Route Planning of Order Picking System

According to the well order picking routing planning, it can make the minimize order picking distance, reducing order picking time, and improve order picking performance. Hall [12] supposed that did not consider the width of the aisle, as well as evaluate and compare with different order picking strategies. The order picking strategies included Traversal, Midpoint Return, Largest Gap Return, and the best performance is using Largest Gap Return. Petersen and Schmenner [1] had two major policy decisions that determine the efficiency of order picking operations, which are storage policies and routing policies. It also considered Transversal Strategy, Return Strategy, Midpoint Strategy, Largest Gap Strategy, and Composite Strategy; five different kinds of order picking routing strategies, as well as compare with the optimal solution, the Composite Strategy have the best performance. Ho and Su [13] proposed two kind of heuristic algorithms, which are Nearest Center of Rectangular Insertion (NCRI) and Minimum Traveling Loop Insertion (MTLI). He also compared with previous scholar’s method, for example, Largest Gap Strategy, Nearest Center of Geometry Insertion Heuristic, the results shown that the two heuristic algorithms which is proposed by author has the better performance.

Ratliff and Rosenthal [2] discuss the influence of add the cross aisle of order picking routing, the results shown that the order picking routing planning will become more complex in warehouse which has cross aisles.

Roodbergen and Koster [7] focused on estimate variety kinds of order picking strategy to compare different number of aisles, different number of items and different width of aisles. The algorithms to evaluate the shortest path included S-shape Heuristic, Largest Gap Heuristic, Aisle-by-aisle Heuristic, Optimal Algorithm, Combined Heuristic, and Combine⁺ Heuristic. The best performance is Combine⁺ strategy. Hsieh et al. [8]

applying PSO in order picking routing and storage assignment, and compare with previous scholar, it verified that applying PSO has the better performance.

2.2 Particle Swarm Optimization

Kennedy, J. and R. C. Eberhart [6] proposed Particle Swarm Optimization (PSO) in 1995. It is similar to John Holland [10] proposed Genetic Algorithms (GA) in 1960. They are all belonging to Evolutionary computation and within the evolutionary generation to optimal solutions. The main concept of GA is the survival of the fittest which is proposed by Charles Darwin. That is using three basic operations, which is Reproduction, Crossover, and Mutation to imitate natural evolutionary process, and according to the evolutionary generation to optimal solutions. Therefore, PSO has no crossover and mutation, it is easier than GA, but is has better global optimal solution ability.

PSO and Dorigo [10] proposed Ant Colony Optimization (ACO) in 1992 is all Swarm Intelligence algorithms that are according to swarm intelligence to solve problems. ACO is a cooperative heuristic searching algorithm inspired by the methodological study on the behavior of ants. The ants can find out the food is done by an indirect communication known as pheromone, left by the ants on the paths, and constructive to the shortest distance between the nest and food.

PSO is according to three factors to find out the optimal solution, that is (1) the current moving direction by itself, (2) the previous experiment by itself, (3) the swarm experiments, and compare with Fitness Value which is computed by Fitness Function to revise the velocity and position of itself.

The definitions of PSO related variances, Xid^l is the particle i, d dimension, l stage position. Xid^l+1 is the particle i, d dimension, in l+1 stage position. Pid represents the optimum position recorded by the i^th particle in d dimension. Pgd is the optimum position resolved by a population of particles in d dimension.

idl

V is the velocity of the i^th particle, d dimension in l stage. Vid^l+1 is the velocity of the ith particle, d dimension in l+1 stage. rand is random number between [0, 1]. c() 1 and c2 are learning factors which controls the acceleration of particle velocity. w is the inertial constant that allows user to control the parameters. A small w value will direct searches within current space, and a large w value will indicate searches in new space. Appropriate selection of w value, c₁ and c₂ learning factors can expand search space to achieve a balanced result. The velocity and position update formula is shown in Formula (1) and Formula (2).

) X P ( () rand c

) X P ( () rand c V w

V^idl+1 = ⋅ ^idl+ ₁⋅ ⋅ ^id− ^idl + ₂× ⋅ ^gd− ^idl (1)

1 l

l id

1 id

idl X V

X ⁺ = + ⁺ (2)

The original two scholars which is proposed PSO is not using inertia weightw. The inertia weight w is proposed by Shiand and Eberhart [11] in 1998, illustrated inertia weight w using can make the solution process to find out the global best solution faster. The characteristic of inertia weight w is similar to cooling parameter of Simulated Annealing (SA) that can make the solution become convergence. Shi and Eberhart also illustrates w between 0.8 and 1.2, it has more chance to find out the global solution.

3 Model Construction

3.1 Model Constructing

This research probes into the warehouse environment layout is shown in Fig. 1. There are 10 aisles, in each aisle of left hand side and right hand side all have 20 storage locations, so total locations are 400. Suppose the depth of storage is 1m, the width is 1m; the main aisle width is 2.5m, sub-aisle length is 10m, and width is 2.5m. There has front aisle, end aisle, and 1 cross aisle, the width all are 2.5m. The input depot and output depot is the same point in the front of left side. The experiment assumes that order pickers begin the tour at the input depot and end at the output depot. Thus, upon completing the retrieval of the order, the order picker immediately begins retrieval of the next order released. In order to show actual situation, the rectilinear distance is considered for calculation, and give the each locations a number according to the distance between the locations to I/O depot.

Because the well storage strategy can reduce the moving distance between in warehouse and out warehouse, reducing operation time, and full using storage space. Therefore, it adapted classification storage, put the high frequency produce near the I/O depot, and put the low frequency product far away I/O depot in this paper. It can reducing the order picking distance, and improves the order picking efficiency. The access frequency is adapted 80/20 method, the meaning is 20% products is own order picking activity 80%. For this reason, we put these 20% products near the I/O depot.

The part of order batching is adapted the single order method. This method is the general method in industry. The advantage of this method is can reduce the complex of order picking, this is different order batching which has more consuming time to separate the combine order products.

3.2 Route Planning of Order Picking System

The main discussion of this paper is focus on order picking routing planning. First, we introduced PSO, and the two order picking method in literatures (Nearest Center of Rectangular Insertion; NCRI and Minimum Traveling Loop Insertion; MTLI). Then we introduced Maximum Loop Insertion which is proposed in this paper. We try to use the planning result computed by the algorithm in this paper to PSO, and expect PSO can find the better planning solution. Take the one order for example, which is shown in Fig. 1, the order should pick of location 23, 121, 36, 66, 114, and 368. The order picking sequence is a, b, c, d, e, and f in Fig. 1.

117 118 157 158 195 196 233 234 273 274 317 318 349 350 371 372 389 390 399 400

107 108 147 148 185 186 225 226 265 266 307 308 341 342 365 366 385 386 397 398

99 100 139 140 177 178 217 218 257 258 299 300 335 336 361 362 381 382 395 396

91 92 131 132 169 170 209 210 249 250 291 292 329 330 357 358 377 378 393 394

81 82 121 122 159 160 199 200 239 240 281 282 321 322 351 352 373 374 391 392

73 74 111 112 149 150 189 190 229 230 271 272 311 312 343 344 367 368 387 388

67 68 103 104 141 142 181 182 221 222 263 264 303 304 337 338 363 364 383 384

61 62 95 96 133 134 173 174 213 214 255 256 295 296 331 332 359 360 379 380

55 56 87 88 125 126 165 166 203 204 247 248 287 288 325 326 355 356 375 376

47 48 77 78 115 116 155 156 193 194 237 238 277 278 315 316 347 348 369 370

31 32 53 54 85 86 123 124 163 164 207 208 245 246 285 286 323 324 353 354

25 26 45 46 75 76 113 114 153 154 197 198 235 236 275 276 313 314 345 346

21 22 41 42 69 70 105 106 145 146 187 188 227 228 267 268 305 306 339 340

17 18 37 38 63 64 97 98 137 138 179 180 219 220 259 260 297 298 333 334

13 14 33 34 57 58 89 90 129 130 171 172 211 212 251 252 289 290 327 328

9 10 27 28 49 50 79 80 119 120 161 162 201 202 241 242 279 280 319 320

7 8 23 24 43 44 71 72 109 110 151 152 191 192 231 232 269 270 309 310

5 6 19 20 39 40 65 66 101 102 143 144 183 184 223 224 261 262 301 302

3 4 15 16 35 36 59 60 93 94 135 136 175 176 215 216 253 254 293 294

1 2 11 12 29 30 51 52 83 84 127 128 167 168 205 206 243 244 283 284

Aisle 1 Aisle 10

I/O

Front Aisle Black Aisle

Cross Aisle

(a)

36

a

b CoR

23

117 118 157 158 195 196 233 234 273 274 317 318 349 350 371 372 389 390 399 400

107 108 147 148 185 186 225 226 265 266 307 308 341 342 365 366 385 386 397 398

99 100 139 140 177 178 217 218 257 258 299 300 335 336 361 362 381 382 395 396

91 92 131 132 169 170 209 210 249 250 291 292 329 330 357 358 377 378 393 394

81 82 121 122 159 160 199 200 239 240 281 282 321 322 351 352 373 374 391 392

73 74 111 112 149 150 189 190 229 230 271 272 311 312 343 344 367 368 387 388

67 68 103 104 141 142 181 182 221 222 263 264 303 304 337 338 363 364 383 384

61 62 95 96 133 134 173 174 213 214 255 256 295 296 331 332 359 360 379 380

55 56 87 88 125 126 165 166 203 204 247 248 287 288 325 326 355 356 375 376

47 48 77 78 115 116 155 156 193 194 237 238 277 278 315 316 347 348 369 370

31 32 53 54 85 86 123 124 163 164 207 208 245 246 285 286 323 324 353 354

25 26 45 46 75 76 113 114 153 154 197 198 235 236 275 276 313 314 345 346

21 22 41 42 69 70 105 106 145 146 187 188 227 228 267 268 305 306 339 340

17 18 37 38 63 64 97 98 137 138 179 180 219 220 259 260 297 298 333 334

13 14 33 34 57 58 89 90 129 130 171 172 211 212 251 252 289 290 327 328

9 10 27 28 49 50 79 80 119 120 161 162 201 202 241 242 279 280 319 320

7 8 23 24 43 44 71 72 109 110 151 152 191 192 231 232 269 270 309 310

5 6 19 20 39 40 65 66 101 102 143 144 183 184 223 224 261 262 301 302

3 4 15 16 35 36 59 60 93 94 135 136 175 176 215 216 253 254 293 294

1 2 11 12 29 30 51 52 83 84 127 128 167 168 205 206 243 244 283 284

I/O

c d e

f

(b)

End AreaFront Area

Figure 1: NCRI Order Picking Routing

3.2.1 Nearest Center of Rectangular Insertion (NCRI)

In this sub-section, we will introduce the Nearest Center of Rectangular Insertion (NCRI) which is proposed by Ho and Su [13]. It supposed the pickers walked in the middle of the aisle, the pickers can pick the two sides products in the same time. Consequently, the two sides locations can considered the same point, and supposed the I/O point is (0,0), and (xj, yj) is means mi products in the order of each item j’s location, such as

∀j =1,2,..., mi.

First, we are choosing the nearest two order picking points from I/O, such as the point a, b, in Fig. 1 (a).

These two points and I/O depot of the practice traveling path is surrounded to rectangular circle. All have picked order picking points will form to the Loop Set (LS). According to the Formula (3), and compute the all picking points’ location in LS, which form to Center of Rectangular (CoR).

{ } { } { } { }_⎟

⎠

⎜ ⎞

⎝

⎛ ∈ + ∈ ∈ + ∈

= 2

LS n

; y min LS n

; y ,max 2

LS n

; x min LS n

; x

CoR max ^{n n n n} (3)

Calculation the distance between all other order picking points j to CoR, which is calculated by Formula (4).

We find the nearest distance order picking point k, and insert it into the LS, shown in Formula (5). If there are more than two orders picking points are all the same nearest distance of CoR, then choosing whichever one to insert.

LS j

; y y x x

d_CoR,j = _j− _CoR + _j− _CoR ∀∉ (4)

{

^{d ;j LS}

}

min

d_CoR,k = _CoR,j ∉ (5)

The pickers from order picking point u' to order picking u", the practical traveling distances is TDu'u''. If the

order picking point u' and u" are both in cross aisle’s front area or end area, the computation formula is shown in Formula (6). The W is sub-aisle’s length, if in different areas, then using the Formula (7).

( )

⎪⎩

⎪⎨

⎧

=

−

≠

−

− +

+

= −

x x if

; y y

x x if

; y y W 2 , y y min x TD x

"

u ' u

"

u ' u

"

u ' u

"

u ' u

"

u ' u

"

u ' u u u^'"

(6)

⎪⎩

⎪⎨

⎧

=

−

≠

− +

= −

x x if

; y y

x x if

; y y x TD x

"

u ' u

"

u ' u

"

u ' u

"

u ' u

"

u ' u u

u^'" (7)

Find out the edge u'u'' of loop L, insert the point k, and the practical distance increasing at least (TDu'k + TDku'' − TDu'u''), then repeat the previous step and compute. Insert the other order picking point to insert to the loop, until included all order picking point of order i, which is shown in Fig. 1 (b). Then, we will get the order picking sequence of I/O, 23, 121, 114, 66, 36, 368, and I/O. Finally, compute the order picking distance of order i. (Formula (8))

∑

∈

= u,'u" mi u'u"

i TD

D (8)

3.2.2 Minimum Traveling Loop Insertion (MTLI)

In this sub-section, we illustrate the Ho and Su [13] proposed the Minimum Traveling Loop Insertion (MTLI).

First, find out the order picking point nearest the I/O point, shown in Fig. 2 (a), point a. The particle traveling path of this point and I/O depot form Traveling Loop. Then find out the other order picking points which point insert to loop L will add the shortest distance. By Formula (4) or Formula (5), find each order picking point j to insert into the edge of the loop L will add the shortest traveling distance (TDu'j + TDju'' − TDu'u''). Hence, it can from all order picking points j, to find a point k to add the shortest distance. Then, using the same method, repeat, and find the next order picking point, until included all order picking points in order i, shown in Fig. 2 (b), and obtained the order sequence I/O, 121, 368, 114, 66, 36, 23, and I/O. Finally, compute the order picking distance of order i.

Figure 2: MTLI Order Picking Routing

3.2.3 Particle Swarm Optimization

Particle Swarm Optimization is an optimal tool of evolutionary generation, and is Swarm Intelligence algorithm. It found the each particle by self optimal memory solution, and swarm optimal solution. Then update the velocity and position until all particles find out the global optimal solution.

3.2.3.1 PSO Parameter Setting

According to result of Hsieh et al. [9], the parameters setting is as following:

Number of Particles: The Particle setting is 30. Maximum Velocity: Because the storage locations added to 400, so in this paper, we raises the velocity Vid^l is between (-80, 80), then the maximum velocity is at 160.

Learning Factor: Learning factors of c1 and c2 usually have a value of 2. Inertia Weight: PSO with an inertia weight is set 0.8. Stop Condition: The maximum number of iterations is 200 or all particles converge in the same point.

3.2.3.2 PSO Fitting Function

The function of the PSO fitting equation is evaluate the particle obtain the optimal solution or not. Therefore, it set up different function based on different problem. In this paper, the main objective is minimizing total order picking distances.

3.2.3.3 PSO Algorithm Process

The PSO algorithm process is shown in Fig. 3

117 118 157 158 195 196 233 234 273 274 317 318 349 350 371 372 389 390 399 400

107 108 147 148 185 186 225 226 265 266 307 308 341 342 365 366 385 386 397 398

99 100 139 140 177 178 217 218 257 258 299 300 335 336 361 362 381 382 395 396

91 92 131 132 169 170 209 210 249 250 291 292 329 330 357 358 377 378 393 394

81 82 121 122 159 160 199 200 239 240 281 282 321 322 351 352 373 374 391 392

73 74 111 112 149 150 189 190 229 230 271 272 311 312 343 344 367 368 387 388

67 68 103 104 141 142 181 182 221 222 263 264 303 304 337 338 363 364 383 384

61 62 95 96 133 134 173 174 213 214 255 256 295 296 331 332 359 360 379 380

55 56 87 88 125 126 165 166 203 204 247 248 287 288 325 326 355 356 375 376

47 48 77 78 115 116 155 156 193 194 237 238 277 278 315 316 347 348 369 370

31 32 53 54 85 86 123 124 163 164 207 208 245 246 285 286 323 324 353 354

25 26 45 46 75 76 113 114 153 154 197 198 235 236 275 276 313 314 345 346

21 22 41 42 69 70 105 106 145 146 187 188 227 228 267 268 305 306 339 340

17 18 37 38 63 64 97 98 137 138 179 180 219 220 259 260 297 298 333 334

13 14 33 34 57 58 89 90 129 130 171 172 211 212 251 252 289 290 327 328

9 10 27 28 49 50 79 80 119 120 161 162 201 202 241 242 279 280 319 320

7 8 23 24 43 44 71 72 109 110 151 152 191 192 231 232 269 270 309 310

5 6 19 20 39 40 65 66 101 102 143 144 183 184 223 224 261 262 301 302

3 4 15 16 35 36 59 60 93 94 135 136 175 176 215 216 253 254 293 294

1 2 11 12 29 30 51 52 83 84 127 128 167 168 205 206 243 244 283 284

I/O

a

(a) (b)

117 118 157 158 195 196 233 234 273 274 317 318 349 350 371 372 389 390 399 400

107 108 147 148 185 186 225 226 265 266 307 308 341 342 365 366 385 386 397 398

99 100 139 140 177 178 217 218 257 258 299 300 335 336 361 362 381 382 395 396

91 92 131 132 169 170 209 210 249 250 291 292 329 330 357 358 377 378 393 394

81 82 121 122 159 160 199 200 239 240 281 282 321 322 351 352 373 374 391 392

73 74 111 112 149 150 189 190 229 230 271 272 311 312 343 344 367 368 387 388

67 68 103 104 141 142 181 182 221 222 263 264 303 304 337 338 363 364 383 384

61 62 95 96 133 134 173 174 213 214 255 256 295 296 331 332 359 360 379 380

55 56 87 88 125 126 165 166 203 204 247 248 287 288 325 326 355 356 375 376

47 48 77 78 115 116 155 156 193 194 237 238 277 278 315 316 347 348 369 370

31 32 53 54 85 86 123 124 163 164 207 208 245 246 285 286 323 324 353 354

25 26 45 46 75 76 113 114 153 154 197 198 235 236 275 276 313 314 345 346

21 22 41 42 69 70 105 106 145 146 187 188 227 228 267 268 305 306 339 340

17 18 37 38 63 64 97 98 137 138 179 180 219 220 259 260 297 298 333 334

13 14 33 34 57 58 89 90 129 130 171 172 211 212 251 252 289 290 327 328

9 10 27 28 49 50 79 80 119 120 161 162 201 202 241 242 279 280 319 320

7 8 23 24 43 44 71 72 109 110 151 152 191 192 231 232 269 270 309 310

5 6 19 20 39 40 65 66 101 102 143 144 183 184 223 224 261 262 301 302

3 4 15 16 35 36 59 60 93 94 135 136 175 176 215 216 253 254 293 294

1 2 11 12 29 30 51 52 83 84 127 128 167 168 205 206 243 244 283 284

I/O

b c d e

f

Figure 3: Flow Chart of Pso

3.2.4 Maximum Loop Insertion (MLI)

According to previous scholars, who proposed the order picking method, almost using the shortest distance to construct order picking routing. Hence, in this paper, we proposed the Maximum Loop Insertion (MLI), that makes solution has whole concept of all order picking points, and improve the solution performance of algorithms.

This algorithm first focus on the all order picking points, and find out the three order picking points to form a maximum loop. The first order picking point can search all aisles having order picking points. Then, find out the nearest aisle from I/O depot, and find the nearest order picking point from I/O in that aisle, in Fig. 4 (a), point a. The second order picking point, find the farthest order picking point from I/O point on Y axis. If there are order picking points with the same distance, then choosing the nearest order picking point from I/O depot, in Fig. 4 (a), point b. The third order picking point, finding all aisles which has order picking points, and find the farthest aisle from I/O depot. Then, find the nearest order picking point from I/O in that aisle, shown in Fig.

4 (a), point c. After got these three points, it need to check the points, if any one repeats, then delete the repeat point, then according to the remnant points and I/O point, using the shortest path to construct the maximum loop path.

Although, it called Maximum Loop path, but when finished order picking routing planning, the traveling distance of this path is the must traveling distance picking the outside boundary locations. So, it must has the whole conception of must order picking locations. Then, find the others of each order picking point j, insert into any edge of the maximum loop, that make additional distance (TDu'j + TDju'' − TDu'u'') shortest. Then,

using the same method to repeat, and find the next order picking point, until included all order picking points of order i, shown in Fig. 4 (b). Then, obtained the order picking sequence, I/O, 23, 121, 368, 114, 66, 36, and I/O. Finally, calculated the order picking distance of order i, it can avoid when construct the path, according to the shortest distance, then fall in local solution.

Figure 4: MLI Order Picking Routing

The MLI algorithm process is as following:

Step 1: First, find the nearest aisle which has order picking points from I/O depot. Then, find out the nearest order picking point from I/O in that aisle, shown in Fig. 4 (a), point a.

Step 2: Find the farthest depth order picking point from I/O depot. If there are the same depth of order picking points, then choosing the nearest order picking point from I/O, shown Fig. 4 (a), point b.

Step 3: Find the farthest aisle from I/O depot, and then find the nearest order picking point from I/O depot, shown in Fig. 4 (a), point c.

Step 4: Check the previous three steps, and find is it repeated or not. If there is repeat one, then delete the repeat point, then using remnant points and I/O depot, and construct the maximum loop traveling routing with the shortest traveling distance.

Step 5: According to the shortest insert distance, then from the non choosing points to find the insert order picking point k which add the shortest distance.

Step 6: Insert this order picking point k in the loop, it formed to a new loop. If there are the same shortest distance points, then choosing by random.

Step 7: Check the constructed loop included all order picking points or not. If already included all order picking points, then dropped to step 8, if not then go back to step 5.

Step 8: Compute the traveling distance of the constructed loop, then finished the order picking routing planning.

(a)

117 118 157 158 195 196 233 234 273 274 317 318 349 350 371 372 389 390 399 400

107 108 147 148 185 186 225 226 265 266 307 308 341 342 365 366 385 386 397 398

99 100 139 140 177 178 217 218 257 258 299 300 335 336 361 362 381 382 395 396

91 92 131 132 169 170 209 210 249 250 291 292 329 330 357 358 377 378 393 394

81 82 121 122 159 160 199 200 239 240 281 282 321 322 351 352 373 374 391 392

73 74 111 112 149 150 189 190 229 230 271 272 311 312 343 344 367 368 387 388

67 68 103 104 141 142 181 182 221 222 263 264 303 304 337 338 363 364 383 384

61 62 95 96 133 134 173 174 213 214 255 256 295 296 331 332 359 360 379 380

55 56 87 88 125 126 165 166 203 204 247 248 287 288 325 326 355 356 375 376

47 48 77 78 115 116 155 156 193 194 237 238 277 278 315 316 347 348 369 370

31 32 53 54 85 86 123 124 163 164 207 208 245 246 285 286 323 324 353 354

25 26 45 46 75 76 113 114 153 154 197 198 235 236 275 276 313 314 345 346

21 22 41 42 69 70 105 106 145 146 187 188 227 228 267 268 305 306 339 340

17 18 37 38 63 64 97 98 137 138 179 180 219 220 259 260 297 298 333 334

13 14 33 34 57 58 89 90 129 130 171 172 211 212 251 252 289 290 327 328

9 10 27 28 49 50 79 80 119 120 161 162 201 202 241 242 279 280 319 320

7 8 23 24 43 44 71 72 109 110 151 152 191 192 231 232 269 270 309 310

5 6 19 20 39 40 65 66 101 102 143 144 183 184 223 224 261 262 301 302

3 4 15 16 35 36 59 60 93 94 135 136 175 176 215 216 253 254 293 294

1 2 11 12 29 30 51 52 83 84 127 128 167 168 205 206 243 244 283 284

I/O

a b

c

(b)

117 118 157 158 195 196 233 234 273 274 317 318 349 350 371 372 389 390 399 400

107 108 147 148 185 186 225 226 265 266 307 308 341 342 365 366 385 386 397 398

99 100 139 140 177 178 217 218 257 258 299 300 335 336 361 362 381 382 395 396

91 92 131 132 169 170 209 210 249 250 291 292 329 330 357 358 377 378 393 394

81 82 121 122 159 160 199 200 239 240 281 282 321 322 351 352 373 374 391 392

73 74 111 112 149 150 189 190 229 230 271 272 311 312 343 344 367 368 387 388

67 68 103 104 141 142 181 182 221 222 263 264 303 304 337 338 363 364 383 384

61 62 95 96 133 134 173 174 213 214 255 256 295 296 331 332 359 360 379 380

55 56 87 88 125 126 165 166 203 204 247 248 287 288 325 326 355 356 375 376

47 48 77 78 115 116 155 156 193 194 237 238 277 278 315 316 347 348 369 370

31 32 53 54 85 86 123 124 163 164 207 208 245 246 285 286 323 324 353 354

25 26 45 46 75 76 113 114 153 154 197 198 235 236 275 276 313 314 345 346

21 22 41 42 69 70 105 106 145 146 187 188 227 228 267 268 305 306 339 340

17 18 37 38 63 64 97 98 137 138 179 180 219 220 259 260 297 298 333 334

13 14 33 34 57 58 89 90 129 130 171 172 211 212 251 252 289 290 327 328

9 10 27 28 49 50 79 80 119 120 161 162 201 202 241 242 279 280 319 320

7 8 23 24 43 44 71 72 109 110 151 152 191 192 231 232 269 270 309 310

5 6 19 20 39 40 65 66 101 102 143 144 183 184 223 224 261 262 301 302

3 4 15 16 35 36 59 60 93 94 135 136 175 176 215 216 253 254 293 294

1 2 11 12 29 30 51 52 83 84 127 128 167 168 205 206 243 244 283 284

I/O

d f

e

4 Simulation Analysis

According to the 3.1 sub-section warehouse layout, we use eM-plant 7.0 to construct the order picking environment system in distribution center in this paper. We repeat the simulations 30 times, and generate the 100 orders by computer randomly. It compared with NCRI, MTLI, MLI, PSO and MLI combined PSO, considered the difference between the performances of each order picking method. The MLI combine PSO, means using MLI solution to be the initial solution of PSO. The analysis by SPSS 10.0, and expect the shortest average total order picking distance (unit: m), and the shortest CPU run time (unit: s).

From the average total order picking distance, we use 95% confidence level to do the variances analysis, shown in Table 1. The P value is less than 0.05, so the different order picking method has significance difference in average order picking distance. Therefore, using Duncan Test, it will cluster each order picking method, which shown in Table 2. It clusters the four group of order picking method, it found MLI combine with PSO, and MLI all fall in the first group, has the best performance. It verified that we proposed MLI in this paper is better than the literature algorithms (MTLI, NCRI) and PSO, all that has significance difference.

If using the MLI initial solution to PSO, can make PSO to find the better order picking routing, and improve the PSO solution performance.

Table 1: Variances Analysis of Average Total Order Picking Distance

Table 2: Duncan Test of Average Total Order Picking Distance

Duncan Group Order Picking

Method

Numbers

1 2 3 4 MLI Combine

with PSO 30 14275.62

MLI 30 14335.65 MTLI 30 14696.25 NCRI 30 14970.45

PSO 30 16239.18 Significance 0.536 1.000 1.000 1.000

From the average total CPU run time, we use 95% confidence level to do variance analysis, shown in Table

Order Picking

Method Numbers Average

Standard

deviation F Test P Value NCRI 30 14970.45 369.1524 135.1036 0.000 MTLI 30 14696.25 335.0943

MLI 30 14335.65 310.091 PSO 30 16239.18 518.9535

3. We can see from P value less than 0.05, different order picking method has significance difference to the average total CPU run time. Therefore, using Duncan Test, it cluster all order picking methods, shown in Table 4, it clustered the order picking method by three groups, that NCRI, MTLI and MLI all has the best performance, and fall in the same group. It all in 1 second finished 100 orders of order picking routing. We can see form Table 4, it also can found that PSO is the worst performance of average total CPU run time, but if using MLI initial solution to PSO, it can reducing CPU run time efficiency, it can improve the solution efficiency.

Table 3: Variance Analysis of Average Total CPU Run Time

Order Picking

Method Numbers Average

Standard

deviation F Test P Value NCRI 30 0.619 0.038 3544.853 0.000 MTLI 30 1.561 0.126

MLI 30 1.954 0.170 PSO 30 188.215 15.820 MLI Combine

with PSO 30 150.591 10.750

Table 4: Duncan Test of Average Total CPU Run Time

Duncan Group Order Picking

Method

Numbers

1 2 3

NCRI 30 0.619

MTLI 30 1.561

MLI 30 1.954

MLI Combine with

PSO 30 150.591

PSO 30 188.215

Significance .573 1.000 1.000

5 Conclusions

The main purpose of this paper is discussing the improvement of order picking operations in distribution center. It expects according to order picking method to improve order picking routing planning, and improves the order picking performance in distribution center. Therefore, it discusses all kinds of order picking methods influence the order picking performance. And this research verified the performance of MLI. It is significance reducing order picking distance, and using the solution to be an initial solution of PSO, and find the better

order picking routing. The contributions in this paper are generation as following:

The MLI which is proposed in this paper exactly has the significance improve of order picking performance.

The average total order picking distance is significance better than the better performance algorithms in literatures (NCRI and MTLI). In the meantime, the algorithm MLI has the better performance in the average total CPU run time, and the same as NCRI, and MTLI.

In this study, we try to combine MLI and PSO by putting the solution of MLI as the initial solution of PSO, and verified if it is a better solution to do the initial solution of PSO, then can find the better solution by PSO.

It also can improve the PSO solution efficiency, avoid the blindly searching solution, and has the better solution of average total order picking distance, reducing solution time, and CPU run time. It makes the PSO more suitable in practice.

In a practical sense, this paper adapted 80/20 method to deal with products locations, using classification storage, and adding cross aisles between storage spaces. The method which proposed in this paper, also verified can improve the overall efficiency of the distribution center and it can be a good reference for distribution industries to consult.

ACKNOWLEDGEMENT

The author would like to thank The National Science Council, Republic of China, for financially supporting this research under the grant number of NSC-96-2221-E-216-002-.

References

[1] C. G. Petersen II, R. W. Schmenner, “An Evaluation of Routing and Volume-based Storage Policies in an Order Picking Operation,” Decision Sciences, Vol. 30, No. 2, pp. 481-501, 1999.

[2] H. D. Ratliff, A. S. Rosenthal, “Order-picking in a rectangular warehouse: a solvable case of the traveling salesman problem,” Operations Research, Vol. 31, pp. 507-521, 1983.

[3] J. A. Tompkins, J. A. White, Y. A. Bozer, E. H. Frazelle, J. M. A. Tanchoco, J. Trevino, “Facilities Planning,” Wiley New York, 1996.

[4] J. Holland, “Adaptation in Natural and Artificial Systems,” University of Michigan Press Ann Arbor, 1975.

[5] J. J. Coyle, E. J. Bardi, C. J. Langley, “The Management of Business Logistics,” (St Paul, MN: West), 1996.

[6] J. Kennedy, R. C. Eberhart, “Particle swarm optimization,” Proceedings IEEE International Conference on Neural Networks, Vol. 4, 1942-1948, 1995.

[7] K. J. Roodbergen, R. D. Koster, “Routing method for warehouse with multiple aisles,” International Journal of Production Research, Vol. 39, No. 9, pp. 1865-1883, 2001.

[8] L. F. Hsieh, C. J. Huang, C. L. Huang, “Applying Particle Swarm Optimization to Plan Picking Routing

在文檔中 行政院國家科學委員會專題研究計畫 成果報告 (頁 36-47)