\mathrm{e}\mathrm{d}\mathrm{w}\mathrm{i}\mathrm{t}\mathrm{h}L\right)\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{c}\mathrm{e}\mathrm{s}\mathrm{s}p\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{j}\mathrm{e}\mathrm{c}\mathrm{t}v$
- ${j}_{vpF}\mathrm{f}\mathrm{i}\mathrm{r}\mathrm{s}\mathrm{t}\mathrm{t}\mathrm{a}\mathrm{s}\mathrm{k}\left(\mathrm{i}\mathrm{n}\mathrm{d}\mathrm{e}\mathrm{x}\mathrm{e}\mathrm{d}\mathrm{w}\mathrm{i}\mathrm{t}\mathrm{h}F\right)\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{c}\mathrm{e}\mathrm{s}\mathrm{s}p\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{j}\mathrm{e}\mathrm{c}\mathrm{t}v$
- ${S}_{v}\mathrm{s}\mathrm{e}\mathrm{t}\mathrm{o}\mathrm{f}\mathrm{a}\mathrm{l}\mathrm{l}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{c}\mathrm{e}\mathrm{s}\mathrm{s}\mathrm{p}\mathrm{r}\mathrm{e}\mathrm{c}\mathrm{e}\mathrm{d}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{e}\mathrm{r}\mathrm{e}\mathrm{l}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{s}\mathrm{h}\mathrm{i}\mathrm{p}\mathrm{s}\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{j}\mathrm{e}\mathrm{c}\mathrm{t}v$
- ${Q}_{vp}\mathrm{s}\mathrm{e}\mathrm{t}\mathrm{o}\mathrm{f}\mathrm{a}\mathrm{l}\mathrm{l}\mathrm{t}\mathrm{a}\mathrm{s}\mathrm{k}\mathrm{p}\mathrm{r}\mathrm{e}\mathrm{c}\mathrm{e}\mathrm{d}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{e}\mathrm{r}\mathrm{e}\mathrm{l}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{s}\mathrm{h}\mathrm{i}\mathrm{p}\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{c}\mathrm{e}\mathrm{s}\mathrm{s}p\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{j}\mathrm{e}\mathrm{c}\mathrm{t}v$
- ${M}_{vpj}\mathrm{s}\mathrm{e}\mathrm{t}\mathrm{o}\mathrm{f}\mathrm{m}\mathrm{o}\mathrm{d}\mathrm{e}\mathrm{s}\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{t}\mathrm{a}\mathrm{s}\mathrm{k}j\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{c}\mathrm{e}\mathrm{s}\mathrm{s}p\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{j}\mathrm{e}\mathrm{c}\mathrm{t}v$
- $G\mathrm{s}\mathrm{e}\mathrm{t}\mathrm{o}\mathrm{f}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{o}\mathrm{u}\mathrm{r}\mathrm{c}\mathrm{e}\mathrm{g}\mathrm{r}\mathrm{o}\mathrm{u}\mathrm{p}\mathrm{s},g\in G$
- ${K}_{g}\mathrm{s}\mathrm{e}\mathrm{t}\mathrm{o}\mathrm{f}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{e}\mathrm{w}\mathrm{a}\mathrm{l}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{o}\mathrm{u}\mathrm{r}\mathrm{c}\mathrm{e}\mathrm{s}\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{g}\mathrm{r}\mathrm{o}\mathrm{u}\mathrm{p}g,k\in {K}_{g}$
- $T\mathrm{s}\mathrm{e}\mathrm{t}\mathrm{o}\mathrm{f}\mathrm{t}\mathrm{i}\mathrm{m}\mathrm{e}\mathrm{p}\mathrm{e}\mathrm{r}\mathrm{i}\mathrm{o}\mathrm{d}\mathrm{s}\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{j}\mathrm{e}\mathrm{c}\mathrm{t},t\in T$

#### 5.9.2. Parameters

- ${EE}_{vpj}\mathrm{e}\mathrm{a}\mathrm{r}\mathrm{l}\mathrm{i}\mathrm{e}\mathrm{s}\mathrm{t}\mathrm{f}\mathrm{i}\mathrm{n}\mathrm{i}\mathrm{s}\mathrm{h}\mathrm{t}\mathrm{i}\mathrm{m}\mathrm{e}\mathrm{o}\mathrm{f}\mathrm{t}\mathrm{a}\mathrm{s}\mathrm{k}j\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{c}\mathrm{e}\mathrm{s}\mathrm{s}p\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{j}\mathrm{e}\mathrm{c}\mathrm{t}v$
- ${LL}_{vpj}\mathrm{l}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{s}\mathrm{t}\mathrm{f}\mathrm{i}\mathrm{n}\mathrm{i}\mathrm{s}\mathrm{h}\mathrm{t}\mathrm{i}\mathrm{m}\mathrm{e}\mathrm{o}\mathrm{f}\mathrm{t}\mathrm{a}\mathrm{s}\mathrm{k}j\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{c}\mathrm{e}\mathrm{s}\mathrm{s}p\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{j}\mathrm{e}\mathrm{c}\mathrm{t}v$
- ${E}_{vp}\mathrm{e}\mathrm{a}\mathrm{r}\mathrm{l}\mathrm{i}\mathrm{e}\mathrm{s}\mathrm{t}\mathrm{f}\mathrm{i}\mathrm{n}\mathrm{i}\mathrm{s}\mathrm{h}\mathrm{t}\mathrm{i}\mathrm{m}\mathrm{e}\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{c}\mathrm{e}\mathrm{s}\mathrm{s}p\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{j}\mathrm{e}\mathrm{c}\mathrm{t}v$
- ${L}_{vp}\mathrm{l}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{s}\mathrm{t}\mathrm{f}\mathrm{i}\mathrm{n}\mathrm{i}\mathrm{s}\mathrm{h}\mathrm{t}\mathrm{i}\mathrm{m}\mathrm{e}\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{c}\mathrm{e}\mathrm{s}\mathrm{s}p\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{j}\mathrm{e}\mathrm{c}\mathrm{t}v$
- ${d}_{vpjm}\mathrm{d}\mathrm{u}\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{o}\mathrm{f}\mathrm{t}\mathrm{a}\mathrm{s}\mathrm{k}\mathrm{s}j\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{c}\mathrm{e}\mathrm{s}\mathrm{s}p\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{j}\mathrm{e}\mathrm{c}\mathrm{t}v,\mathrm{o}\mathrm{p}\mathrm{e}\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{n}\mathrm{g}\mathrm{o}\mathrm{n}\mathrm{m}\mathrm{o}\mathrm{d}\mathrm{e}m$
- ${r}_{vpjgkm}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{e}\mathrm{w}\mathrm{a}\mathrm{b}\mathrm{l}\mathrm{e}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{o}\mathrm{u}\mathrm{r}\mathrm{c}\mathrm{e}k\mathrm{o}\mathrm{f}\mathrm{g}\mathrm{r}\mathrm{o}\mathrm{u}\mathrm{p}g\mathrm{u}\mathrm{s}\mathrm{a}\mathrm{g}\mathrm{e}\mathrm{o}\mathrm{f}\mathrm{t}\mathrm{a}\mathrm{s}\mathrm{k}j\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{c}\mathrm{e}\mathrm{s}\mathrm{s}p\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{j}\mathrm{e}\mathrm{c}\mathrm{t}v,$
- $\mathrm{o}\mathrm{p}\mathrm{e}\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{n}\mathrm{g}\mathrm{o}\mathrm{n}\mathrm{m}\mathrm{o}\mathrm{d}\mathrm{e}m$
- ${dd}_{v}\mathrm{a}\mathrm{s}\mathrm{s}\mathrm{i}\mathrm{g}\mathrm{n}\mathrm{e}\mathrm{d}\mathrm{d}\mathrm{u}\mathrm{e}\mathrm{d}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{j}\mathrm{e}\mathrm{c}\mathrm{t}v$
- ${ddd}_{vp}\mathrm{d}\mathrm{u}\mathrm{e}\mathrm{d}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{c}\mathrm{e}\mathrm{s}\mathrm{s}p\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{j}\mathrm{e}\mathrm{c}\mathrm{t}v$
- ${c}_{v}\mathrm{r}\mathrm{e}\mathrm{l}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{v}\mathrm{e}\mathrm{w}\mathrm{e}\mathrm{i}\mathrm{g}\mathrm{h}\mathrm{t}\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{j}\mathrm{e}\mathrm{c}\mathrm{t}v$
- ${c}_{vp}\mathrm{r}\mathrm{e}\mathrm{l}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{v}\mathrm{e}\mathrm{w}\mathrm{e}\mathrm{i}\mathrm{g}\mathrm{h}\mathrm{t}\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{c}\mathrm{e}\mathrm{s}\mathrm{s}p\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{j}\mathrm{e}\mathrm{c}\mathrm{t}v$
- ${b}_{gk}\mathrm{u}\mathrm{n}\mathrm{i}\mathrm{t}\mathrm{c}\mathrm{o}\mathrm{s}\mathrm{t}\mathrm{o}\mathrm{f}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{e}\mathrm{w}\mathrm{a}\mathrm{b}\mathrm{l}\mathrm{e}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{o}\mathrm{u}\mathrm{r}\mathrm{c}\mathrm{e}k\mathrm{b}\mathrm{e}\mathrm{l}\mathrm{o}\mathrm{n}\mathrm{g}\mathrm{i}\mathrm{n}\mathrm{g}\mathrm{t}\mathrm{o}\mathrm{g}\mathrm{r}\mathrm{o}\mathrm{u}\mathrm{p}g$

#### 5.9.3. Decision Variables

- ${x}_{vpjmt}=\left\{\right)separators="|">\begin{array}{c}1,\mathrm{i}\mathrm{f}\mathrm{a}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{v}\mathrm{i}\mathrm{t}\mathrm{y}j\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{c}\mathrm{e}\mathrm{s}\mathrm{s}p\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{j}\mathrm{e}\mathrm{c}\mathrm{t}v\mathrm{o}\mathrm{p}\mathrm{e}\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{n}\mathrm{g}\mathrm{o}\mathrm{n}\mathrm{m}\mathrm{o}\mathrm{d}\mathrm{e}\mathrm{m}\mathrm{i}\mathrm{s}\mathrm{f}\mathrm{i}\mathrm{n}\mathrm{i}\mathrm{s}\mathrm{h}\mathrm{e}\mathrm{d}\mathrm{a}\mathrm{t}\mathrm{p}\mathrm{e}\mathrm{r}\mathrm{i}\mathrm{o}\mathrm{d}t\\ 0,\mathrm{o}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{r}\mathrm{w}\mathrm{i}\mathrm{s}\mathrm{e}\end{array}$
- ${TC}_{v}=\mathrm{W}\mathrm{e}\mathrm{i}\mathrm{g}\mathrm{h}\mathrm{t}\mathrm{e}\mathrm{d}\mathrm{t}\mathrm{a}\mathrm{r}\mathrm{d}\mathrm{i}\mathrm{n}\mathrm{e}\mathrm{s}\mathrm{s}\mathrm{c}\mathrm{o}\mathrm{s}\mathrm{t}\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{j}\mathrm{e}\mathrm{c}\mathrm{t}v$
- ${TC}_{vp}=\mathrm{W}\mathrm{e}\mathrm{i}\mathrm{g}\mathrm{h}\mathrm{t}\mathrm{e}\mathrm{d}\mathrm{t}\mathrm{a}\mathrm{r}\mathrm{d}\mathrm{i}\mathrm{n}\mathrm{e}\mathrm{s}\mathrm{s}\mathrm{c}\mathrm{o}\mathrm{s}\mathrm{t}\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{c}\mathrm{e}\mathrm{s}\mathrm{s}p\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{j}\mathrm{e}\mathrm{c}\mathrm{t}v$
- ${BR}_{g}=\mathrm{N}\mathrm{u}\mathrm{m}\mathrm{b}\mathrm{e}\mathrm{r}\mathrm{o}\mathrm{f}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{e}\mathrm{w}\mathrm{a}\mathrm{b}\mathrm{l}\mathrm{e}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{o}\mathrm{u}\mathrm{r}\mathrm{c}\mathrm{e}\mathrm{s}\mathrm{i}\mathrm{n}\mathrm{g}\mathrm{r}\mathrm{o}\mathrm{u}\mathrm{p}g\mathrm{p}\mathrm{e}\mathrm{r}\mathrm{p}\mathrm{e}\mathrm{r}\mathrm{i}\mathrm{o}\mathrm{d}t$

- ${BR}_{vg}=\mathrm{N}\mathrm{u}\mathrm{m}\mathrm{b}\mathrm{e}\mathrm{r}\mathrm{o}\mathrm{f}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{e}\mathrm{w}\mathrm{a}\mathrm{b}\mathrm{l}\mathrm{e}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{o}\mathrm{u}\mathrm{r}\mathrm{c}\mathrm{e}\mathrm{s}\mathrm{i}\mathrm{n}\mathrm{g}\mathrm{r}\mathrm{o}\mathrm{u}\mathrm{p}g\mathrm{p}\mathrm{e}\mathrm{r}\mathrm{p}\mathrm{e}\mathrm{r}\mathrm{i}\mathrm{o}\mathrm{d}t\mathrm{d}\mathrm{e}\mathrm{d}\mathrm{i}\mathrm{c}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{d}\mathrm{t}\mathrm{o}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{j}\mathrm{e}\mathrm{c}\mathrm{t}v$

#### 5.9.4. Mathematical Model

#### 5.10. Resource Planning Model (Scenario VI)

#### 5.10.1. Sets and Indices

- $W\mathrm{s}\mathrm{e}\mathrm{t}\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{j}\mathrm{e}\mathrm{c}\mathrm{t}\mathrm{w}\mathrm{o}\mathrm{r}\mathrm{k}\mathrm{g}\mathrm{r}\mathrm{o}\mathrm{u}\mathrm{p}\mathrm{s},w\in W$
- ${M}_{w}\mathrm{s}\mathrm{e}\mathrm{t}\mathrm{o}\mathrm{f}\mathrm{m}\mathrm{o}\mathrm{d}\mathrm{e}\mathrm{s}\mathrm{i}\mathrm{n}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{j}\mathrm{e}\mathrm{c}\mathrm{t}\mathrm{w}\mathrm{o}\mathrm{r}\mathrm{k}\mathrm{g}\mathrm{r}\mathrm{o}\mathrm{u}\mathrm{p}w$

#### 5.10.2. Parameters

- ${r}_{vpjgkm}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{e}\mathrm{w}\mathrm{a}\mathrm{b}\mathrm{l}\mathrm{e}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{o}\mathrm{u}\mathrm{r}\mathrm{c}\mathrm{e}k\mathrm{o}\mathrm{f}\mathrm{g}\mathrm{r}\mathrm{o}\mathrm{u}\mathrm{p}g\mathrm{u}\mathrm{s}\mathrm{a}\mathrm{g}\mathrm{e}\mathrm{o}\mathrm{f}\mathrm{t}\mathrm{a}\mathrm{s}\mathrm{k}j\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{c}\mathrm{e}\mathrm{s}\mathrm{s}p\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{j}\mathrm{e}\mathrm{c}\mathrm{t}v,$
- $\mathrm{o}\mathrm{p}\mathrm{e}\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{n}\mathrm{g}\mathrm{o}\mathrm{n}\mathrm{m}\mathrm{o}\mathrm{d}\mathrm{e}m$

#### 5.10.3. Decision Variables

- ${x}_{vpjmt}=\left\{\right)separators="|">\begin{array}{c}1,\mathrm{i}\mathrm{f}\mathrm{a}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{v}\mathrm{i}\mathrm{t}\mathrm{y}j\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{c}\mathrm{e}\mathrm{s}\mathrm{s}p\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{j}\mathrm{e}\mathrm{c}\mathrm{t}v\mathrm{o}\mathrm{p}\mathrm{e}\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{n}\mathrm{g}\mathrm{o}\mathrm{n}\mathrm{m}\mathrm{o}\mathrm{d}\mathrm{e}\mathrm{m}\mathrm{i}\mathrm{s}\mathrm{f}\mathrm{i}\mathrm{n}\mathrm{i}\mathrm{s}\mathrm{h}\mathrm{e}\mathrm{d}\mathrm{a}\mathrm{t}\mathrm{p}\mathrm{e}\mathrm{r}\mathrm{i}\mathrm{o}\mathrm{d}t\\ 0,\mathrm{o}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{r}\mathrm{w}\mathrm{i}\mathrm{s}\mathrm{e}\end{array}$
- ${TC}_{vp}=\mathrm{W}\mathrm{e}\mathrm{i}\mathrm{g}\mathrm{h}\mathrm{t}\mathrm{e}\mathrm{d}\mathrm{t}\mathrm{a}\mathrm{r}\mathrm{d}\mathrm{i}\mathrm{n}\mathrm{e}\mathrm{s}\mathrm{s}\mathrm{c}\mathrm{o}\mathrm{s}\mathrm{t}\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{c}\mathrm{e}\mathrm{s}\mathrm{s}\mathrm{p}\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{j}\mathrm{e}\mathrm{c}\mathrm{t}v$
- ${y}_{vw}=\left\{\right)separators="|">\begin{array}{c}1,\mathrm{i}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{j}\mathrm{e}\mathrm{c}\mathrm{t}v\mathrm{i}\mathrm{s}\mathrm{i}\mathrm{n}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{w}\mathrm{o}\mathrm{r}\mathrm{k}\mathrm{g}\mathrm{r}\mathrm{o}\mathrm{u}\mathrm{p}w\\ 0,\mathrm{o}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{r}\mathrm{w}\mathrm{i}\mathrm{s}\mathrm{e}\end{array}$
- ${BR}_{gk}=\mathrm{N}\mathrm{u}\mathrm{m}\mathrm{b}\mathrm{e}\mathrm{r}\mathrm{o}\mathrm{f}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{e}\mathrm{w}\mathrm{a}\mathrm{b}\mathrm{l}\mathrm{e}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{o}\mathrm{u}\mathrm{r}\mathrm{c}\mathrm{e}k\mathrm{o}\mathrm{f}\mathrm{g}\mathrm{r}\mathrm{o}\mathrm{u}\mathrm{p}g\mathrm{p}\mathrm{e}\mathrm{r}\mathrm{p}\mathrm{e}\mathrm{r}\mathrm{i}\mathrm{o}\mathrm{d}t$

#### 5.10.4. Mathematical Model

#### 5.11. A Case Study for Resource and Project Planning

#### 5.11.1. Inter-Scenarios Comparisons

#### 5.11.2. Scenario I vs. IV

#### 5.11.3. Scenario I vs. II

#### 5.11.4. Scenario II vs. V

#### 5.11.5. Scenario II vs. III

#### 5.11.6. Scenario III vs. VI

#### 5.11.7. Scenario IV vs. V

#### 5.11.8. Scenario V vs. VI

#### 5.11.9. Intra-Scenario Comparisons

#### 5.11.10. Scenario I (6 Resources vs. 9 Resources)

#### 5.11.11. Scenario II (6 Resources vs. 30 Resources)

#### 5.11.12. Scenario III (6 Resources vs. 18 Resources)

#### 5.11.13. Scenario IV (10 Projects vs. 20 Projects)

#### 5.11.14. Scenario V (6 Type of Resources vs. 3 Type of Resources)

#### 5.11.15. Scenario VI (2 Work Groups vs. 3 Work Groups)

#### 5.12. Computational Effort

#### 5.13. Cost Analysis

## 6. Discussion and Conclusions

## 7. Future Research

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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Number of Participants | Duration of Study | Purpose | |
---|---|---|---|

Phase 1 | 20 to 100 | Several months | Safety and dosage |

Phase 2 | Several hundreds | Several months to 2 years | Efficacy and side effects |

Phase 3 | 300 to 3000 | 1 to 4 years | Efficacy and monitoring of adverse reactions |

Phase 4 | Several thousands | Not available | Safety and efficacy (post-market safety monitoring) |

CRO Agent | Description |
---|---|

Budget Agent | Ensures costs are and will be under budget. |

Accounting Agent | Keeps track of expenses and costs for each project. |

Supplies Inventory Agent | Ensures that enough supplies with available shelf lives are available at each site before patient visits. |

Procurement Agent | Responsible for contacting other suppliers for procurement processes. |

Patient Management Agent | Updates the patient enrollment list to plan the upcoming supplies production. |

Sample Inventory Agent | Ensures that the data, regarding samples, have been correctly collected. |

Production Agent | Coordinates all the requirements for production. |

Process Management Agent | Assigns and implements the required processes for a clinical trial |

Resource Management Agent | Plans the required resources for every task involved in a clinical trial according to the CRO’s objectives or criteria. |

Shipment Tracking Agent | Coordinates, tracks sample, and supplies shipments according to the requirements. |

Quality Control Agent | Checks the quality of the data associated with the supplies and services that the CRO is providing to be within the quality standards. |

Change Management Agent | Applies the required changes to the data and processes of a clinical trial. Proactively predicts the consequences of the changes and coordinates them with other system components or agents. |

Site Agent | Description |
---|---|

Patient management agent | Responsible for managing the data regarding patients. The data can be patient enrollment logs and progress of each patient (Case Report Form or CRF). |

Sample Inventory Agent | Ensures that the data, regarding samples, have been correctly collected. |

Supplies Inventory Agent | Ensures that enough supplies with available shelf lives are available at each site before patient’s visits. |

Process Management Agent | Assigns and implements the required processes for a clinical trial. |

Courier Company Agent | Description |
---|---|

Shipment Tracking Agent | Tracks shipments and coordinates the pickup and drop off of supplies and sample shipments. Handles delays for temperature dependents biological specimen shipments. |

Process Management Agent | Customizes the specific process for clinical trials shipments according to the requirements, e.g., short delivery time and cold supply chain procedures. |

Laboratory Agent | Description |
---|---|

Sample Inventory Agent | Keeps track of samples received and processed. |

Lab Analysis Agent | Ensures the analysis results for each sample is performed and communicated with the sponsor agent. |

Process Management Agent | Customizes the specific process for clinical trials samples according to the requirements. |

Sponsor Agent | Description |
---|---|

Budget Agent | Ensures costs are and will be under budget. |

Change Management Agent | Applies the required changes to the data and processes of a clinical trial. Proactively predicts the consequences of the changes and coordinates them with other system components and agents. |

Auditing Agent | Audits the specific data points in the documents to ensure procedures meet the quality standards. |

Process Management Agent | Customizes a specific process for clinical trials according to the requirements. |

Other Suppliers Agent | Description |
---|---|

Budget Agent | Ensures costs are and will be under budget. |

Accounting Agent | Keeps track of expenses and costs for each project. |

Supplies Inventory Agent | Ensures that enough supplies with available shelf lives are available at each site before the patient’s visits. |

Patient Management Agent | Updates the patient enrollment list to plan the upcoming supplies production. |

Process Management Agent | Assigns and implements the required processes for a clinical trial. |

Change Management Agent | Applies the required changes to the data and processes of a clinical trial. |

Project Phase | Human Resources |
---|---|

Contract and budget phase | CT and QC |

Study Setup (labels, lab manuals, kits) | PM, OA, and QC |

Study Management (kits management, samples management, change orders) | PM, OA, QC, and CT |

Closing | PM |

Project Phase | Processes | Due Dates |
---|---|---|

Budget (Amendments or change orders) | Budget Estimate Process | Required finish time of the last task in the Budget Process (usually a few due dates due to amendments). |

Study Setup | Label Process | Required finish time of the last task in the Project Setup Process (usually a few due dates due to amendments). |

Study Management | Kit Production Process | Required finish time of the last task in Kit Production process. |

Sample Shipment Process | Required finish time of the last task in Sample Management Process. | |

Closing | Closing Process | Required finish time of the last task in Closing Process. |

Purpose of Model | Planning Clinical Trial Projects | ||
---|---|---|---|

Number of Work Group | None | w | |

Number of Projects | v | ||

Number of Processes | p, where p > v | ||

Source Model | Refs. [66,67] | ||

Resource Configuration | One or more resource groups in each mode | ||

Non-dedicated Resources | Dedicated Resources | Resources in Work Groups | |

Task Planning Model | Fixed ($B{R}_{g}$)–Scenario I | Fixed ($B{R}_{vg}$)–Scenario II | Fixed ($B{R}_{g}$)–Scenario III |

Resource Planning Model | Variable ($B{R}_{g}$)–Scenario IV | Variable ($B{R}_{vg}$)–Scenario V | Variable ($B{R}_{g}$)–Scenario VI |

Project # | Process # | Duration | Arrival Date | Due Date | Early Finish | Late Finish |
---|---|---|---|---|---|---|

1 | 1.1 | 11 | 6 | 19 | 16 | 23 |

1 | 3.1 | 5 | 18 | 24 | 22 | 28 |

1 | 3.2 | 5 | 23 | 29 | 27 | 33 |

2 | 1.1 | 11 | 6 | 19 | 16 | 28 |

2 | 3.1 | 5 | 18 | 24 | 22 | 33 |

3 | 3.1 | 5 | 14 | 20 | 18 | 18 |

3 | 3.2 | 5 | 19 | 25 | 23 | 23 |

3 | 3.3 | 5 | 24 | 30 | 28 | 28 |

3 | 3.4 | 5 | 29 | 35 | 33 | 33 |

4 | 4.1 | 5 | 15 | 21 | 19 | 33 |

5 | 3.1 | 5 | 14 | 20 | 18 | 33 |

6 | 1.1 | 11 | 9 | 23 | 19 | 33 |

7 | 3.1 | 5 | 16 | 22 | 20 | 33 |

8 | 3.1 | 5 | 15 | 21 | 19 | 33 |

9 | 3.1 | 5 | 16 | 22 | 20 | 23 |

10 | 3.1 | 5 | 17 | 23 | 21 | 28 |

10 | 3.2 | 5 | 22 | 28 | 26 | 33 |

Processing Time (Days) | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|

Role | Task 1 | Task 2 | Task 3 | Task 4 | Task 5 | Task 6 | Task 7 | Task 8 | Task 9 | Task 10 |

PM | 2 | 1 | 1 | |||||||

QC | 1 | 1 | 1 | 1 | ||||||

OA | 1 | 1 | 1 | 1 |

Purpose of Model | Planning Clinical Trial Projects (Baseline) | ||
---|---|---|---|

Number of Work Groups (w) | 1 | 2 | |

Number of Projects (v) | 10 | ||

Number of Processes (p) | 17 | ||

Source Model | Refs. [66,67] | ||

Data | Clinical Trials Example | ||

Number of Modes (m) | 1 | 2 | 2 |

Resource Configuration | One or more resource types in each mode | ||

Non-dedicated Resources | Dedicated Resources | Resources in Work Groups | |

Task Planning Model | Scenario I | Scenario II | Scenario III |

Input: 10 Projects 6 Resources BR[PM] = 2, BR[QC] = 2, BR[OA] = 2 | Input: 10 Projects 6 Resources BR[PM1] = 1, BR[PM2] = 1 BR[QC1] = 1, BR[QC2] = 1 BR[OA1] = 1, BR[OA2] = 1 Projects of PM1 = {1,2,3,4,5} Project of PM2 = {6,7,8,9,10} Projects of QC1 = {1,2,3,4,5} Project of QC2 = {6,7,8,9,10} Projects of OA1 = {1,2,3,4,5} Project of OA2 = {6,7,8,9,10} | Input: 10 Projects 6 Resources w1 = {PM1, QC1, OA1}, w2 = {PM2, QC2, OA2} BR[PM1] = 1, BR[QC1] = 1, BR[OA1] = 1 BR[PM2] = 1, BR[QC2] = 1, BR[OA2] = 1 | |

Output: Total Tardiness = 66 days | Output: Total Tardiness = 96 days | Output: Projects of work group 1 = {1,5,6,8,10} Projects of work group 2 = {2,3,4,7,9} Total Tardiness = 68 days | |

Resource Planning Model | Scenario IV | Scenario V | Scenario VI |

Input: 10 Projects | Input: 10 Projects 6 Type of Resources Projects of PM1 = {1,2,3,4,5} Project of PM2 = {6,7,8,9,10} Projects of QC1 = {1,2,3,4,5} Project of QC2 = {6,7,8,9,10} Projects of OA1 = {1,2,3,4,5} Project of OA2 = {6,7,8,9,10} | Input: 10 Projects 2 Work Groups | |

Output: BR[PM] = 2, BR[QC] = 3, BR[OA] = 4 Total Tardiness = 0 | Output: BR[PM1] = 3, BR[PM2] = 2 BR[QC1] = 2, BR[QC2] = 3 BR[OA1] = 3, BR[OA2] = 2 Total Tardiness = 0 | Output: BR[PM1] = 2, BR[QC1] = 4, BR[OA1] = 3 BR[PM2] = 1, BR[QC2] = 2, BR[OA2] = 3 Projects of work group 1 = {2,3,5,6,9,10} Projects of work group 2 = {1,4,7,8} Total Tardiness = 0 |

Scenario I (Baseline) | Scenario I (Second Example) |
---|---|

Input: 10 Projects 6 Resources BR[PM] = 2, BR[QC] = 2, BR[OA] = 2 | Input: 10 Projects 9 Resources BR[PM] = 3, BR[QC] = 3, BR[OA] = 3 |

Output: Total Tardiness = 66 days | Output: Total Tardiness = 8 days |

Scenario II (Baseline) | Scenario II (Second Example) |
---|---|

Input: 10 Projects 6 Resources BR[PM1] = 1, BR[PM2] = 1 BR[QC1] = 1, BR[QC2] = 1 BR[OA1] = 1, BR[OA2] = 1 Projects of PM1 = {1,2,3,4,5} Project of PM2 = {6,7,8,9,10} Projects of QC1 = {1,2,3,4,5} Project of QC2 = {6,7,8,9,10} Projects of OA1 = {1,2,3,4,5} Project of OA2 = {6,7,8,9,10} | Input: 10 Projects 30 Resources BR[v,g] = 1 for every g and v |

Output: Total Tardiness = 96 days | Output: Total Tardiness = 0 |

Scenario III (Baseline) | Scenario III (Second Example) |
---|---|

Input: 10 Projects 6 Resources w1 = {PM1, QC1, OA1}, w2 = {PM2, QC2, OA2} BR[PM1] = 1, BR[QC1] = 1, BR[OA1] = 1 BR[PM2] = 1, BR[QC2] = 1, BR[OA2] = 1 | Input: 10 Projects 18 Resources w1 = {PM1, QC1, OA1}, w2 = {PM2, QC2, OA2}, w3 = {PM3, QC3, OA3} BR[PM1] = 2, BR[QC1] = 2, BR[OA1] = 2 BR[PM2] = 2, BR[QC2] = 2, BR[OA2] = 2 BR[PM3] = 2, BR[QC3] = 2, BR[OA3] = 2 |

Output: Total Tardiness = 68 days Projects of work group 1 = {1,5,6,8,10} Projects of work group 2 = {2,3,4,7,9} | Output: Total Tardiness = 10 days Projects of work group 1 = {1,7,8} Projects of work group 2 = {4,5,6,10} Projects of work group 3 = {2,3,9} |

Scenario IV (Baseline) | Scenario IV (Second Example) |
---|---|

Input: 10 Projects | Input: 20 Projects |

Output: BR[PM] = 2, BR[QC] = 3, BR[OA] = 4 Total Tardiness = 0 | Output: BR[PM] = 3, BR[QC] = 7, BR[OA] = 10 Total Tardiness = 0 |

Scenario V (Baseline) | Scenario V (Second Example) |
---|---|

Input: 10 Projects 6 Type of Resources Projects of PM1 = {1,2,3,4,5} Project of PM2 = {6,7,8,9,10} Projects of QC1 = {1,2,3,4,5} Project of QC2 = {6,7,8,9,10} Projects of OA1 = {1,2,3,4,5} Project of OA2 = {6,7,8,9,10} | Input: 10 Projects 3 Type of Resources (PM,QC,OA) |

Output: BR[PM1] = 3, BR[PM2] = 2 BR[QC1] = 2, BR[QC2] = 3 BR[OA1] = 3, BR[OA2] = 2 Total Tardiness = 0 | Output: BR[v,g] = 1 for every g and v Total Tardiness = 0 |

Scenario VI (Baseline) | Scenario VI (Second Example) |
---|---|

Input: 10 Projects 2 Work Groups | Input: 10 Projects 3 Work Groups |

Output: BR[PM1] = 2, BR[QC1] = 4, BR[OA1] = 3 BR[PM2] = 1, BR[QC2] = 2, BR[OA2] = 3 Projects of work group 1 = {2,3,5,6,9,10} Projects of work group 2 = {1,4,7,8} Total Tardiness = 0 | Output: BR[PM1] = 1, BR[QC1] = 2, BR[OA1] = 1 BR[PM2] = 2, BR[QC2] = 3, BR[OA2] = 3 BR[PM3] = 1, BR[QC3] = 2, BR[OA3] = 2 Projects of work group 1 = {1,7} Projects of work group 2 = {2,3,6,8,10} Projects of work group 3 = {4,5,9} Total Tardiness = 0 |

Scenario | Number of Projects | CPU Time (Seconds) | MIP Gap |
---|---|---|---|

IV | 70 | 0.50 | 0.0001 |

V | 70 | 0.70 | 0.0001 |

VI | 70 | 5.85 | 0.0001 |

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## Share and Cite

**MDPI and ACS Style**

Sadoon, E.; Venkatadri, U.; Ghasemi, A.
A Conceptual Framework for Logistics Management and Project Planning in the Clinical Trials Industry. *Logistics* **2023**, *7*, 88.
https://doi.org/10.3390/logistics7040088

**AMA Style**

Sadoon E, Venkatadri U, Ghasemi A.
A Conceptual Framework for Logistics Management and Project Planning in the Clinical Trials Industry. *Logistics*. 2023; 7(4):88.
https://doi.org/10.3390/logistics7040088

**Chicago/Turabian Style**

Sadoon, Emad, Uday Venkatadri, and Alireza Ghasemi.
2023. "A Conceptual Framework for Logistics Management and Project Planning in the Clinical Trials Industry" *Logistics* 7, no. 4: 88.
https://doi.org/10.3390/logistics7040088