# An Efficient Approach to Investigate the Tradeoff between Double Handling and Needed Capacity in Automated Distribution Centers

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## Abstract

**:**

## 1. Introduction

_{2}emissions were found in the literature [3]. Stacker cranes are one important type for automation where Automated Storage and Retrieval Systems (AS/RS) are used [4]. If the automated warehouse stores pallets, it is called a unit-load AS/RS. If the system is for carton cases or other types of bins, then it is called a mini-load system. In many cases, both types exist in the same distribution center. The products are shipped from the second automated warehouse to retail stores or wholesalers [5].

## 2. Literature Review

_{2}emissions are affected by decisions about supply lead times, reorder quantities, and storage equipment [10].

#### 2.1. Material Flow and Warehouse Design

_{2}was introduced in the design problem by Rajković et al. [3]. This is in addition to minimizing costs and travel time. Lewczuk et al. [21] analyzed the energy consumption of a warehouse in various configurations. They presented a method for calculating energy consumption and predicting storage space for each configuration. The costs were also reduced by investigating the path planning problem of AS/RS [22]. Zaerpour et al. [23] proposed a decision tool for selecting the appropriate type of storage system that minimizes investment and operational costs while meeting warehouse design requirements, specifically storage capacity and throughput.

#### 2.2. Two Warehouses Design Problem

#### 2.3. Double Handling and Study Contribution

## 3. Methodology

_{o}) moved to the depalletizer and the reversed half full pallets (HPL

_{I}) depend on the strategy used. The strategy will determine if the lot size will cover only the daily demand or more. More HPL

_{I}means more double handling. If only demand is moved forward, the rest of the pallet will come back again to WH1 again. The objective is to reduce the total costs of the system. The costs are for the storage location space in two warehouses and the number of stacker cranes including the maintenance costs of them. Different lot sizing rules can be used for different classes of materials. An MS Excel tool has been designed for this study. The tool contains both the formulas and the simulation analysis. The simulations needed in the conceptual design are simple and static, and therefore did not map the operating dynamics of the stacker cranes. Therefore, simulation did not consider parameters such as the stacker cranes accelerations, double cycles, or different jobs assignments. This tool can be used by decision makers to determine the optimal solution. Generally, providing the formula for the capacity or throughput, whenever possible, is better to generalize the investigation, and make the study applicable for other parameters values. However, sometimes the formula is difficult to obtain due to the complexity of the system. In this case, simulation is used.

#### 3.1. Study Scenarios and Assumptions

- Daily demand is less than a layer size (assumed to be C items in this study);
- Daily demand is equal to or greater than a layer size, but less than or equal to a pallet size (assumed to be B items in this study);
- Daily demand is greater than pallet size (assumed to be A items in this study).

- Scenario 1 (daily demand): Only the daily demand is depalletized and moved to the mini-load system.
- Scenario 2 (full layers): Lot size is an integer number of pallet layer. For example, if the current demand is 7 cases, and each layer is 5 cases, then 10 cases (two layers) must be depalletized and moved to the mini-load system.
- Scenario 3 (full pallets): Whole pallets are depalletized. For example, if the demand is 60 cases, and the pallet size is 50 cases, then two pallets must be depalletized and sent to the mini-load system.

- The capacity of the mini-load system;
- The capacity of the unit-load AS/RS (the first warehouse);
- The level of double handling in the first warehouse, which defines the warehouse throughput (the daily demand also affects the throughput);

- Try not to use the first scenario for C items.
- If scenario 1 is to be used for C items, it is better to wait until the order comes, and then cases are shipped directly without going to the second warehouse.
- If a new order for a C item comes after the first shipment in the same day, then there should be some safety stock in the second warehouse, and the extra demand is satisfied from this safety stock.

- The depalletized cases must cover at least the daily demand. In other words, the daily demand is not very large to the level it needs to be divided into several lot sizes every day.
- Before commencing the retrieval order from the first warehouse, the total daily demand for an item by all customers can be known with reasonable accuracy. Pooling the demand by all the customers can reduce the fluctuations of the demand for that item.
- Pallets come in only one size (measured in number of cases).
- Average service time for stacker cranes in each warehouse was assumed to be known.
- The variability in the total number of daily active items is not very high. Active items today are the items needed today.
- The new batch of cases of a certain item will come to the mini-load system just in time, when the old cases are consumed.
- Cross docking, in which full pallets are transshipped directly to the customer from the first warehouse, is not considered in this study.
- In reality, when an order comes for an item that is currently in the depalletizer, cases of that item can be shipped without being stored in the second warehouse. Therefore, there is no need for the capacity of the cases of that item on the second warehouse. This fact was ignored in this paper because of the dynamic nature of demand and in order to provide more buffer of capacity in the second warehouse. In other words, this capacity may be required for safety stock in order to hedge against demand uncertainty. The best safety stock level can be investigated in future research.
- The maximum inventory level (T) in the system is given. This maximum value contains the inventory in both warehouses. It should cover the demand for a certain number of days. Different classes of items can have different coverage periods. T-value can be the order quantity (Q) plus the safety stock (SS). The Q-value depends on factors such as lead time, minimum size of shipment, and setup costs. The safety stock level is also given. The total capacity of two warehouses is not exactly as the total inventory because the capacity should cover the maximum value in the beginning and the end of the day. That might also lead to different total capacity for different scenarios.

_{t1}and M

_{t2}were assumed to be fixed in the table for simplicity in the conceptual design; however, the exact capacities of the stacker cranes depend on the length, the height of the racks, the number of storage locations in each aisle, the uneven (or not) distribution of the tasks among the aisles, and the possibility of using double cycles by the stacker cranes. The unit-load AS/RS capacity depends on Q and SS values. Simulation was used in this study to find the WH1 capacity for different scenarios as will be shown later in the section of results and analysis. The needed capacity for WH2 is independent from the Q and SS values, and it depends on the demand and the scenario used.

#### 3.2. Scenario 1

_{O}is much larger than D. This is because that not all of the pallets coming out of the unit-load AS/RS are full. The total throughput for the unit-load AS/RS is the total storage and retrieval movements for the A, B, and C classes of items, which can be found as follows:

_{O}and HPL

_{I}depend on the size of the daily demand. The reverse movement (HPL

_{I}) represents the double handling of pallets. The values for D

_{A}, D

_{B}, and D

_{C}are given in Table 1.

#### 3.2.1. WH1 Throughput When Daily Demand Is Less Than One Pallet

_{O}) depends on the number of different item types and the daily demand per item. When the half-full pallet in the unit-load AS/RS is insufficient, a new pallet must be opened (NPO). If the average daily demand for that item is 20% of the pallet size, this NPO occurs every 5 days, except when the total demand of the five days is exactly 100% of the pallet size. The probability of obtaining such a volume is usually small. Therefore, we can assume it to be zero to simplify the formula. In other words, if we assume that the PPI

_{B}and PPI

_{C}are less than 1, then:

_{O}and HPL

_{I}represents the empty pallets.

#### 3.2.2. Throughput When Daily Demand Is Greater Than One Pallet

_{OA}+ HPL

_{IA}

_{,}when the daily demand for a certain item is more than one pallet, a different approach must be followed. In this case, the number of full pallets leaving the unit-load AS/RS (PL

_{OAF}) equals the number of different items multiplied by the lower rounding of the average daily demand per item ($PP{I}_{A}{N}_{A}$). If the daily demand is greater than 2 pallets for example, then the number of different items must multiplied by 2. The half full pallets moving out the unit-load AS/RS (PL

_{OAH}) are two types. The first one is already opened from a previous day, and second type is the new opened ones. The first type occurs almost every day for each item, and therefore we can assume it will be as the number of different items (N

_{A}). The frequency of the second type can be found by taking the last digits of the daily demand and multiplying them by the number of different types (${N}_{A}\left(PP{I}_{A}-PP{I}_{A}\right)$). Therefore, the total number of moving pallets out the unit-load AS/RS is

_{IA}can be assumed to be as the number of different items. Therefore, it is possible to write

_{A}, D

_{B}, and D

_{C}were added to represent the entering pallets from the suppliers.

#### 3.2.3. Capacity of the Mini-Load System

#### 3.3. Scenario 2

#### 3.3.1. Throughput When Daily Demand Is Greater Than One Pallet

#### 3.3.2. Throughput When Daily Demand Is Less Than One Pallet

_{O}) and (HPL

_{I}) in Formulas (9)–(12) are less than the variables in Formulas (2)–(5), which are for scenario 1.

_{A}+ PL

_{OA}+ HPL

_{IA}, results of the simulation must be obtained at first as in the results and analysis section. Even though the throughput in this case can be estimated using formulas without the need for simulation, using simulation can be useful to compare the formulas with the results of simulation. Table 2 shows how to find the needed throughput for class B (scenario 2) for 10 days. To obtain accurate results, 1000 days were used. Demand was assumed to be Poisson distributed. Four columns are needed to track the throughput. There were no full pallets moved because the demand was assumed to be 10 cases (20% of the pallet size). There are two columns for the half pallets. Column (2) is for the pallets which were reassigned again to WH1. Then, they are needed again to satisfy the demand. The demand of the first six days consumes the first pallet plus 20% of a new pallet. Column (3) is for the pallets that are opened for the first time, but only some of the cases in the pallet are needed. On day 6, 20% of the pallet is used. The left 80% goes back to WH1 again. On day 7, only 10% of the pallet is used, and therefore 70% goes back again to WH1. This cycle continues until the end of the simulation. The output pallets (PL

_{O}) is computed by counting how many nonzero in the columns (1), (2), and (3). The reversed moving pallets (HPL

_{I}) is computed by counting how many nonzero in column (4). The throughput is the summation of both of them plus the entering pallets to WH1 from suppliers. The summation of the “total handling (PL)” column represents these entering pallets.

#### 3.3.3. Capacity of the Mini-Load System

#### 3.4. Scenario 3

#### 3.4.1. Throughput of WH1

#### 3.4.2. Capacity of the Mini-Load System

#### 3.5. Costs Model

_{1}for WH1 and Y

_{2}for WH2) is found based on the needed throughput and the capacity for each stacker crane (M

_{t1}for stacker cranes in WH1 and M

_{t2}for stacker cranes in WH2).

_{2}is fixed regardless of the scenario used. This is because it depends on the throughput of WH2, which depends directly on the daily demand, and has nothing to do with double handling of pallets as in WH1. The throughput of WH1 is determined based on Equation (1). The maintenance costs can be found as follows

_{1}, WH1 capacity, and WH2 capacity. Assume that X

_{Ai}, X

_{Bi}, and X

_{Ci}are defined as follows

_{A}

_{2}will be found by simulation in the next section. Equation (20) should be used to find the value of Y

_{1}as in Equation (15). Then, this value is used in Equation (20). The other design parameter is defined as follows

_{ij}means the needed capacity in WH1 allocated for “i” items based on “j” scenario. The nonlinear integer programming model has the objective function of TC defined in Equation (19). The constraints are Equations (15) and (20) used to define Y

_{1}; Equation (21) to define WH2 capacity; and Equation (22) to define WH1 capacity. However, later in the next section Equation (21) can be rewritten to include Cap2

_{C}

_{2}and Cap2

_{B}

_{3}based on the insights from simulation as in Equation (28). Moreover, Equation (20) can be rewritten as in Equation (24) in the next section to include the value of Th1

_{A}

_{2}found based on simulation. The three variables Cap2

_{C}

_{2}, Cap2

_{B}

_{3}and Th1

_{A}

_{2}were difficult to find based on analytical investigation. Therefore, simulation was used to define them. The previous equations from (1) to (14) and from (16) to (18) are included in the nonlinear integer model (OF defined in (19), and constraints defined in (15), (20), (21), and (22)). The results of the model are based on the values found using the shown formulas, except when there is a need for simulation for some variables. In this case, the average values of simulation results are used.

## 4. Results and Analysis

#### 4.1. Scenario 1

#### 4.2. Scenario 2: Simulation for WH1 Throughput of A Items

_{OAF}) and half full (PL

_{OAH}) movements of WH1 were obtained for one item. The in WH1 movements (HPL

_{IA}) were also obtained. Figure 3 shows the ratio between output and input pallets (R

_{IOA}= (PL

_{OA}+ HPL

_{IA})/D

_{A}) for WH1 when the full layers are depalletized. According to the ratio found, the throughput is D

_{A}R

_{IOA}+ D

_{A}= 140 × 2.31 + 140 = 463. Figure 3 is useful to cover the simulation results of different average demand values. The ratio R

_{IOA}is used to find the WH 1 throughput of A items.

#### 4.3. Scenario 2: Simulation for WH2 Capacity of C Items

_{c}

_{2}is the needed capacity for the C items if scenario 2 is used. The pallet size (PL

_{C}) is used in the formula to determine the capacity in cases instead of pallets. For example, if the layer size is L

_{s}= 5 and the average daily demand is PPI

_{C}= 1.429 cases per item, then the ratio between the average daily demand to the layer size is 0.29. The needed capacity for one item is 3.51 (which is 2.45 × 1.429). To check the accuracy of the above equation, simulation was used and it was found that the needed capacity is 3.2. The two numbers are not identical but the formula can be used as a reasonable approximation. If simulation result is utilized, 700 different items will need approximately 2240 storage locations on WH2. However, the number of 700 different items is only for the current day. There are, however, other items active in other days. If the total number of C items are three times the daily active ones, then the total needed capacity will be 6720 storage locations. So the equation will be

#### 4.4. Scenario 3: Simulation for WH2 Capacity for B and C Items

_{C}

_{3}) is found using simulation. Table 5 (the third part) summarizes the calculations needed for WH1 throughput and WH2 needed capacity

#### 4.5. Results of the Three Scenarios and the Optimal Solution

_{2}= 13) is always the same because the throughput is always the daily demand (10,000 in and 10,000 out of WH2 = 20,000). The throughput per hour for the mini-load system is 2500. The costs found depend on the cost parameters found in Table 1. The total costs include the investment and maintenance costs of stacker cranes and space costs in two warehouses. For example, to calculate the needed WH2 capacity for the first best solution, Equation (28) is used. To determine the variables of this equation, the needed capacity for A items is just the daily demand, the needed capacity for B items is estimated based on Equation (27) which was found based on Figure 4, after extensive simulation. The needed capacity for C items according to scenario 2 is estimated based on Equation (25).

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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Symbol | Meaning | Value | Unit | Formula (If Any) |
---|---|---|---|---|

A. Basic known parameters | ||||

PL_{c} | Pallet size | 50 | cases | |

I_{d} | Different number of active items in one day | 1000 | item types | |

d | Average daily demand of all items | 10,000 | cases/day | |

I_{A} | Percent of number of different A items | 10 | % | |

I_{B} | Percent of number of different B items | 20 | % | |

I_{C} | Percent of number of different C items | 70 | % | |

V_{A} | Percent of demand volume for A items | 70 | % | |

V_{B} | Percent of demand volume for B items | 20 | % | |

V_{C} | Percent of demand volume for C items | 10 | % | |

N_{L} | Number of layers per pallet | 10 | layers | |

A_{c} | Percent of daily active C items | 33.33 | % | |

B. Input parameters for the cost model | ||||

M_{t1} | WH 1 maximum throughput per aisle | 50 | PL/hour | |

M_{t2} | WH 2 maximum throughput per aisle | 200 | case/hour | |

S_{c1} | WH 1 stacker crane cost | 350,000 | dollar | |

S_{c2} | WH 2 stacker crane cost | 250,000 | dollar | |

L_{c1} | WH 1 storage location cost | 150 | dollar | |

L_{c2} | WH 2 storage location cost | 30 | dollar | |

M_{c} | Maintenance cost % | 5 | % | |

W_{p} | Working period | 20 | years | |

d_{f} | Discount factor | 0.2 | ||

C. Calculated parameters | ||||

D | Daily demand in pallets | 200 | pallets | d/PL_{c} |

D_{A} | Daily demand in pallets of class A items | 140 | pallets | V_{A} D |

D_{B} | Daily demand in pallets of class B items | 40 | pallets | V_{B} D |

D_{C} | Daily demand in pallets of class C items | 20 | pallets | V_{C} D |

N_{A} | Number of different A items | 100 | item types | I_{d} I_{A} |

N_{B} | Number of different B items | 200 | item types | I_{d} I_{B} |

N_{C} | Number of different C items in one day | 700 | item types | I_{d} I_{C} |

d_{A} | Daily demand (in cases) of class A | 7000 | cases | d V_{A} |

d_{B} | Daily demand (in cases) of class B | 2000 | cases | d V_{B} |

d_{C} | Daily demand (in cases) of class C | 1000 | cases | d V_{C} |

PPI_{A} | Daily demand per item of class A | 1.4 | pallets per item | N_{A}/D_{A} |

PPI_{B} | Daily demand per item of class B | 0.2 | pallets per item | N_{B}/D_{B} |

PPI_{C} | Daily demand per item of class C | 0.03 | pallets per item | N_{C}/D_{C} |

L_{s} | Layer size | 5 | cases per layer | PL_{c}/N_{L} |

TN_{C} | Total number of different C items | 2100 | cases | N_{C}/A_{c} |

D. Model decision variables | ||||

Y_{1} and Y_{2} | Number of stacker cranes in WH1 and WH2 | Equations (15) and (16) | ||

Cap1 | WH1 capacity | storage locations (Pallets) | Equation (22) | |

Cap2 | WH2 capacity | storage locations (cases) | Equation (28) | |

Cap2_{xi} | Needed capacity of WH2 for x items based on scenario i | cases | Equations (26) and (27) | |

Th1 | WH1 throughput | PL/day | Equation (24) | |

Th1_{i} | Total WH1 throughput if scenario i is used | PL/day | Equations (8), (13) and (14) | |

Th1_{xi} | WH1 throughput for x items if scenario i is used | PL/day | Part of Th1_{i} or Simulation | |

SCC | Storage capacity cost | dollar | Equation (18) | |

TMC | Total maintenance costs | dollar | Equation (17) | |

TC | Total costs | dollar | Equation (19) |

Day | Random “d” | Accumulated “d” | Round Up | Lot Size | Total Handling (PL) | Throughput | Empty Pallets | |||
---|---|---|---|---|---|---|---|---|---|---|

Full Pallet (1) | First Half Pallet (2) | Second Half Pallet (3) | Reverse Pallet Size (4) | |||||||

1 | 9 | 9 | 10 | 10 | 0.2 | 0 | 0.2 | 0 | 0.8 | 0 |

2 | 10 | 19 | 20 | 10 | 0.4 | 0 | 0.2 | 0 | 0.6 | 0 |

3 | 14 | 33 | 35 | 15 | 0.7 | 0 | 0.3 | 0 | 0.3 | 0 |

4 | 7 | 40 | 40 | 5 | 0.8 | 0 | 0.1 | 0 | 0.2 | 0 |

5 | 5 | 45 | 45 | 5 | 0.9 | 0 | 0.1 | 0 | 0.1 | 0 |

6 | 11 | 56 | 60 | 15 | 1.2 | 0 | 0.1 | 0.2 | 0.8 | 1 |

7 | 7 | 63 | 65 | 5 | 1.3 | 0 | 0.1 | 0 | 0.7 | 0 |

8 | 15 | 78 | 80 | 15 | 1.6 | 0 | 0.3 | 0 | 0.4 | 0 |

9 | 13 | 91 | 95 | 15 | 1.9 | 0 | 0.3 | 0 | 0.1 | 0 |

10 | 11 | 102 | 105 | 10 | 2.1 | 0 | 0.1 | 0.1 | 0.9 | 1 |

Scenario 1 | Scenario 2 | Scenario 3 | ||||
---|---|---|---|---|---|---|

Item | WH 1 Throughput | WH 2 Capacity | WH 1 Throughput | WH 2 Capacity | WH 1 Throughput | WH 2 Capacity |

A | Formula | Formula | Simulation | Formula | Formula | Formula |

B | Formula | Formula | Formula | Formula | Formula | Simulation |

C | Formula | Formula | Formula | Simulation | Formula | Simulation |

Item Class | Scenario 1 | Scenario 2 | Scenario 3 |
---|---|---|---|

A (Q = 5 PL, SS =2 PL) | 6.4 | 6.4 | 5.54 |

B (Q = 2 PL, SS =1 PL) | 2.5 | 2.5 | 1.6 |

C (Q = 1 PL, SS =1 PL) | 2 | 1.94 | 1 |

Item | PL_{O} | HPL_{I} | Th1 (PLO + HPL_{I} + D) | Cap2 |
---|---|---|---|---|

A. Scenario 1 | ||||

A | 240 | 100 | 480 | 7000 |

B | 240 | 200 | 480 | 2000 |

C | 720 | 700 | 1440 | 1000 |

Total | 2447 | 10,000 | ||

B. Scenario 2 | ||||

A | 323 * | 463 | 7000 | |

B | 220 | 180 | 440 | 2000 |

C | 210 | 190 | 420 | 6720 * |

Total | 1323 | 15,720 | ||

C. Scenario 3 | ||||

A | 140 | 0 | 280 | 7000 |

B | 40 | 0 | 80 | 6000 * |

C | 20 | 0 | 40 | 54,600 * |

Total | 400 | 67,600 |

Day | Number of Cases at the Beginning of Day (1) | Batch Size (2) | Needed Capacity (Max (1, 2)) | Number of Cases at the End of Day |
---|---|---|---|---|

1 | 50 | 0 | 50 | 30 |

2 | 30 | 0 | 30 | 10 |

3 | 10 | 50 | 50 | 40 |

4 | 40 | 0 | 40 | 20 |

5 | 20 | 0 | 20 | 0 |

Average | 38 | 20 |

Average Daily Demand Per Item | Average Needed Capacity in WH2 |
---|---|

5 | 27.5 |

10 | 30 |

15 | 36 |

20 | 38 |

25 | 37.5 |

30 | 44 |

35 | 47 |

40 | 48 |

45 | 49.5 |

50 | 50 |

# | Scenarios for | WH1 Throughput (Pallets/hour) | WH1 Number of Stacker Cranes | WH 1 Capacity (Pallets) | WH 2 Capacity (Cases) | Total Cost (USD MM) | % Stacker Cranes Costs | ||
---|---|---|---|---|---|---|---|---|---|

A Items | B Items | C Items | |||||||

1 | 3 | 3 | 2 | 97.5 | 2 | 4938 | 19,720 | 6.24 | 78.7 |

2 | 3 | 1 | 2 | 147.5 | 3 | 5118 | 15,720 | 6.59 | 81.2 |

3 | 3 | 2 | 2 | 142.5 | 3 | 5118 | 15,720 | 6.59 | 81.2 |

4 | 2 | 3 | 2 | 120.4 | 3 | 5024 | 19,720 | 6.69 | 79.9 |

5 | 1 | 3 | 2 | 122.5 | 3 | 5024 | 19,720 | 6.69 | 79.9 |

6 | 3 | 3 | 3 | 50.0 | 1 | 2974 | 67,600 | 6.95 | 64.4 |

7 | 2 | 2 | 2 | 165.4 | 4 | 5204 | 15,720 | 7.03 | 82.2 |

8 | 2 | 1 | 2 | 170.4 | 4 | 5204 | 15,720 | 7.03 | 82.2 |

9 | 1 | 2 | 2 | 167.5 | 4 | 5204 | 15,720 | 7.03 | 82.2 |

10 | 1 | 1 | 2 | 172.5 | 4 | 5204 | 15,720 | 7.03 | 82.2 |

11 | 3 | 2 | 3 | 95.0 | 2 | 3154 | 63,600 | 7.29 | 67.4 |

12 | 3 | 1 | 3 | 100.0 | 2 | 3154 | 63,600 | 7.29 | 67.4 |

13 | 3 | 3 | 1 | 225.0 | 5 | 5074 | 14,000 | 7.40 | 84.0 |

14 | 2 | 3 | 3 | 72.9 | 2 | 3060 | 67,600 | 7.40 | 66.4 |

15 | 1 | 3 | 3 | 75.0 | 2 | 3060 | 67,600 | 7.40 | 66.4 |

16 | 2 | 3 | 1 | 247.9 | 5 | 5160 | 14,000 | 7.41 | 83.9 |

17 | 1 | 3 | 1 | 250.0 | 5 | 5160 | 14,000 | 7.41 | 83.9 |

18 | 3 | 2 | 1 | 270.0 | 6 | 5254 | 10,000 | 7.74 | 85.9 |

19 | 3 | 1 | 1 | 275.0 | 6 | 5254 | 10,000 | 7.74 | 85.9 |

20 | 2 | 2 | 3 | 117.9 | 3 | 3240 | 63,600 | 7.74 | 69.1 |

21 | 2 | 1 | 3 | 122.9 | 3 | 3240 | 63,600 | 7.74 | 69.1 |

22 | 1 | 2 | 3 | 120.0 | 3 | 3240 | 63,600 | 7.74 | 69.1 |

23 | 1 | 1 | 3 | 125.0 | 3 | 3240 | 63,600 | 7.74 | 69.1 |

24 | 2 | 2 | 1 | 292.9 | 6 | 5340 | 10,000 | 7.75 | 85.8 |

25 | 2 | 1 | 1 | 297.9 | 6 | 5340 | 10,000 | 7.75 | 85.8 |

26 | 1 | 2 | 1 | 295.0 | 6 | 5340 | 10,000 | 7.75 | 85.8 |

27 | 1 | 1 | 1 | 300.0 | 6 | 5340 | 10,000 | 7.75 | 85.8 |

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## Share and Cite

**MDPI and ACS Style**

Alnahhal, M.; Salah, B.; Ruzayqat, M.
An Efficient Approach to Investigate the Tradeoff between Double Handling and Needed Capacity in Automated Distribution Centers. *Sustainability* **2022**, *14*, 7678.
https://doi.org/10.3390/su14137678

**AMA Style**

Alnahhal M, Salah B, Ruzayqat M.
An Efficient Approach to Investigate the Tradeoff between Double Handling and Needed Capacity in Automated Distribution Centers. *Sustainability*. 2022; 14(13):7678.
https://doi.org/10.3390/su14137678

**Chicago/Turabian Style**

Alnahhal, Mohammed, Bashir Salah, and Mohammed Ruzayqat.
2022. "An Efficient Approach to Investigate the Tradeoff between Double Handling and Needed Capacity in Automated Distribution Centers" *Sustainability* 14, no. 13: 7678.
https://doi.org/10.3390/su14137678