# Efficient Dynamic Cost Scheduling Algorithm for Financial Data Supply Chain

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## Abstract

**:**

## 1. Introduction

- Consider all types of costs related to the batch process which are the servers and software basic leasing cost, rental cost for additional resources needed in case of overload and extra work, penalty cost of failing to execute the batch process as per the Service Level Agreement (SLA), and the opportunity cost representing the cost of idling a resource for any period of time due to inefficient task allocation.
- Develop an iterative dynamic scheduling algorithm (DCSDBP) to optimize the data batch processing considering the different costs, availability of resources, and customer service level agreement (SLA) along with the rest of the batch process factors such as the clients′ priorities, tasks predecessors and time.
- Utilize the created optimization model to address the problem of controlling the availability of resources such as processors and software required to process input batches and balance the usage of current owned resources and the need to rent additional ones while maintaining the lowest possible cost for the whole data batch processing.

## 2. Literature Review

## 3. Data Batch Algorithm

#### 3.1. Dynamic Cost Scheduling Algorithm for Data Batch Processing (DCSDBP)

- The service-providing company lease a fixed number of data processors.
- Reserving processors is not allowed at the beginning or during the batch process scheduling. A processor is immediately acquired once a decision is made to rent it.
- The characteristics of data files that will be processed as batches such as size and priorities are specified at the beginning of the scheduling process.
- Hardware and software costs are incurred for processing data.
- The hardware cost is a fixed amount.
- Software cost will have fixed and variable cost amounts; the variable cost is charged based on usage per unit time.
- Additional processors can be rented anytime during the execution; however, costs will be higher, 1.25 times, than the currently leased processors′ hardware and software fixed cost. Also, a software variable cost is charged per unit time of usage. These assumptions are derived from practices in the field.
- Additional processors are rented only if there is a chance of not meeting the SLA.
- When an additional processor is acquired, it will be accounted for from the time it is acquired until the end of the batch window.
- Whenever an additional processor is rented at any time unit T, the endorsed fixed hardware and software costs will be calculated from the time of renting until the end of the batch process.
- Each leased or additionally rented processor executes a single task at a time.
- Different tasks can be processed in parallel. Parallel processing can occur only if there is no restriction due to priorities and predecessors relations provided in advance.
- A single data file containing multiple tasks can be multi-processed on multiple processors at the same time if it is allowed by the tasks predefined predecessors relations and the hardware and software resources are available.
- The iteration clock time unit is estimated by the time it takes to process the smallest size unit of the data file.
- The total DBP time is a multiple of the iteration unit time. Files are allocated to processors until a predetermined SLA time is reached. A penalty cost is imposed on each delay unit of time if the SLA is exceeded. The total penalty cost is calculated by multiplying the time delay by the penalty cost per unit time.
- At the beginning of each time unit T, files are allocated and resources are captured. However, at the end of the time period T, all resources are freed and ready for the next time period T.

#### 3.1.1. Indices

i,j | Data file. |

k | Leased processor |

r | Rented processor. |

T | Clock discrete time |

#### 3.1.2. Problem Parameters

I | Set of data files. |

$I{\prime}^{T}$ | Subset of the data files that are available for processing at any time T. |

${n}_{i}$ | Required processing time for data file i. |

SLA | Batch process time as agreed on in the SLA. |

K | Set of all leased processors. |

R | Set of rented processors. |

${V}^{T}$ | Number of rented extra processors that can be acquired at any discrete time T. |

${l}_{ij}^{T}$ | Binary parameter equal to 1 if data file j immediately precedes data file i, and 0 otherwise (parameters of precedence/dependency matrix). |

${\alpha}_{i}^{T}$ | Data file weight based on precedence/dependency matrix. |

${\beta}_{i}$ | Data file scheduling priority provided by the client. |

${l}_{ij}^{T}$ | Precedence/dependency matrix at each period T. |

BW | Available batch process window. |

Csf | Leased processor software fixed leasing cost. |

Csv | Variable leasing cost per unit time of a processor software. |

Ch | Leased processor hardware cost. |

Cesf | Fixed rental cost per unit time of additional processor software. |

Cesv | Variable rental cost per unit time of additional processor software. |

Ceh | Rental cost per unit time of additional processor hardware. |

Cp | Penalty cost per unit time for failing to execute the batch process as per the SLA. |

e_{i} | Number of times file i can be multi processed. |

TCp | Delay time total penalty cost. |

T_{H} | Total cost of renting one additional processor at any time unit T. |

${D}^{T}$ | Available files total multiprocessing ei at any time T. |

${T}^{r}$ | Clock discrete time at which extra processor r is rented. |

END | End of batch process. |

TBC | Total batch process cost. |

#### 3.1.3. Problem Variables

P_{k} | Binary variable equal to1 if processor k is available and 0 otherwise. |

W_{r} | Binary variable equal to1 if processor r is available and 0 otherwise. |

${f}_{i}^{T}$ | Binary variable equal to 1 if data file i is available for processing at discrete time T, and 0 otherwise. |

${q}_{i}^{T}$ | Number of times data file i has been processed. It is incremented by one every time data file i being processed. |

${A}^{T}$ | Binary variable equal to 1 if T > SLA, and 0 otherwise. |

U^{T} | $\mathrm{Critical}\mathrm{path}\mathrm{at}\mathrm{time}T\mathrm{for}\mathrm{each}\mathrm{file}i\mathrm{included}\mathrm{in}\mathrm{the}\mathrm{subset}I{\prime}^{T}.$ |

$E{S}_{i}^{T}$ | Early start of file i. |

$L{S}_{i}^{T}$ | Late start of file i. |

${S}_{i}^{T}$ | Slack (the difference between early start and late start) of file i. |

${O}_{i}^{T}$ | $\mathrm{Binary}\mathrm{variable}\mathrm{equal}\mathrm{to}1\mathrm{if}{n}_{i}-{q}_{i}^{T}$ > 0, and 0 otherwise. |

#### 3.1.4. Problem Decision Variables

${X}_{}{}_{iK}^{T}$ | Binary variable equal to 1 if data file i allocated to processor k, and 0 otherwise. |

${Y}_{}{}_{ir}^{T}$ | Binary variable equal to 1 if data file i is allocated to extra processor r, and 0 otherwise. |

- Step 1: Preparatory and Initialization Stage

- The extra processors′ utilization parameter to zero indicating that no extra processor is used at the beginning of the allocation process.
- The data files processing parameters to zero meaning that files are not being processed yet. In addition to that, the time loop is initialized where time is set to zero. At the end of the step, we initialize all data needed to start the iterative algorithm.

_{k}is set to 1.

_{r}is set to 1.

^{T}= 0

^{T}is zero.

- Step 2: Set of Files Available for Processing

- Step 3: Allocation of Files to Processors

_{i}at any time unit T. The second term considers the opportunity cost of not utilizing the leased processors at any time unit T. The third term handles the cost of renting additional processors, weight ${\alpha}_{i}^{T}$ and priority β

_{i}at any time unit T. The fourth term considers the opportunity cost of not utilizing the additionally rented processors at any time T. the last term is concerned with the penalty cost of exceeding the SLA. The ${\beta}_{i}{\alpha}_{i}^{T}$ used in terms 1 and 3 ensures that files with higher priority and weight are scheduled first. BW is the available time during which processing can take place. It is used in Equation (11) to find what the fixed cost of resources per unit time is.

_{i}or the total number of available basic and extra processors (K,V) for any file i at a certain time T.

_{ik}is binary, meaning that file i either be assigned to a leased processor or not.

_{ir}is binary, meaning that a file i either be assigned to an additionally rented processor or not.

- Step 4: Update Utilized Extra Processors

^{T}is found for the files with slack equal to zero (${S}_{i}^{T}$ = 0).

^{T}≥ SLA−T

_{p}= C

_{p}∗ (U

^{T}−(SLA−T))

_{p}= 0

_{p}for all cases of critical path duration against SLA.

^{T}≥ SLA−T

_{H}= (Cesf + Cesh + Cesv) ∗ U

^{T}

_{H}= 0

_{H}in case of a delay.

_{p}is greater than the extra processor renting cost T

_{H}.

- Step 5: Update the Availability of Files

- Step 6: Check Termination Condition

- Step 7: Update Clock

## 4. Illustrative Example

_{i}= 0 which means they won′t be allocated to any processor. The reason of their existence is to start and end the network for critical path calculation purposes.

## 5. Sensitivity Analysis

#### 5.1. Parameters Variation Analysis

#### 5.1.1. Varying Number of Processors Available to Rent

#### 5.1.2. Changing SLA Value

#### 5.1.3. Varying Penalty Cost per Time Unit

#### 5.1.4. Changing the Processor Rental Costs

#### 5.2. Jobs Network Size Analysis

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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File | ${\mathit{e}}_{\mathit{i}}$ | ${\mathit{n}}_{\mathit{i}}$ | ${\mathit{\beta}}_{\mathit{i}}$ | ${\mathit{\alpha}}_{\mathit{i}}^{\mathit{T}=\mathit{0}}$ | ${\mathit{L}}_{\mathit{i}\mathit{j}}$ |
---|---|---|---|---|---|

0 | 0 | 0 | 1 | 1 | 1 |

1 | 3 | 9 | 2 | 6 | 1 |

2 | 1 | 1 | 3 | 5 | 1 |

3 | 2 | 8 | 2 | 5 | 1 |

4 | 3 | 9 | 4 | 4 | 1 |

5 | 1 | 3 | 2 | 4 | 3 |

6 | 1 | 1 | 5 | 4 | 1 |

7 | 1 | 3 | 2 | 3 | 3 |

8 | 1 | 8 | 2 | 3 | 3 |

9 | 2 | 4 | 2 | 3 | 1 |

10 | 2 | 8 | 2 | 3 | 1 |

11 | 1 | 1 | 1 | 4 | 7 |

12 | 6 | 12 | 1 | 4 | 5 |

13 | 3 | 9 | 1 | 4 | 5 |

14 | 1 | 2 | 2 | 2 | 4 |

15 | 1 | 4 | 2 | 2 | 4 |

16 | 0 | 0 | 1 | 1 | 1 |

Leased Processors | Rented Processors | (10) Total Cost/Time Period $ | |||||||
---|---|---|---|---|---|---|---|---|---|

(1) T | (2) No. of P | (3) No. of Acquired P | (4) Allocation Variable cost $ | (5) Oppo. Cost $ | (6) No. of P | (7) No. of Acquired P | (8) Total Allocation Cost $ | (9) Oppo. Cost $ | |

0 | 2 | 2 | 4.00 | 0.00 | 0 | 0 | 0.00 | 0.00 | 4.00 |

1 | 2 | 2 | 4.00 | 0.00 | 1 | 1 | 8.75 | 0.00 | 12.75 |

2 | 2 | 2 | 4.00 | 0.00 | 2 | 2 | 17.50 | 0.00 | 21.50 |

3 | 2 | 2 | 4.00 | 0.00 | 3 | 3 | 26.25 | 0.00 | 30.25 |

4 | 2 | 2 | 4.00 | 0.00 | 4 | 4 | 35.00 | 0.00 | 39.00 |

5 | 2 | 2 | 4.00 | 0.00 | 4 | 4 | 35.00 | 0.00 | 39.00 |

6 | 2 | 2 | 4.00 | 0.00 | 4 | 4 | 35.00 | 0.00 | 39.00 |

7 | 2 | 2 | 4.00 | 0.00 | 4 | 4 | 35.00 | 0.00 | 39.00 |

8 | 2 | 2 | 4.00 | 0.00 | 4 | 4 | 35.00 | 0.00 | 39.00 |

9 | 2 | 2 | 4.00 | 0.00 | 4 | 4 | 35.00 | 0.00 | 39.00 |

10 | 2 | 2 | 4.00 | 0.00 | 4 | 4 | 35.00 | 0.00 | 39.00 |

11 | 2 | 2 | 4.00 | 0.00 | 4 | 3 | 32.50 | 6.25 | 42.75 |

12 | 2 | 2 | 4.00 | 0.00 | 4 | 0 | 25.00 | 25.00 | 54.00 |

13 | 2 | 1 | 2.00 | 5.00 | 4 | 0 | 25.00 | 25.00 | 57.00 |

14 | 2 | 2 | 4.00 | 0.00 | 4 | 4 | 35.00 | 0.00 | 39.00 |

15 | 2 | 2 | 4.00 | 0.00 | 4 | 4 | 35.00 | 0.00 | 39.00 |

16 | 2 | 2 | 4.00 | 0.00 | 4 | 0 | 25.00 | 25.00 | 54.00 |

17 | 2 | 2 | 4.00 | 0.00 | 4 | 0 | 25.00 | 25.00 | 54.00 |

18 | 2 | 1 | 2.00 | 5.00 | 4 | 0 | 25.00 | 25.00 | 57.00 |

19 | 2 | 1 | 2.00 | 5.00 | 4 | 0 | 25.00 | 25.00 | 57.00 |

Total dynamic cost $ for all periods | 795.25 | ||||||||

Penalty cost $ | 400.00 | ||||||||

Leased processors fixed costs $ | 220.00 | ||||||||

Remaining opportunity cost for Leased processors $ | 20.00 | ||||||||

Batch Process Total Cost $ | 1435.25 |

No. of Network Activities | Complexity Index I2 | Run Time (s) |
---|---|---|

15 | 0.2 | 2 |

0.5 | 3 | |

0.8 | 3 | |

25 | 0.2 | 5 |

0.5 | 2 | |

0.8 | 4 | |

50 | 0.2 | 11 |

0.5 | 13 | |

0.8 | 14 | |

100 | 0.2 | 33 |

0.5 | 34 | |

0.8 | 34 |

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## Share and Cite

**MDPI and ACS Style**

Al Sadawi, A.; Shamayleh, A.; Ndiaye, M.
Efficient Dynamic Cost Scheduling Algorithm for Financial Data Supply Chain. *Algorithms* **2021**, *14*, 211.
https://doi.org/10.3390/a14070211

**AMA Style**

Al Sadawi A, Shamayleh A, Ndiaye M.
Efficient Dynamic Cost Scheduling Algorithm for Financial Data Supply Chain. *Algorithms*. 2021; 14(7):211.
https://doi.org/10.3390/a14070211

**Chicago/Turabian Style**

Al Sadawi, Alia, Abdulrahim Shamayleh, and Malick Ndiaye.
2021. "Efficient Dynamic Cost Scheduling Algorithm for Financial Data Supply Chain" *Algorithms* 14, no. 7: 211.
https://doi.org/10.3390/a14070211