Scheduling of Order-picking with Replenishment
in a Warehouse Environment
Jie GONG,

Hirofumi TAMURA,# Toshimitsu HIGASHI,+ and Jun OTA

In this paper, given the orders and stock in a warehouse, we present a metaheuristic-based scheduler that aims to solve ascheduling problem of order-picking with replenishment. Our objective is to minimize the maximum operation time oforder-picking carts. The problem is described with respect to the carts to replenish and pick up products separately within thesame period. Sub-problems in this research are (1) how to reduce delays among carts and (2) how to reduce the carts’ travel
distance. Several operators aiming to generate transitions in the schedule are implemented. After that, a local search procedure isused to solve the routing problem and reduce the delays among carts. The experiment results show that the metaheuristic canmake significant improvements with respect to minimizing the operation time.
Key words: warehouse management, order-picking, replenishing, metaheuristics, schedulingIn this problem, the regular replenishment quantity from thereserve to the forward area is concerned.
On the operational level, the picking problem has beenaddressed as a routing method problem, which aims to sequence
the picking items to ensure a good route [9][10]. Such a picking
problem can be represented in the form of the Traveling Salesman
Problem (TSP) and solved with adequate algorithms [11]. In thesestudies, one important assumption is that the stock (productquantity in the storage location) is unlimited and there is no needto replenish the product supplies. The replenishment problem on
the operational level has been discussed in [12]. The warehouseenvironment discussed in the paper is somewhat specific, whereas
the replenishment area and the picking area are completely
separate. Therefore, it is difficult to apply the method directly to a
general warehouse environment.
In previous studies, the replenishment problem was mainly
addressed on a tactical level, such as the forward-reserve problem.
On the operational level, only a few studies have been conductedwith regard to order-picking with replenishment. Thus, in this

1. INTRODUCTION
1.1 Background
Improvements in warehouse management in recent years arebeing attributed to gains in logistics. Logistics improvements leadto increased efficiency in warehouse operations and to morereliable customer service. The main operations for warehouseinclude receiving, storing, order-picking, and shipping. One study
has shown that order-picking accounts for as much as 55% of thetotal warehouse operating cost [1].
Pallets and products are picked from the storage locations bypickers. With common low-level order-picking systems, pickers
are humans employing carts.
Nowadays, order-picking is the costliest activity in a warehouse.
It is divided into a reserve area and a picking area (forward area).
Because of the shortage products during intensive order-picking,replenishment is very important [2]. The replenishment activity
becomes more frequent and crucial during a busy picking period.
More attention is currently being given to such problems as timing
and replenishment.
1.2 Literature Survey
Warehouse design has traditionally been divided into tactical or
operational levels [3]. On a tactical level, replenishment is mainly
discussed in the field of inventory theory. Many studies have been
made in this field [4]-[6]. Such studies have dealt with amulti-retailer problem, multi-item problems, and thelimited-capacity problem of warehouses. Several studies on layout
design have also been conducted [7]. Another issue is storageassignment, which involves the number of products to be placed inforward and reserve areas. The decisions concerning the problems
described are commonly called the forward-reserve problem [8].

1 2 3

…

*

Department of Precision Engineering, Graduate School ofEngineering, The University of Tokyo
7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan# Murata Systems, Ltd.
3 Minamiochiai-cho, Kisshoin, Minami-ku, Kyoto 601-8326, Japan.
+
Murata Machinery, Ltd.
2 Nakajima, Hashizume, Inuyama-shi, Aichi 484-8502, Japan.

…nFig. 1 A model of order-picking in a warehouse(Received December 28, 2007)33

unload the products. This is referred to as a trip and assigned tocarts. Figure 2 shows an example of the trip. In this case, the trip
connects four picking locations.
As the products are picked up, the stock decreases, and it isnecessary to replenish them at the storage sites. As in the pickup
process, the products in shortfall are uploaded on the carts fromthe AS/RS and replenished to the sites. When the cart is empty, it
returns to the AS/RS and uploads products for the next
replenishment round. This circuitous route is called areplenishment trip. The carts undertake multiple pickup trips thatare started and completed at a shed.
We then determine the cart sequence for pickup andreplenishment, which is the output as shown in Fig. 3. Here, aschedule composed of two carts (C1 and C2) is shown. The
numbers without parentheses correspond to storage locations,while the numbers in parentheses are the numbers of items to bepicked or replenished at the corresponding locations. The start oftrip is denoted by “s” or “r.” Here, “s” represents the shed and “r”
represents AS/RS. Here, we define the action as the element of
one pickup/replenishment operation, which contains the cart
activity information. The information includes the cart ID, its
location ID, and the type of action: replenishment, pickup, or loadquantity.
Carts are scheduled to complete the order-picking andreplenishment operations as soon as possible. However, becauseof the existence of picking and replenishment tasks in the same
period, several delays occur and increase the difficulty of solving
the problem. There are several types of delays experienced bycarts.
1) Loading Queue Delay (Dlq): This type of delay occurs
when carts must load and unload products at the same site and at
the same time. These interactions are not only variable but also
unpredictable and they can cause a cart to diverge from its basetime significantly. If the two carts have to do the same operations(replenishment or picking) at the same location in the same period,
the carts operate in the order in which they arrive, that is, first in,

Table 1 An example of the order list by shops
Shop
Produ
Produ
Produ
… Produ
ct 1
ct 2
ct 3
ct n
Shop A10
2
0…
0
Shop B
40
35
15
…
20
…
…
…
…
…
…
Shop M010
0…
60
Table 2 An example of the stock sheet
Location
Product
Quantity
1

AA

40

2

AB

50

3

AC

80







n

CY

20

research, our objective is to model and present a search-based
metahueristic to solve the problems related to order-picking with
replenishment on the operational level.
The problem of order-picking with replenishment differs fromtypical order-picking problems. Both of the replenishment
operation and the picking operation are made in the common
working area. Both the replenishment and picking operations
occur in a common work area. A primary constraint is that thepicking cart operation cannot be completed until the products thatare in short supply are replenished.
1.3 A Warehouse Model
A warehouse model is shown in Fig. 1. The storage locations
hold initial quantities of products (stock). Each location has its
own location number, as shown in the figure. The items to bepicked from given locations are obtained from the orders sent byshops. The items in short supply are transported by carts from an
Automated Storage and Retrieval System (AS/RS) to replenish thestorage sites. The items selected from a corresponding order are
picked up and deposited at the shed for loading into trucks anddelivery to the customers. Order-picking schedules are made byclustering tasks and by assigning them to carts assignments.
The rest of this paper is organized as follows: Section 2 offers
an overview of the problem of order-picking with replenishment;
Section 3 is a discussion of the methodology of the research;
Section 4 is a presentation of the experiment results; and Section 5
is the conclusion.

: pickup locations

3

2. Problem Statement
54

An overview of the warehouse picking problem is given first.
The products are stored in stationary storage locations throughout
the warehouse (Fig. 1). Each location holds quantities of uniquetypes of products and has a unit quantity called a case. The shop
order and the stock for every product serve as inputs to the picking
problem, as shown in Tables 1 and 2, respectively. For one storage
location, there is a capacity that is represented by CAPs. If thequantity of products exceeds the capacity, the unloading time ofthe exceeding part is assumed to be Npu times more than normal.
The orders placed on the warehouse should be picked up by thecarts from the storage locations and transferred to the shed. A cart
will start from the shed and pick up the products at the various
locations. If the quantity reaches the capacity of the cart,
represented as CAPa, the cart will return to the shed and will

74

82

Fig. 2 An example of a cart routing trip
c1 s 82(20) 54(25) 3(5)74(10) s 15(60) s 75(53)c2 r 54(25) 74(10) r 75(53) r 15(60) r 82(20)Fig. 3 Cart schedule example

34

3(5)

3.

first out. The waiting time is called the loading queue delay time.
2) Replenishment Wait Delay (Drw): This type of delay occurs
when a picking cart waits for the replenishment at the sites inshort until the replenishment cart finishes its task. The waitingtime is referred to as the replenishment delay.
3) Punishment Loading Delay (Dpl): This type of delay occurs
when the number of products after replenishment exceeds thecapacity at the storage location. The load or pick time for the
products that exceeds the capacity takes Npu (>1) times than thestandard load or pick time. This type of delay is referred to as apunishment loading delay.
4) Collision Avoidance Delay (Dac): This type of delay occurs
when a cart requires extra time to avoid a collision with anothercart.
As the problem is stated in this paper, the density of carts is
relatively low and because mutual avoidance ability of cart drivers
is so high, the degree of delay is not so large even two carts go
through each other. Therefore, the fourth collision avoidance delay
remains small compared to the total operation time and otherdelays. Thus, we ignore the collision avoidance delays and focus
on the other three types of delays.
The problem is presented as follows. Let:

Research Methodology

3.1 Approach
Scheduling is defined as the allocation of carts to a collection oftasks. The transition from one solution to another can improve theefficiency of finding a better solution. In most schedulingproblems, tasks have been determined beforehand and neverchange in the scheduling process. In the field of split delivery
vehicle routing problems (SDVRP), the concept of task splitting is
introduced for deriving solutions [11]. Similarly, in the paper, we
propose several operators introducing task splitting during thesearch process.
In many warehouses, orders required for a specific day are just
fixed several minutes before the warehouse opens. Then theplanned/scheduled tasks must be finished in several minutes. Thus,
maximum computation time tmax is an important condition.
The metaheursitic based on Simulated Annealing (SA) is
described in this section. First, we introduce the Simulated
Annealing structure, and then, a general heuristic to generate an
initial schedule is introduced in paragraph 3.3. Operators to moveaction from cart to cart are described in detail in paragraph 3.4.
Local Search as a procedure will be proposed in paragraph 3.5; itaims to minimize the routing cost and reduce the delay caused byinteraction between carts.
3.2 SA Scheduler Structure
Simulated Annealing is a popular metaheuristic that has foundextensive use for solving complex combinatorial optimization
problems [13]. In SA, the search begins at an initial temperature
Tinit and proceeds until the stopping conditions are satisfied. We
used one stopping condition when the current computation timereached the maximal computation time tmax. The flowchart of the
SA scheduler is shown in detail in Fig. 4.
The algorithms about initial schedule generation, operator
selection, and local search will be discussed in detail in paragraphs
3.3, 3.4, and 3.5, respectively.
3.3 Initial Schedule Generation
The initial schedule is generated by a strategy that is widelypracticed due to its ease of implementation. The current scheduler
generates trips by clustering the orders as a modified S-shaped
pattern explained in Section 4.1. The products are picked up or
replenished based on an S-shaped routing [14], which involves around trip to all of the shelves, shed, and AS/RS, as shown in Fig.

C  {c1 , c2 ,, ck } : a set of carts

Ai  {ai1 , ai 2 ,, aini }(i  C ) : a set of actions of the cart ik : total number of carts

ni : total number of actions assigned to cart i (i  C )i : operation time of cart i with delay time (i  C )max( i ) : total makespaniC

Objective function: M  min.

BEGIN
Initial schedule (s0) generation
T TinitOperator selection
Local search
Route generation
Trip exchanges generated stateIFrand (0,1)  exp(( f ( s0 )  f ( s)) / T )THEN

s0  sT aT
NComputationaltime > tmax?
Y
END

Fig. 4 Flowchart of the proposed scheduler

Fig. 5 An example of S-shape route35

Table 3 Four methods

5. If the quantities to be picked up during the trip will exceed thecapacity of cart (CAPa) at the next picking location, the cart willstop picking and will return to the shed or AS/RS. At the
beginning, all the carts start at the AS/RS to replenish products.
The next generated trip will be assigned to the cart that returns
first. This is repeated until there are no more unassigned
replenishments in the warehouse. At that time, the carts tasked
with replenishment will be reassigned to pick-up trips from thelast site of replenishment. If there are no more picking trips to be
assigned, no further activity is required.
3.4 Operator Selection
The operators in a scheduling problem relocate actions fromone cart to another. The three types of operators are defined
below: Action Transfer (total transfer), Action Exchange (total
action swap), and Action Split (partial transfer).
1) Action Transfer: Action Transfer is a move wherein Aik of Ci istransferred from Ci to another cart Cj. The transfer is done suchthat a new trip is constructed for Aik at the end of the action
sequence of Cj. Here, i, j, and k are randomly selected.
2) Action Exchange: An Action Exchange is a move in which the
Aik from Ci is relocated to another Cj. Similarly, the Ajl of Cj isrelocated to Ci. After this operation, both Ci and Cj will add one
new trip containing Ajl and Aik at the end of the respective action
sequences. Here, i, j, k, and l are randomly selected.
3) Action Split: If actions are split, a better balance can beachieved among the carts. The Action Split operator is anextension of the Action Transfer that allows partial relocation ofan action from one cart to another, as shown in Fig. 6.

cjs

Rep:50Location:4s

Pick:8Location:25

ci s

Rep:26
Location:10s

Pick:20
Location:18

cj

Rep:50Location:4s

Pick:8Location:25

action exchange or the action transfer by utilizing i

Pick:8Location:6

Pick:8Location:6s*

at Step 3.

On the other hand, in Split_R and Non-split_R, we select theaction exchange and the action transfer randomly. We canconsider other classes to include the split operation or not. Split_I
and Split_R include the split operation, and Non-split_I and
Non-split_R do not, and we proceed from Step 1 to Step 3,
skipping Step 2. The relationship of the four methods is shown in
Table 3.
3.5 Local Search
The proposed operators just described are easy to implement.
However, these operators will cause the following two problems.
a) The travel distance for the related carts will be affected andresult in longer makespans.
b) Some delays may occur in the unchecked new schedule.
The next two parts deals with “a)” and “b)” respectively.
The first problem is to determine how to change the sequence of
the actions and how to cluster the actions into some trips tominimize the traveling cost.
After the routing problem has been solved, the next step is tominimize the delays caused by the interactions between carts.
Trip Exchange is a simple process that aims to minimize thedelays by exchanging the trip sequence inside the corresponding
cart. The Trip Exchange is different according to the type of delay.
1)
Determine which trip causes loading queue delays andexchange this trip with the last trip.
2)
Determine which replenishment trip to remedy a
product shortfall produces a delay (causing
replenishing waiting delay) and exchange that trip withthe first trip.

4.

i*
s

Non-split_R

In the Split_I and Non-split_I, we make a decision to select the(1)

Pick:50
Location:18

Split_R

Step 4: Do Action Transfer to Cj. End.
Step 5: Generate Ajl in Cj, Do Action Exchange. End.

We propose the Split_I methodology to implement the above
three operations. The algorithm will be explained as follows.

s

Randomly Decided

Step 3: If i*  numik , go to Step 4. Otherwise, go to Step 5.

i and  j .

Rep:26
Location:10

Non-split_I

and go to Step 4.

2Tloadci sSplit_I

Step 2: Create a new action Aik for i * and set the new action to Ci,

action split operation. Tp is the increased travel cost of the newtrip of a new split action, which is moved to Cj. Tload is the
Loading time per one case. Equation (1) is constructed to create abalance between

Decided by i*

Step 2. Otherwise, go to Step 3.

i and  j are the makespans of Ci and Cj before theIn (1),

Non-split

0  i*  numik (the number of items in Aik), and then go tofrom Ci to another cart Cj in order to achieve a better makespanbalance between two carts.

i   j  T p

Split

Step 1: Randomly select i, j, k, and l. Calculate i * , if

We can estimate the amount to items i * of Aik to be moved

i* 

Split
Condition
Swap(Step1)
Condition(Step3)

Pick:30
Location:18

SIMULATION AND RESULTS

4.1 The Reference Scheduler Here, for a comparison, we
introduce the reference scheduler that is currently employed by
the industrial partner in this research [15]. The strategy is selected

Fig.6 Action split operation that can produce a better
makespan36

Table 4 Simulation environment

Cart speed

1 meter/second

the cart’s makespans. Both Non-Split_I and Split_I show better
results than Non-Split_R and Split_R. Especially, Split_I achieved
the best result, i.e., a 1.9 % improvement, compared with
nonSplit_R. It is a feasible to determine the operator by

Loading time per one case (Tlead)

1 second/case

calculating the i * .

Item

Npu
Average stock

Quantity

2Then, we evaluate the improvement of 3 instances by increasing
the number of shops. The trend is for the makespans of thereference scheduler to increase in a linear manner as the numberof items increases. Split-I can achieve more improvement by
increasing the number of shops. It is possible that, as the picking
intensity increases, the items tend to concentrate on several
specific locations and loading que delay will increase. Under thiscondition, the proposed metaheurstic is more efficient to reducethe delays and results of minimizing the makespans. The
improvement of 3 instances does not show much difference when
the number of shops is low (e.g., 2 or 3). However, when thenumber of shops increases (e.g., when the number of shops is 5 or

30 cases/location

Cart number

4

Location size
Number of locations

1 1 m84

Location capacity (CAPs)

60 cases2

Cart capacity (CAPa)

60 cases

Loading time at shed or AS/RS

60 seconds

Tinit

1000

A

0.9

due to the following two reasons: (a) there have been no former
algorithms in the literature that deal with the same problem
statement in this paper, and (b) the problem is still solved in real
warehouses with a specific rule-based algorithm. Therefore theproposed algorithm is modeled as the reference scheduler in orderto evaluate the proposed algorithm quantitatively. The reference
scheduler is similar to the heuristic of the Initial Schedule
mentioned in Section 3. The carts based on the S-shaped routing
will add products to the trip until the capacity of the trip isreached. The remaining products will be picked up on the next trip.
When order-picking starts, all carts will start from the AS/RS tounload replenishments. The picking tasks will not start until all
replenishing tasks are finished. The advantage of this scheduler isthat the Replenishment Waiting Delay will not occur because
stock products are sufficient after replenishing.
4.2 Simulation Results
First, we evaluate the performance of the metaheuristic-based
SA scheduler with different operators in computer experiments.
The maximal computation time tmax is set to be 3 minutes underthe environment of a Pentium4 1.2GHz with 1GB RAM. Table 4shows the simulation environment. The input orders are assignedwith respect to shops that represent the regions to which products
are delivered. A comprehensive set of data instances is used toevaluate the schedulers. The basic data instances are 3 data as
follows:
Instance 1: 720 cases/shop distributed in 75 locations

Instance 2: 720 cases/shop distributed in 45 locations

Instance 3: 720 cases/shop distributed in 30 locations
These data are created based on the orders of real warehouses.
The number of shops is set at 2 to 6. Restriction in generating trips
is as follows:
For the picking tasks, trips must consist of products from thesame shop.
For the replenishment tasks, no restriction exists as to the
products in the same trip.
Figure 7 shows the average values of makespan (in seconds)
with input of Instance 1 to 3. All four sets of operators showed
better performances than the reference scheduler. If we compare
Split-I with the reference scheduler, a significant improvement(21.9% - 45.3%) is achieved. Both Split_R and Split_I show better
performance than Non-Split_R and Non-Split_I. Comparing with
Non-Split, Split can achieve, on average, a 2.4% improvement.
Thus, the Action Split operator is proved to be efficient to balance

Reference
Non-Split_R
Non-Split_I
Split-R
Split-I(a) For Instance 1
Reference
Non-Split_R
Non-Split_I
Split-R
Split-I(b) For Instance 2

Reference
Non-Split_R
Non-Split_I
Split-R
Split-I(c) For Instance 3
Fig. 7 Makespans of 5 schedulers with respect to the number of
shops

37

6), the low-density instance (Instance 1) shows better
improvement than the high-density instance (Instance 3).
In a multi-shop picking environment, orders from different
shops with a few items each will be combined into one picking
instance to improve the picking efficiency. When the number ofshops is not large, combining their orders into one picking event
will not have a significant effect. On the other hand, as the numberof shops increases, combination of the order can produce a highefficiency.
The obtained results of Split-I method has varied even with thesame condition because it is a kind of a random-search method. Inorder to see the influence of the variance, simulations are made for
Split-I with 30 times when the number of shops is 2 and in thecase of Instance 1, in which the difference between the result of
Split-I and that of the reference sheduler is smallest. As a result,the standard score of the value for the reference scheduler has thestandard score of -13.6, which means that the result of Split-I andthat of the reference schduler is significantly different.
The reason can be concluded from the comparison of three
delays, total Dlq, total Dpl, and total Drw in the reference scheduler
and Split-I. This is the result when the number of shops is 2 and in
the case of Instance 1 (Figure 8). In the reference scheduler,although there are no Drw in the reference scheduler because of
first replenishment next picking policy, many Dlq and Dpl make themakespan longer. The reasoning behind this improvement can beapplied to the following items.
- The proposed algorithm can produce a good schedule withshorter makespans.
- Local Search has succeeded in restraining Dlq and Dpl
through Trip Exchange.
For other instances and for other number of shops, almost thesame tendency can be obtained with the above-mentioned
discussions.

5.

Exchange, and Action Split, are identified. All operators are
involved in the transfer of action between agents. The split andswap conditions are two determinations with which we areconcerned. According to the two conditions, we conclude that
there are four sets of operators for the transition of a schedule.
Instances are arranged according to varying the number ofshops. Many experiments have been conducted in different
instances and in a class-based storage assignment condition.
Experiment results proved that a kind of SA scheduler, Split-I had
a little improvement than three other scheduler (Split-R,
Non-Split-I, Non-Split-R). By comparison with the reference
scheduler, the Split-I SA scheduler was efficient enough to balance
the makespans between agents. Experimental results revealed that
the Split-I SA scheduler can achieve a significant improvement(averaged about 31%) in comparison to the reference scheduler.
The trend is for the average improvement increase as the numberof shops increases. When the pickup intensity increases, so does
the volume of stock in one location, and, as a result, the greater
the possibility of a long delay. Under this condition, the proposed
metaheuristic is more efficient to reduce the delays and result of
minimizing the makespans.
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Route Generation for Warehouse Management using Fast Heuristics,

CONCLUSION

In this paper, the problem of ordering-picking with
replenishment has been addressed.
This research aims to generate the agents’ scheduling and makethe agents finish the tasks as soon as possible, that is, minimizing
makespans. An efficient search-based metaheuristic is proposed
because it is known to give optimal or near-optimal results.
In the metaheuristic, the transition from one solution to a new
solution is a serious problem, especially in a complex system.
Thus, we presented operators that aim to implement the transition
from one schedule to another by way of relocating (moving) theactions between agents. Three operators, Action Transfer, Action

Fig. 8 Comparison of the Split-I scheduler and the reference
scheduler for the case of Instance 1; the number of shops is 2.

38

Proceedings of the 2004 IEEE/RSJ International Conference onIntelligent Robots and Systems, 2093/2098 (2004).
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[13] Kirkpatrick, S., Gelatt, C.D., and Vecchi, M.P.: Optimization by
Simulated Annealing, Science, 220, 671/680 (1983).
[14] Roodbergen, K.J., and De Koster, R.: Routing Methods for
Warehouses with Multiple Cross Aisles,” International Journal of
Production Research, 39-9, 1865/1883 (2001).
[15] Gong, J., Ota, J., Tamura, H., and Higashi, T.: A Model and Efficient
Heuristics of Order-Picking with Replenishment in a Warehouse,
Preprints of the 16th Intelligent Systems Symposium, 161/166(2006).

Hirofumi Tamura
Mr. Hirofumi Tamura works for Murata
Systems, Ltd. He is engaged inresearch and development on logistic
information systems.

Toshimitsu Higashi (Member)Dr. Toshimitsu Higashi works for
Murata Machinery Ltd. He is engaged
in research and develoment on thecontrol system of logistic systems,sway control systems and distributed
autonomous robotic systems.

Jie Gong
Mr. Jie Gong graduated from mastercourse of Graduate school of Engineering,
the University of Tokyo in 2007. His
research
interest
waswarehousemanagement system and logistics during
his stay in the university.

Jun Ota (Member)
Professor Jun Ota is an associate
professor at Dept. of Precision
Engineering, Graduate School ofEngineering, the University ofTokyo. His research interest ismulti-agent robotics and logistic
systems.

39