# Marketplace Location Decision Making and Tourism Route Planning

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Literature Review

## 3. Problem Description and Mathematical Formulation

#### 3.1. Data Collection

#### 3.2. Mathematical Model

_{ij}= 1 when the trip goes from the tourist attraction i to tourist attraction j, and 0 otherwise; Y

_{fj}= 1 When delivery occurs from farm f to tourist attraction j, and 0 otherwise; ${\mathrm{R}}_{\mathrm{j}}^{1}$ = 1 when the outlet at tourist attraction j is open, and 0 otherwise; and ${\mathrm{R}}_{\mathrm{j}}^{2}$ = 1 when the level of importance of the tourist attraction j is 5 star at the outlet, and 0 otherwise. The parameters are: A = Time spent traveling (min to km), B

_{k}= Earliest allowed arrival time at outlet k (min), C

_{k}= Latest allowed arrival time at outlet k (min), E

_{k}= Time spent visiting at outlet k (min), G = Maximum time spent on each trip(min), H = Maximum number of vehicles (car), U

_{i}= The reward points of each tourist attraction I, W

_{k}= Time of the vehicle to the point of outlet K, M = The capacity of the car in goods transportation to the outlet, S = The tourist attraction was chosen as the location for the product, ${\mathrm{Q}}_{\mathrm{i}}$ = Weight classification points that give attractions, ${\mathrm{D}}_{\mathrm{i}\mathrm{j}}^{1}$ = Distance from tourist attraction i to tourist attraction j (km), and ${\mathrm{D}}_{\mathrm{f}\mathrm{j}}^{2}$ = Distance of tourism product shipment from farm f to tourist attraction j (km).

## 4. Adaptive Large Neighborhood Search Algorithm

#### 4.1. ALNS Algorithm

Algorithm 1: Adaptive Large Neighborhood Search (ALNS) algorithm of tourism route planning. |

1. Construct a feasible solution s; |

2. s*←s; |

3. Initialize weights; |

4. If the stopping criterion is not met, then |

4.1 Select q, r $\in $ R, d $\in $ D according to probabilities p |

4.2 s′ = r(d(s)) |

4.3 If the acceptance criterion is satisfied, then s←s′; |

If s is better than s*, then s*←s′; |

4.4 Adjust weights; |

5. Return s*. |

- (1)
- The feasible solution initially generated is s.
- (2)
- The initial solution s is the best solution s*.
- (3)
- Determine the random probability initial weight for the destruction and reconstruction operator.
- (4)
- Repeat this procedure until stopped:
- 4.1
- Both the number of destruction d and repair r are selected by a random probability with a dependent weight value.
- 4.2
- The destruction d and repair r of current solution s is a creative new solution s′.
- 4.3
- If the current solution s indicates a new solution s′, this conforms to the acceptance condition.
- 4.4
- The weight is adjusted for the new solution when s is better than the last solution s*.

- (5)
- New solution s* is returns to step 3–5 for destruction and proceeds until a new best solution is created and then stops.

Algorithm 2: Feasible solution construction. |

1. L_{t} <- {1, 2, …, n} travel places for construct travel routes |

1.1 Construct route r_{1} |

1.2 S = {r_{1}} |

2. While L is not empty |

2.1 Randomly select travel place c_{t} $\in $ L_{t} |

2.2 Insert travel place c_{t} at r_{k} $\in $ S; r_{k} is the best feasible all route in the solution |

2.3 If there is no feasible solution, then create new route S |

2.4 L_{t} ← L_{t} − {c_{t}} |

3. L_{f} <- {1, 2, …, m} farm places for construct suitable center |

4. While L_{f} is not empty |

4.1 Randomly select farm location c_{f} L_{f} |

4.2 Assign farm c_{f} to its best feasible depot in best route r_{k} S |

4.3 L_{f} ← L_{f} − {c_{f}} |

5. return S |

#### 4.2. Destruction Methods

#### 4.2.1. Random Removal

- Step 1
- The sort of TARR or FRR is selected randomly for sort destroying.
- Step 2
- The number of sort destroying is selected randomly for finding the number of point removals.
- Step 3
- If there is a random number of points, the operation removes the points from the route.

#### 4.2.2. K-Route Removal

- Step 1
- A route is selected randomly from all the routes; the route randomly selected is one or more from route R $\subseteq $ S |R| = K.
- Step 2
- Determine A as an array of destination point R.
- Step 3
- Randomly select the removal method from all route removals.
- Step 4
- The route is selected from Step 1 is destroyed for finding L, where L is solution set to be removed.

#### 4.2.3. Entire Route Removal

- Step 1
- A route is selected randomly from all the routes, where route random selection is one or more than route R $\subseteq $ S |R| ≥ 1.
- Step 2
- Determine if A is an array of destination point R.
- Step 3
- Route was selected for removal from all routes.
- Step 4
- A route is selected from Step 1 is destroyed for finding L, where L is the solution set to be removed.

#### 4.2.4. Worst Removal

Algorithm 3: Worst removal algorithm. |

1. L ← {}; |

2. While |L| < q do |

2.1 Array: A = an array containing all tourism attractions or farms request from s not in L; |

2.2 Sort A such that (i < j) → cost(A[i]) < cost(A[j]); |

2.3 Choose a random number x from the interval(0,1); |

2.4 L ← L $\cup $ {A[x^{p} |A|]}; |

3. remove the requests in L from s; |

4. return L |

- Step 1
- The initiation is a vacant set.
- Step 2
- Find L by repeating this procedure completely for the number of q:
- 2.1
- Array A is a created number of all tourism attractions or farms but set L is untraceable.
- 2.2
- Array A member is sorted by using cost function removal.
- 2.3
- Random x is an interval in the range 0–1.
- 2.4
- A tourism attraction or farm is a selected value in array A, in which an attraction point is random. Then, add a tourism attraction point or farm point to the set of L, where the value p is a random weight. A low value of p corresponds to greater randomness.

- Step 3
- The member completely removes point L from the solution.
- Step 4
- Return L is Step 2, where L is found in the next iteration.

#### 4.2.5. Related Removal

Algorithm 4: Related removal algorithm. |

1. L ← {}; |

2. Random centroids p(lat,lng) |

3. While |L| < q, then |

3.1 Find c_{t} is a nearly centroid tourism attraction point or farm point with Euclidean distance |

3.2 L ← L $\cup $ {c_{t}}; |

3.3 Update centroids p(lat,lng) = centroids(L) = $\frac{{\displaystyle \sum _{\mathrm{i}}^{\left|\mathrm{L}\right|}\mathrm{L}\left[\mathrm{i}\right]}}{\left|\mathrm{L}\right|}\mathrm{lat},\frac{{\displaystyle \sum _{\mathrm{i}}^{\left|\mathrm{L}\right|}\mathrm{L}\left[\mathrm{i}\right]}}{\left|\mathrm{L}\right|}\mathrm{lng}$; |

4. return L |

- Step 1
- A single tourism attraction position or single farm position is selected randomly from all the tourism attractions or farm locations, respectively, which is removed from the solution.
- Step 2
- The generated group set removal is an initial member c
_{t}. - Step 3
- Finding L involves a repeated procedure for the number of q.
- 3.1
- One tourism attraction position or farm position is chosen at random from the set of L.
- 3.2
- Array A is a created member of all solutions but untraceable from set L.
- 3.3
- Array A member is sorted by using the function relation R(c
_{1},c_{2}) from less to more valuable. The defined relationship is a distance between c_{1}and c_{2}plus the opening time of destination c_{1},c_{2}finding from R(c_{1},c_{2}) = α dist(c_{1},c_{2}) + β|tac_{1}− tac_{2}|. - 3.4
- Random x is an interval ranging from 0–1.
- 3.5
- A point of tourism attraction or farm is a selected value in array A, of which the tourism attraction point or farm point is a random value. After that, the tourism attraction point or farm point is added to set L, where the value p is of random weight random, and a low value of p corresponds to greater randomness.

- Step 4
- When the member is completely removed, point L is the solution.
- Step 5
- Return L is Step 2, where L is found in the next iteration.

#### 4.2.6. Cluster Removal

Algorithm 5: Cluster removal algorithm. |

1. Randomly select a tourism attraction or farm c_{t} and remove it from the solution; |

2. L ← {c_{t}}; |

3. while |L| < q then |

3.1 c ← randomly select a travel place in L; |

3.2 Array: A = an array containing all request from s not in L; |

3.3 Sort A such that (i < j) → R(c,A[i]) < R(c,A[j]); |

3.4 Choose a random number x from the interval [0,1); |

3.5 L ← L $\cup $ {A[x^{p} |A|]}; |

4. remove the requests in L from s; |

5. return L |

- Step 1
- The initiation is a vacant set.
- Step 2
- Randomly choose centroids for removal.
- Step 3
- Finding L was repeated for the number of q.
- 3.1
- Find point c
_{t}as a nearly centroid point using the Euclidian distance method. - 3.2
- A point is added in set L.
- 3.3
- The updated centroid is an improvement in the solution route.

- Step 4
- Remove L from solution S.
- Step 5
- Return L is Step 2 that found L in the next iteration.

#### 4.3. Repairing Operation

#### 4.3.1. Greedy Insertion

- Step 1
- Determine S as a solution set member {r
_{1}, r_{2}, ..., r_{k}}. - Step 2
- Repeat each r
_{k}$\in $ S to find the difference in the lowest cost with insertion c into i of r_{k}Δf_{c,k}. - Step 3
- The destination position is inserted into different lowest-cost routes of all routes, as shown in Equation (37):$$\mathrm{c}=\mathrm{m}\mathrm{i}{\mathrm{n}}_{\mathrm{c}\in \mathrm{L}}\Delta {\mathrm{f}}_{\mathrm{c},\mathrm{k}}\text{}$$

#### 4.3.2. Regret-H Insertion

_{c,h}$\in $ {1, 2, …, H} for insertion into the solution as shown in Equation (38):

_{c,h}is the point of insertion for destination point c and is a sequential insertion to h. The destination shows the highest value of sequence H-regret insertion, which is inserted at the position of lowest cost.

#### 4.3.3. Greedy Insertion with New Route Opening

- Step 1
- Total number of routes is determined as the highest number of routes.
- Step 2
- When the number of routes is less than the prescribed route:
- 2.1
- If the creative new route is less expensive than the cost of greedy insertion, the new route is created.
- 2.2
- Vise versa: if the creative new route is not better than the cost of greedy insertion, the greedy insertion is selected for insertion.

- Step 3
- If the new route is over prescribed, the greedy insertion is selected instead of a new route.

#### 4.3.4. Two-Option Route Repairing

#### 4.3.5. Exchange Route Repairing

#### 4.4. Acceptance Criterion

## 5. Results and Discussion

## 6. Conclusions

#### Case Study

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A

Order | Tourism Attraction | Latitude | Longitude | Open-Close Times |
---|---|---|---|---|

0 | Rest | 19.925738 | 99.82364 | 8:00 a.m.–6:00 p.m. |

1 | Wat Rong Khun | 19.824285 | 99.763159 | 7:00 a.m.–6:00 p.m. |

2 | Boonrod farm | 19.852997 | 99.743386 | 6:00 a.m.–8:00 p.m. |

3 | Wat Phra Sing Chiang rai | 19.911672 | 99.830615 | 8.00 a.m.–6:00 p.m. |

4 | Wat Phra Kaew | 19.91171 | 99.827718 | 6:00 a.m.–6:00 p.m. |

5 | Wat Huai Pla Kha | 19.948406 | 99.806396 | 7:00 a.m.–6:00 p.m. |

. . . . | . . . . | . . . . | . . . . | . . . . |

113 | Bak International Port | 20.275078 | 100.40596 | 8.00 a.m.–7:00 p.m. |

114 | Saturday Night Market | 20.25453 | 100.410303 | 4.00 a.m.–9.00 p.m. |

115 | Wat Luang | 20.043683 | 100.379802 | 8.00 a.m.–6:00 p.m. |

Order | Farm | Latitude | Longitude |
---|---|---|---|

1 | Mae Kao Tom | 20.009389 | 99.912778 |

2 | Mae Kon | 19.849194 | 99.732778 |

3 | Ban Du | 19.977111 | 99.831444 |

4 | Rim Kok | 19.985417 | 99.935472 |

5 | San Sai | 19.856694 | 99.815528 |

. . . . | . . . . | . . . . | . . . . |

23 | San Klang | 19.592139 | 99.707333 |

24 | Pa Hung | 19.567889 | 99.702972 |

25 | Wiang Hao | 19.525389 | 99.85355 |

Order | Parameter | Set |
---|---|---|

1 | Attraction number | 1–115 |

2 | Farm number | 1–25 |

3 | Score | 1–10 |

4 | Level | 1–5 |

5 | Opening time | 180–510 min |

6 | Closing time | 1020–1380 min |

7 | Time spent at attraction | 60 min |

**Table A4.**Normality testing of data provided in Table 1.

Normality Testing | Problem Size | |||||
---|---|---|---|---|---|---|

Small | Medium | Large | ||||

Lingo | ALNS | Lingo | ALNS | Lingo | ALNS | |

p-value | 0.119 | 0.119 | 0.419 | 0.388 | 0.430 | 0.100 |

Results | normal | normal | normal | normal | normal | normal |

Cost Per Unit (Bath/km) | Route | Distance (km) | Traveling Cost (Bath) |
---|---|---|---|

2.35 | 1 | 55.60 | 130.66 |

2 | 279.40 | 656.59 | |

3 | 379.80 | 892.53 | |

4 | 171.95 | 404.08 | |

5 | 119.63 | 281.13 | |

6 | 202.79 | 476.55 | |

7 | 209.70 | 492.79 | |

8 | 337.50 | 793.12 | |

9 | 184.40 | 433.34 | |

10 | 234.60 | 551.31 | |

11 | 201.85 | 474.34 | |

12 | 133.40 | 313.49 | |

13 | 27.40 | 64.39 | |

Total | 2538.02 | 5964.34 |

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Study | Topic | Approach | % Gap | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

TTN | GA | DE | TS | NNW | PTA | RA | CSCRA | LP | |||

Wang et al. (2018) | Electric vehicle tour planning | ✔ | 0 | ||||||||

Lim et al. (2018) | Tour recommendation and itinerary planning | ✔ | 2.5–15 | ||||||||

Liao and Zheng (2018) | Tourist trip design problem; TTDP | ✔ | ✔ | 1.98–13.10 | |||||||

Wu et al. (2017) | Tour route planning problem | ✔ | - | ||||||||

Nedjati et al. (2017) | Tour location routing problem | ✔ | - | ||||||||

Kotiloglu et al. (2017) | Multi-period tour | ✔ | 0.04 | ||||||||

Zheng et al. (2017) | Design personalized day tour route | ✔ | ✔ | 3.50–5.85 | |||||||

Xiao et al. (2017) | Tourism route planning | ✔ | - | ||||||||

Gavalas et al. (2014) | Time-dependent team orienteering problem | ✔ | 3.4–14 | ||||||||

Rodríguez et al. (2012) | Development of tool for individual tourists | ✔ | 2.17–4.28 | ||||||||

Zhu et al. (2012) | Tour planning problem | ✔ | 0.12–2.84 |

Problem Size | No. | Parameter | Lingo Program | ALNS | Difference | |||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Result | Result | |||||||||||

i, j | f | Status | Total Distance (km) | Processing Time (h) | Total Distance (km) | Processing Time (h) | Total Distance (km) | Processing Time (h) | Gap in Distance Traveled (%) | Processing Time Gap (%) | ||

Small | S-1 | 10 | 5 | Global Opt | 109.90 | 00:00:01 | 109.90 | 00:00:01 | 0 | 0 | 0.0 | 0.0 |

S-2 | 10 | 5 | Global Opt | 164.40 | 00:00:01 | 164.40 | 00:00:01 | 0 | 0 | 0.0 | 0.0 | |

S-3 | 10 | 5 | Global Opt | 302.60 | 00:00:33 | 302.60 | 00:00:33 | 0 | 0 | 0.0 | 0.0 | |

S-4 | 10 | 5 | Global Opt | 308.73 | 00:00:58 | 308.73 | 00:00:58 | 0 | 0 | 0.0 | 0.0 | |

S-5 | 10 | 5 | Global Opt | 286.60 | 00:00:37 | 286.60 | 00:00:37 | 0 | 0 | 0.0 | 0.0 | |

Average | 234.45 | 00:00:24 | 234.45 | 00:00:24 | 234.45 | 0 | 0.0 | 0.0 | ||||

Medium | M-1 | 40 | 15 | Feasible | 898.65 | 40:59:27 | 901.50 | 00:05:05 | −2.85 | 40:54:22 | −0.32 | 99.88 |

M-2 | 40 | 15 | Feasible | 1157.84 | 60:17:21 | 1161.01 | 00:05:05 | −3.17 | 60:12:16 | −0.27 | 99.92 | |

M-3 | 40 | 15 | Feasible | 997.78 | 41:49:13 | 1002.37 | 00:05:55 | −4.59 | 41:43:46 | −0.46 | 99.88 | |

M-4 | 40 | 15 | Feasible | 1131.47 | 55:56:29 | 1153.50 | 00:05:25 | −22.03 | 55:51:02 | −1.95 | 99.91 | |

M-5 | 40 | 15 | Feasible | 992.78 | 50:49:25 | 1018.52 | 00:05:45 | −25.74 | 50:44:20 | −2.59 | 99.90 | |

Average | 1035.70 | 49:45:24 | 1047.38 | 00:05:25 | −11.68 | 49:40:28 | −1.12 | 99.90 | ||||

Large | L-1 | 80 | 25 | Lower bound | 2058.56 | >120 | 2077.58 | 00:14:48 | −19.02 | 119:51:52 | −0.92 | 99.88 |

L-2 | 80 | 25 | Lower bound | 1938.81 | >120 | 1987.10 | 00:13:46 | −48.29 | 119:50:54 | −2.49 | 99.89 | |

L-3 | 80 | 25 | Lower bound | 2076.52 | >120 | 2099.13 | 00:15:54 | −22.61 | 119:51:46 | −1.09 | 99.87 | |

L-4 | 80 | 25 | Lower bound | 1965.64 | >120 | 1973.07 | 00:14:51 | −7.43 | 119:50:49 | −0.38 | 99.88 | |

L-5 | 80 | 25 | Lower bound | 2087.31 | >120 | 2092.70 | 00:15:43 | −5.39 | 119:50:57 | −0.26 | 99.87 | |

Average | 2025.37 | 120 | 2045.92 | 00:14:54 | −20.55 | 119:50:48 | −1.03 | 99.88 |

**Table 3.**Results of paired t-test from data in Table 1.

Problem Size | p-Value | |
---|---|---|

Total Traveling Distance | Processing Time | |

Small | 1.000 | 1.000 |

Medium | 0.081 | 0.000 * |

Large | 0.055 | 0.000 * |

Problem | Route | Destinations | Outlet Locations | Farms | Distance (km) | Distant Total (km) |
---|---|---|---|---|---|---|

Case study | 1 | 0-7-15-9-21-0 | 9 | 4,1 | 55.60 | 2538.02 |

2 | 0-81-71-72-77-75-74-91-94-80-3-0 | 71 | 11 | 279.40 | ||

3 | 0-8-28-29-83-103-114-115-113-76-73-79-82-0 | 114 | 22,10 | 379.80 | ||

4 | 0-49-50-52-51-48-106-68-66-0 | 106 | 16,14 | 171.95 | ||

5 | 0-1-27-14-18-0 | 1 | 2,6,7,5 | 119.63 | ||

6 | 0-67-102-99-105-111-112-100-109-107-108-101-104-110-70-32-0 | 108 | 13,15 | 202.79 | ||

7 | 0-11-45-42-41-2-23-0 | 41 | 21 | 209.70 | ||

8 | 0-16-44-46-47-43-88-90-87-85-84-86-89-40-0 | 47 | 20,18 | 337.50 | ||

9 | 0-25-26-22-60-61-58-62-59-69-64-20-0 | 20 | 19,3 | 184.40 | ||

10 | 0-19-95-93-96-97-98-92-78-30-4-0 | 92 | 17,9 | 234.60 | ||

11 | 0-10-31-5-37-34-35-36-39-38-33-24-0 | 34 | 25,24,23 | 201.85 | ||

12 | 0-63-65-55-57-54-56-53-0 | 54 | 8 | 133.40 | ||

13 | 0-13-17-12-6-0 | 12 | 12 | 27.40 |

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## Share and Cite

**MDPI and ACS Style**

Sirirak, W.; Pitakaso, R.
Marketplace Location Decision Making and Tourism Route Planning. *Adm. Sci.* **2018**, *8*, 72.
https://doi.org/10.3390/admsci8040072

**AMA Style**

Sirirak W, Pitakaso R.
Marketplace Location Decision Making and Tourism Route Planning. *Administrative Sciences*. 2018; 8(4):72.
https://doi.org/10.3390/admsci8040072

**Chicago/Turabian Style**

Sirirak, Worapot, and Rapeepan Pitakaso.
2018. "Marketplace Location Decision Making and Tourism Route Planning" *Administrative Sciences* 8, no. 4: 72.
https://doi.org/10.3390/admsci8040072