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A method to choose between carton from rack picking or carton from pallet picking
Computers & Industrial Engineering 126 (2018) 88–98
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Computers & Industrial Engineering journal homepage: www.elsevier.com/locate/caie
A method to choose between carton from rack picking or carton from pallet picking
T
⁎
Daria Battini, Martina Calzavara , Alessandro Persona, Fabio Sgarbossa Department of Management and Engineering, University of Padua, Stradella San Nicola, 3, 36100 Vicenza, Italy
A R T I C LE I N FO
A B S T R A C T
Keywords: Warehouse picking Picker-to-parts Items storage Design methodology
In a manual picker-to-parts picking warehouse, a usual approach is to divide the whole stocking area in two different zones, the reserve and the forward areas. The dimensioning of the forward area, which is dedicated to picking activities, has an important impact on the overall performance of the picking system. Indeed, its size as well as the item allocation deeply influence the travel time of the operators on one side and the frequency of the refilling activities on the other. The present paper aims to provide a new method that can be easily used to assess the most suitable way of storing a product in the forward area, considering the possibility of keeping a product directly in a pallet or storing it in racks. Starting from simple data, such as the picking orders of the items to pick and their physical dimensions, as well as the characteristics of the warehouse, the method focuses on the comparison of the total times to define the Carton Pick from rack Convenience Condition (CPCC). The CPCC formulation and its application methodology allow to quickly establish which items should be stored on pallets and which on racks, with interesting impacts on space and time savings. This is shown also in the reported case study, the results of which prove the effectiveness as well as the easy and full applicability of the methodology, also in different warehouse contexts.
1. Introduction and background Warehouse manual picking is the activity performed within a warehouse by a human operator to retrieve products required by one or more customers. Due to its characteristics, the picking activity is often the target of several studies and debates, which propose various methods that can be used to solve its main issues (Thomas & Meller, 2015). In particular, one of the main topics dealt with in the literature concerns warehouse performance improvement, through the reduction of the time needed to process the picking orders, and, as a consequence, of the time spent travelling from one stock location to another one (De Koster, Le-Duc, & Roodbergen, 2007; Tompkins, White, Bozer, & Tanchoco, 2010). Strictly linked to the question of performance increase and distance reduction is the problem of the dimensioning and allocation of the forward and reserve areas. The forward picking area is generally a subregion of the warehouse dedicated to the pick and the order activities; such activities are often concentrated in a small physical space, in order to warrant more processing efficiency. On the other hand, the reserve area is the part of the warehouse designed for storage of bulk pallets, which are also used for the replenishment of the forward area
(Rouwenhorst et al., 2000; De Koster et al., 2007; Bartholdi & Hackman, 2017). The forward area and the reserve area can also be located in the same zone of the warehouse: in this case, the stockkeeping units (SKUs) of the forward area are on the lower floor of the shelving (ground floor), while on the other upper racks there are the SKUs for bulk storage and replenishment. In such a configuration, also called low-level picker-to-parts system, the SKUs of the forward area are usually pallets, with one pallet for each one of the different product codes that are needed for order picking (Caron, Marchet, & Perego, 2000). The allocation and dimensioning issues for these two warehouse zones have been studied by many researchers, with several proposed models and methods. In general, most of the authors underline that during the design of such zones a fundamental trade-off has to be considered. This deals with the fact that by enlarging the forward area through the introduction of more stock keeping units, there is a saving due to a faster picking and to a reduction in the number of restocks; however, such benefits are inevitably accompanied by an increase of the distances travelled to process the picking orders, leading to a reduction (and in some cases also a nullification) of the first possible saving (Gu, Goetschalckx, & McGinnis, 2007). Hence, it follows that the
⁎
Corresponding author. E-mail addresses: [email protected] (D. Battini), [email protected] (M. Calzavara), [email protected] (A. Persona), [email protected] (F. Sgarbossa). https://doi.org/10.1016/j.cie.2018.09.017 Received 27 January 2017; Received in revised form 9 June 2018; Accepted 7 September 2018 Available online 08 September 2018 0360-8352/ © 2018 Elsevier Ltd. All rights reserved.
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Fig. 1. Carton from pallet picking and carton from rack picking.
space reduction, it is demonstrated that there could be also time savings and ergonomics benefits. The present paper proposes a design methodology that can be used to understand the best way of storing goods in a warehouse forward picking area. Starting from simple information referring to the stored item, including also the characteristics of the carton and pallet employed, together with some typical warehouse times, it allows to establish, for every single product, whether this is more suitable for carton picking from a rack or from a pallet. The proposed method considers a typical picking low-level picker-to-parts warehouse configuration, where the forward area is on the ground level of the shelving, and the various items are stored on pallets, with only one stock location dedicated to each item. Then, the procedure allows to evaluate if this configuration is the most suitable one for a certain item, or if it is better to stock it in a specific warehouse aisle, in which the cartons are stored on racks. Fig. 1 shows the comparison of the two alternatives under study: on the left, the carton from pallet picking configuration; on the right, the carton from rack picking one. Also in this latter case, each stock location is dedicated to one product code. Moreover, according to the depth of the shelving, there could be the possibility of storing more than one carton of the same item in the same stock location, one behind the other. In order to give a clear exposition of the proposed methodology, the remainder of the paper is structured as follows. The following section reports the mathematical modelling of the problem, leading to the introduction of the so-called Carton Pick from rack Convenience Condition (CPCC). Subsequently, two individual cases are presented, referring to as many circumstances that are observable in practice and that can lead to a simplification of the CPCC formula. The same formula is then studied through a parametric analysis, to help understanding which parameters mainly influence the storage decision of a certain product code. Once the mathematical formulation has been described and proved, Section 4 introduces the full decision-making procedure, reporting also an example of application of the method in a real industrial case study. Furthermore, Section 5 comments upon the results obtained, while in the concluding paragraph some final considerations and ideas for further research are suggested.
design of the forward area has to consider both these conflicting aspects: some authors propose models that can be used to assess the most suitable dimensions, while others are focused on the choice of which SKUs should be stored within. The first contribution on the so-called forward-reserve problem is by Bozer (1985), in which it is acknowledged the usefulness of splitting the warehouse shelving into an upper reserve area and a lower forward picking area. Hackman and Rosenblatt (1990) start from this idea proposing a heuristic based on the knapsack problem. The objective is to decide which SKUs have to be assigned to a forward area of a fixed dimension, minimizing the total material handling costs of order picking and refilling. Frazelle, Hackman, Passy, and Platzman (1994) extend this method, modelling the investment costs and the material handling costs and considering the dimension of the forward area as a variable. Van den Berg, Sharp, Gademann, and Pochet (1998) focus on the storage replenishment from the reserve area to the forward one, minimizing the impact of this activity from a time perspective. Bartholdi and Hackman (2008, 2017) deeply study the dimensioning of the forward area, from various points of view, taking into account the trade-off between the number of items to store, the number of restocks and the occupied space. Walter, Boysen and Scholl (2013) propose to investigate discrete forward-reserve problems, comparing them with the fluid ones. The focus is the sizing of the forward area, taking into account space allocation and products selection. 2. Description and aim of the study An interesting question concerning the forward-reserve problem, that until now has received very little attention, concerns the decision on how to store a certain item in the forward area. This problem is typically not often addressed, either in the literature or in industrial contexts, since in many cases the products stocking mode is defined a priori, referring only to people’s experience or common sense and considering only a limited number of the aspects that can, in fact, come into play. For example, warehouse managers could decide to store all the products in a pallet in order to warrant easier warehouse management and maintenance. Alternatively, they could establish that small dimension items have to be stored in cartons and picked directly from racks, without considering how frequently they are ordered. However, an indepth study in this field, leading to an understanding of the possible convenience of storing a certain item in a certain way with respect to another one can bring relevant benefits. Among others, establishing that some product codes are more conveniently picked from racks than from a pallet implies a potential reduction of the space needed for storing such items in the forward area, with a subsequent decrease of the distances travelled by the pickers to process the picking orders and of the overall picking time (Tompkins et al., 2010). A very similar problem has already been addressed successfully in assembly systems design. Various methods and models have been proposed to evaluate and compare the feeding and the picking activity, when these are done with pallets or from boxes (Battini, Calzavara, Otto, & Sgarbossa, 2017; Calzavara, Hanson, Sgarbossa, Medbo, & Johansson, 2017). Besides to a
3. The carton pick from rack convenience condition (CPCC) As far as manual warehouse picking is concerned, there are several factors that can usually influence the outcomes of a picking tour. One of the most widespread and proven ways of describing and evaluating a manual warehouse picking system is to consider the time spent in processing a picking order. In fact, such time is indicative of the overall performance of the picking system, and it can be used as a reference to understand the effectiveness of any change that can be introduced. If a certain change leads to a decrease of the picking time, it means that probably this change deserves to be implemented (Gu, Goetschalckx, & McGinnis, 2010; Tompkins et al., 2010). For the study presented in this paper, the various time components involved in the picking process, in the case of cartons from both pallet 89
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to restore the storage in the reserve area, for both stocking alternatives. In fact, for carton from pallet picking, once a full pallet is moved to the forward area, there is the need of taking another pallet, to fill the empty stock location in the reserve area for that product code. For carton from rack picking, since in the forward area only a part of the full pallet can be stored, there is the need of replacing in the reserve area the remaining pallet. The total time for this activity depends on the average time for performing a single refill activity tR and the refill frequency, obtained by dividing the number of cartons of item i picked in the considered time period Qi (Battini, Calzavara, Persona, & Sgarbossa, 2015) by the maximum number of cartons storable in the forward area (qic in the case of picking from a rack, qi p in the case of picking from a pallet). 2. Cartons refill from pallet to rack: the warehouse operators put the cartons in the racks to restore the forward area for subsequent picking. The time needed depends on the frequency of this action, obtained dividing the number of cartons picked in the considered time period Qi by the number of cartons that can be refilled simultaneously Bi . Of course, this activity is needed only for carton from rack picking. 3. Carton picking: the pickers do the actual physical pick of the carton while processing the picking orders; again, the time needed is proportional to the number of cartons picked in the considered time period Qi . 4. Travel: the pickers move from one stocking location to another while processing the manual picking orders. The corresponding total time depends on the time for processing a single order line in a forward area with pallets, tTp , and the number of times the pickers have to visit the same storage location of item i during the considered time period. This corresponds to Zi , the number of picking lines (and, then, picking orders) requiring item i. Moreover, for carton from rack picking, it is assumed that the travel distance and, then, the travel time, is reduced by a factor that takes into account the different dimensions of a pallet and of a carton. In fact, considering the same space in a forward area, in case of carton from rack picking the different items that can be stored are more than in case of carton from pallet picking, as shown in Fig. 1.
Table 1 Notations. Notation
Description
i Qi Zi Tic
Item index Number of cartons of item i picked in the considered time period Number of picking lines of item i in the considered time period Total time for item i in the case of carton from rack picking
Tip tR tHc Bi tPc
Total time for item i in the case of carton from pallet picking
tPp
Unitary picking time in the case of carton from pallet picking
tTp
Lic
Single order line processing time in the case of carton from pallet picking Carton frontal dimension
Unitary pallet refill time, from reserve area to forward area Unitary carton refill time, from pallet to rack Number of cartons refilled simultaneously from pallet to rack for item i Unitary picking time in the case of carton from rack picking
L ip
Pallet frontal dimension
Dic
Carton depth
Dip
Pallet depth
Hic
Carton height
Hip
Pallet height
Vic
Carton volume
Vip
Pallet volume
Wic
Carton weight
Wtc Dr qic
Threshold for carton weight
qtic
qip
Rack depth Maximum number of cartons storable in the forward area for item i in the case of carton from rack picking Minimum number of cartons to put in the forward area for item i to make the carton from rack picking more convenient than the carton from pallet one Maximum number of cartons storable in the forward area for item i in the case of carton from pallet picking
picking and rack picking, have been considered and compared. It has also been considered that each product code can occupy at maximum one stocking location, both in case of carton from pallet picking and carton from rack picking. Table 1 reports the notations that are used in the formulations. Table 2 shows the different time elements that have been proposed for the analysis. All these time factors refer to a certain time period (e.g. one day, or one month) which is considered to be representative for the analysis and are calculated for each item i. The considered activities and, then, the corresponding times, are:
Considering the time factors introduced, as reported also in Table 2, it can be derived that the total time in the case of carton picking from pallet turns out to be the sum of three time factors:
Tip = tR·
1. Pallet refill from reserve area to forward area: the pallet is moved with a forklift from the reserve area to the forward area. In case of carton from pallet picking, this action is needed to refill the empty storage location with a full pallet. On the other side, in case of carton from rack picking, it is needed to refill the shelving with a part of a pallet, that has then to be replaced in the reserve area. The formulation refers to an average refill time tR , that includes the time to move the pallet from the reserve area to the forward area and the time needed
Qi + tPp·Qi + tTp·Zi qi p
(1)
In the case of carton picking from rack, instead, the times considered lead to the following formula for the total time:
Tic = tR·
L c Hc Dc Qi Q + tHc · i + tPc ·Qi + tTp· ip ip ip ·Zi c qi Bi Li Hi Di
(2)
In order to estimate the possible convenience of picking a product from a rack compared with picking it from a pallet, the two considered global times, Tic and Tip , can be put in a ratio, obtaining the so-called
Table 2 Carton picking time factors.
Carton from pallet picking Carton from rack picking
① Pallet refill from reserve to forward
② Carton refill from pallet to rack
③ Carton picking
④ Travel
Qi p qi Qi tR· c qi
–
tPp·Qi
tTp·Zi
tR·
tHc ·
tPc ·Qi
Qi Bi
90
tTp·
Lic Hic Dic p p p ·Zi Li Hi Di
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After some further mathematical elaborations, the following final relation is obtained:
Carton Pick from rack Convenience Index (CPCI), calculated for a certain product code i:
Tic Tip
CPCIi =
qic tp Qi ⩽ T· p c q q tp Zi tR ⎛ 1− pi i c · tP ·(1−Ric / p ) ⎞ qi − qi R ⎝ ⎠
(3)
In this way, it is easy to assess whether it is more convenient to pick a certain product from a rack than from the pallet, since it is sufficient to verify the following condition:
Tic Tip
CPCIi =
⩽1
in which qi , considering (10), can be substituted with c
Q
i
i
tR·
Qi qip
Lic Hic Dic Z Lip Hip Dip i
+ tPp·Qi + tTp·Zi
⩽1 (5)
At this stage, it is possible to make some algebraic elaborations. First of all, it is possible to define
Dr Dic
qic =
(6)
that is the maximum number of storable cartons in the forward area in case of carton from rack picking, which can be obtained by dividing the depth of the rack Dr by the depth of the carton Dic . On the other side, the maximum number of storable cartons in the forward area in case of carton from pallet picking is:
Vip L p · H p· D p = i c ic ic c Vi Li ·Hi ·Di
qi p =
3.1. Specific cases Starting from the CPCC obtained in the previous section (Eq. (16)), some particular but realistic cases can be presented, leading to a simplification of this formula. The first simplification refers to the case when the carton picking times are comparable (or even equal) for the two alternatives (tPc ≅ tPp or
(7)
Then, the ratio between the terms qic and qi p turns out to be:
qic qi
p
Dr Lic ·Hic ·Dic · Dic Lip ·Hip·Dip
=
tPc = tPp ) and
(8)
qi
p
Lic ·Hic Lip ·Hip
=
Here, by defining x i =
qic ·x i
= qi
qip
(10)
Another simplification is possible when the two picking and tPp , in addition to being equal to each other, are equal also to the unitary carton refill time from pallet to rack (tPc = tPp = tHc ), and when the specific item is refilled from pallet to rack a carton at time (Bi = 1). In fact, in this case the Ric / p ratio is equal to 2, and the CPCC (16) consequently turns out to be
(11)
tp Qi ⩽ T· Zi tR ⎛ 1+ ⎝
t Z qip· H + qip·tPc + tTp· i ·qic Bi Qi
tR Z qip·tPp + tTp· i ·qip Qi
1+
⩽1
tR
which can be elaborated as follows:
qi
qic
qi ·tPp p
p
−1 ⩽
+
Z tTp· Qi ·qi p−(qi p ·tPc i
+
tc qi p · BH i
+
Ric / p =
tR
+
(13)
Hence, Z
qi p ·tPp·(1−Ric / p) + tTp· Qi ·(qi p−qic )
qi
tR
−1 ⩽ c
⎠
(18)
Since formula (16) of the Carton Pick from rack Convenience Condition (CPCC) puts into relation the average number of cartons picked per picking line in the considered time period Qi / Zi to the number of cartons storable in the forward area for that product code qic , it is possible to display this mathematical expression also in a graph. In fact, considering a generic warehouse, in which several different products are stored in pallets in the lower level of the shelving, with various physical and commercial characteristics, it can be useful to have a unique report that shows the items’ different features in order to understand how to
Bi
qi p
tp xi ·q c · P ⎞ xi − 1 i tR
3.2. Parametric analysis
(12)
c tH
tPp
qic
Z tTp· Qi ·qic ) i
At this point, one can introduce the ratio
tPc
(17) times tPc
c
+
Bi
tp Qi ⩽ T ·qic Zi tR
Then, Eq. (5) becomes qic
tc
≪ tPc ( H is negligible). Knowing that tPc refers to the actc
it can also be obtained that
p
Bi
of putting a set of Bi cartons on a rack, all together, BH ≪ tPc is true for i Bi ≫ 1 and for tPc ≅ tHc , expressed in the same time unit. Then, it derives c/p that Ri = 1. Hence, the CPCC formula (16) becomes
(9) Lip Hip , Lic Hic
c tH
tion of picking a single carton from a rack, while tHc refers to the action
And, by assuming that the racks for the cartons have the same depth of the shelving used for pallet storage (Dr = Dip) , the previous equation becomes:
qic
(16)
This last expression represents the general convenience condition for a carton from rack picking with respect to a carton from pallet picking, here called CPCC, the Carton Pick from rack Convenience Condition. This is a comparison that involves the average number of cartons picked for a single order Qi / Zi , the number of cartons stored in the forward area for the product i in the case of cartons from rack picking qic , the refill time tR , the single picking line processing time in the case of pallet storage tTp , the actual pick from pallet time tPp and the ratios Ric / p and x i . This formula represents an easy and effective way of evaluating the possibility of storing a certain item for carton from pallet picking versus carton from rack picking. In particular, assuming such a comparison is true, the corresponding item can be stored on racks; otherwise, it is more suitable to consider storage of the product on pallets.
By substituting the proposed times (1) and (2) and by imposing the CPCI condition (3), the previous formula becomes: Q
x i ·qic :
qi tp Qi ⩽ T· tp Zi tR ⎛ xi 1− ·qic · tP ·(1−Ric / p) ⎞ R ⎝ xi − 1 ⎠
(4)
tR· q ci + tHc · Bi + tPc ·Qi + tTp·
(15)
p
i
(14)
91
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Table 3 Ric / p values varying tPc , tPp and Bi . tPp
Fig. 2. Example of CPCC frontier.
Bi
tPc
8
12
16
1
8 12 16
2.00 3.00
2.00
1.00 1.50 2.00
8 12 16
1.50
2
1.20
5
8 12 16
3.00
1.00 1.50 2.00
0.75 1.50
1.20 1.20
threshold is represented by a straight line (indicating a linear relationship between qic and Qi / Zi ). For this reason, the following analysis shows some of the possible behaviours that can characterize the CPCC frontier according to the values that can be assumed by the different parameters (Fig. 3). The y-axis of the graphs starts from Qi / Zi = 1 since this parameter, representing the average number of picked cartons for item i, is always at least equal to 1. In fact, this means that the picker picks minimum one carton of the product i per picking tour (so each time the picker stops in front of the corresponding picking location he/ she picks no less than one carton of that product). The analysis shown considers the variation of the three variable parameters that characterize the CPCC formula (16): tR, tTp and Ric / p . In
store all these products. In particular, the graph has to report the CPCC as a convenience threshold, and hence as a line on the plot area. Then, products that are placed below the CPCC line should be stored on racks, while those that turn out to be above this line should be stored in pallets (Fig. 2). As can be seen from (16), the profile and the position of the convenience threshold depend on the values of the times (tTp , tR , tPp ) and on the value of xi and Ric / p . For example, when Ric / p = 1 (corresponding xi − 1 to one of the specific cases presented in Section 3.1), the CPCC
Fig. 3. CPCC frontier parametric analysis, varying tR , tTp and Ric / p . 92
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• if W
particular, for Ric / p the displayed values refer to the values of tPc , tPp and Bi as reported in Table 3. Fig. 3 shows that changing the single order line processing time in the case of cartons from pallet picking tTp leads to a shift of the CPCC threshold: by increasing tTp the CPCC threshold moves upwards. In fact, if the time needed to retrieve a general product code from a warehouse in which the items are stored in pallets is higher, it is logical that the convenience of picking cartons from the rack area becomes greater. On the contrary, the increase of the unitary pallet refill time from the forward area to the reserve area tR makes picking the cartons from pallets more convenient, with a lowering of the CPCC threshold. Finally, by varying Ric / p , it is possible to see that with the increase of this parameter the CPCC threshold moves down, always becoming flatter when Ric / p > 1. In fact, for these values of Ric / p the carton from rack convenience area becomes very small and refers only to products that are picked with a few cartons per time (low values of Qi / Zi ). Moreover, from Fig. 3 it can be seen that for Ric / p = 1 the CPCC threshold is represented by a straight line. Then, considering Ric / p as a fixed value, it can be observed that the position of the threshold is influenced more by the change in the values of tR than of tTp .
c i
⩽ Wtc , the procedure can continue with the following steps 3
and 4
4.1.3. CPCC calculation In order to compute the Carton Pick from rack Convenience Condition (CPCC), the parameters qic (Eq. (6)), qi p (Eq. (7)) and, then, x i , have to be calculated for each item i. These are, respectively: the maximum number of cartons storable in the forward area in the case of carton from rack picking, in the case of carton from pallet picking, and their ratio. Moreover, it is necessary to determine the value of the ratio Ric / p with (13). Once all these factors are known, the CPCC (Eq. (16)) can be applied, comparing the way item i is usually picked (Qi / Zi ) with a ratio that depends on its physical characteristics and some general standard times of the warehouse.
4.1.4. Stock mode decision The CPCC (Eq. (16)) allows to establish the best storage and, then, the best picking mode for each item i:
• if
4. Carton picking convenience decision-making methodology
Qi Zi
⩽
tTp
qic
·
p tR ⎛ xi c/p ⎞ c tP ⎜1 − xi − 1 ·qi · tR ·(1 − Ri ) ⎟ ⎝ ⎠
, the cartons of item i should be stored
on a rack and picked from it, with a carton from rack picking approach
4.1. Decision-making methodology description
• if
Starting from the Carton Pick from rack Convenience Condition (16) introduced and studied in the previous section, a decision-making procedure is proposed here. This is composed of four subsequent steps, which lead to the final decision on the storing mode for all items i under study, comparing the carton from pallet picking with the carton from rack picking.
Qi Zi
>
tTp
qic
·
p tR ⎛ xi c/p ⎞ c tP ⎜1 − xi − 1 ·qi · tR ·(1 − Ri ) ⎟ ⎝ ⎠
, item i should be stored on a pallet
and picked directly from it, with a carton from pallet picking approach
• the carton information for each item i: frontal dimension L , depth D , height H , weight W and volume V ; the • orders information for each item i: number of picking lines for
The application of the methodology to all the items under study allows to have a general overview of the different stock modes that are required in the warehouse. This is useful to get a proper dimensioning of the whole stocking area, distinguishing between the picking area with pallets and the one with racks. The here proposed procedure stops with this result, considering the trade-off between reducing the movements of the pallets from the reserve area to the forward area and reducing the distances travelled by the operators, for all the stored items. For now, it is assumed that each item has only one stock location in the forward area, represented by a pallet place or by a place in the rack. The further dimensioning and the design of the picking area is left to a following study (see, for example, Bartholdi & Hackman, 2017).
•
4.2. Decision-making methodology application in a case study
4.1.1. Data collection The application of the decision-making process starts with the retrieval of all the data that are needed for the subsequent computations. These deal with some physical information of all items i, with their picking orders in a certain time period and with some standard times that describe the warehouse configuration in which the items are stored. In particular, they are: c i
c i
•
c i
c i
c i
item i Zi processed in the analysed time period and number of cartons Qi picked in the same time range; the pallet information for each item i: frontal dimension Lip , depth Dip , height Hip , as well as Bi , the number of cartons that are eventually packed together and that can be handled together, corresponding to the number of cartons refilled simultaneously for item i; the standard times data: unitary refill time tR , single order line processing time tTp , picking times tPp and tPc and unitary carton refill time from pallet to rack tHc .
The proposed case study deals with a low-level picker-to-parts manual warehouse of a major supermarkets supplier, where various kinds of food and non-food products are stored. The analysis concerns the picking mode decision for 11,342 different product codes that initially were all stored in EUR-pallets, with a total stocking length of 9,074 m. Seventy pickers are employed on two work shifts per day, for 30 days per month, for a total time of 14,481 h.
4.1.2. Weight threshold application Once all the needed data are known, the next step to perform is a check of the weight. In fact, if the weight of the carton of item i is greater than the carton weight that has been chosen as a threshold Wtc , for example, taking as a reference a specific ergonomic requirement (Waters, Putz-Anderson, Garg, & Fine, 1993), it is suggested to pick the corresponding item directly from pallets. In fact, putting its cartons on the racks would require a double movement of heavy objects, to refill the racks and then to process the picking orders (Calzavara, Glock, Grosse, Persona, & Sgarbossa, 2017). Hence, for each item i it has to be checked:
•
Table 4 Input values (* the same for all items i). Parameter
Value
tR tTp
120 s 30 s
tPp
10 s
L ip Di
if Wic > Wtc , item i has to be stored on pallets, for carton from pallet picking, and the procedure stops here
p
Wtc
93
800 mm* 1200 mm* 5 kg
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Table 5 Classification of the products according to Ric / p and xi xi − 1
they influence the trend of the CPCC frontier. It follows that the various products cannot be studied all together; however, the items can be grouped exactly according to their values of Ric / p and xi . A summary xi − 1 of the results obtained for these two parameters is given in Table 5, reporting a classification of the various product codes according exactly to their Ric / p and xi . It can be observed that most of the product codes
xi . xi − 1
Ric / p 1.0–1.1
1.1–1.2
1.2–1.3
1.3–1.4
1.5–1.6
1.9–2.0
Total
1–2 2–3 3–4 4–5
403 1
59
21
3
9
7,187
7,682 1 0 0
Total
404
59
21
3
9
7,187
7,683
xi − 1
x
have 1 ⩽ x −i 1 < 2 , meaning that x i is often much higher than 1. Then, i there are two main groups of items: one group of 404 items having c/p 1 < Ri ⩽ 1.1 and another one of 7,187 codes having 1.9 < Ric / p ⩽ 2 . As a consequence, the proposed analysis continues with the focus on these two main groups of product codes.
4.2.4. Stock mode decision Fig. 4 shows the application of the CPCC to the first group made up of 404 items, having 1.0 < Ric / p ⩽ 1.1. For each product code, characterised by a specific value of qic and of Qi / Zi , there is a corresponding point on the graph. The figure is focused on the area of the graph that includes the CPCC frontier, which is the line shown. It can be seen that, since Ric / p ≅ 1, the CPCC frontier is very similar to a straight line. The 212 products that turn out to be positioned under the CPCC frontier are those that can be stored for carton from rack picking, while the other 192 that are positioned above the line are more suitable to be picked directly from the pallet. In Fig. 5 some examples of both kinds of products (for pallet picking and for rack picking) are reported: besides their qic and Qi / Zi values, their position on the plot and a generic description are shown. Fig. 6 reports the same analysis, performed for the group of 7,187 products having 1.9 < Ric / p ⩽ 2.0 . In this case, too, the figure is focused on the area of the graph with the CPCC frontier. The products whose results are above the CPCC frontier and that can be picked directly from the pallet number 4,671, while the products that can be stored on the racks and picked from them total 2,516. Some of these products are proposed as an example in Fig. 7. A final comparison useful to understand the potential of such a study is reported on Table 6. This shows the number of items and the total time factors in hours (refill time, picking time, travel time and
4.2.1. Data collection Table 4 reports all the general data that have been calculated and measured for the application of the method introduced before. The data of the picking orders refer to one month, with a total of 1,160,821 picking lines for all codes. The corresponding total time for processing these orders is 14,481 h. 4.2.2. Weight threshold application The weight threshold limit that has been chosen is Wtc = 5 kg . After the application of this filter, the number of items that have to be put directly in a carton from pallet picking mode is 3,659, while those that can be further analysed total 7,683. 4.2.3. CPCC calculation For each of these 7,683 items, the parameters qic and qi p can be calculated with (6) and (7). For qic , it is considered that the carton depth Dic can be approximated with 3 Vic , since at this level of the study it is not important to know exactly how the item is stored on the rack (i.e. which dimension of the carton corresponds to Dic ). Then, in order to continue the study, the ratios Ric / p and xi have to xi − 1 be calculated for each product. In fact, both these parameters vary according to the characteristics of the product but, at the same time,
Fig. 4. Application of the method to the products having 1 ⩽
94
xi xi − 1
< 2 and 1.0 < Ric / p ⩽ 1.1.
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Fig. 5. Examples of products having 1 ⩽
xi xi − 1
< 2 and 1.0 < Ric / p ⩽ 1.1.
Fig. 6. Application of the method to the products having 1 ⩽
xi xi − 1
< 2 and 1.9 < Ric / p ⩽ 2.0 .
picking from racks (18,161 h). In particular, this led to a reduction of the workers employed in the picking activity of about 3%. Moreover, it allows to reach an interesting compromise also in terms of stocking length, with a warehouse length reduction of 2,701 meters compared to the case in which all items are stored on pallets. Finally, Fig. 8 shows the comparison of the starting configuration of the warehouse with the one obtained after the application of the CPCC method, referring to some of the items under study. As can be seen on the left of the figure, some of the items that were stored in pallets are stored in pallets also after the application of the methodology, due to their weight and/or to their picking frequency. On the contrary, on the right of Fig. 8 it is reported the case of some items that have been moved from a carton from pallet picking approach to a carton from rack picking one.
total time) required to process all the considered picking lists for three different cases. The first case deals with the starting configuration, with all items stored in pallets on the ground floor of the warehouse, the second one considers all items stored on a shelving with various levels, while the last one refers to the CPCC method proposed here, with a certain combination of items stored on pallets and items stored on racks. The same table also shows the total stocking length (in meters) resulting from the three different scenarios. This parameter roughly specifies the length of the whole warehouse, and it is calculated considering Lip = 0.8 m for all items and the various Lic , which have also been divided by the number of possible levels of the shelving. It can be seen that the CPCC method leads to a reduction on the total time (14,207 h), both compared to picking from pallets (14,639 h) and 95
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Fig. 7. Examples of products having 1 ⩽
xi xi − 1
< 2 and 1.9 < Ric / p ⩽ 2.0 .
Table 6 Number of items, stocking length and total time factors comparison for all in pallets stocking, all in racks stocking and CPCC method. All in pallets
All in racks
CPCC method
Number of items
On pallets On racks
11,342 –
– 11,342
7,079 4,263
11,342
Stocking length [m]
On pallets On racks
9,074 –
– 1,890
5,663 710
6,373
Total pallet refill time [h]
On pallets On racks
791 –
– 12,627
735 2,107
2,842
Total carton refill time [h]
On pallets On racks
– –
– 835
– 196
196
Total picking time [h]
On pallets On racks
4,175 –
– 4,175
3,193 982
4,175
Total travel time [h]
On pallets On racks
9,673 –
– 524
6,924 70
6,994
Total time [h]
On pallets On racks
14,639 –
– 18,161
10,852 3,355
14,207
5. Discussion of results
As far as the CPCC frontier is concerned, it can be seen that in the case of 1.0 < Ric / p ⩽ 1.1 it intersects the x-axis for qic ≅ 4 , while for 1.9 < Ric / p ⩽ 2.0 the intersection is for qic ≅ 6. Since qic is the maximum number of cartons storable in the forward area, it follows that the products that are more suitable for carton from rack picking are those that have a medium-small carton volume, hence, medium-small average carton physical dimensions and that are picked in small quantities per picking list (right-bottom area of the graph). Then, the convenience threshold has an increasing trend, since the convenience of putting the product in racks with respect to pallets increases if the item has a higher qic . Hence, it has a smaller volume and it occupies a smaller space in the warehouse, even if it is averagely picked at a higher number of cartons per time (higher values of Qi / Zi ). Considering the cases reported in Fig. 5, it emerges, for example, that the products E and F, having a very similar Qi / Zi , are more suitable to be stored in two different ways: the nylon ladle, with a lower qic , can be picked from the pallet, the pencil with eraser (qic = 5.24 ) from the rack. On the other hand, although the products A and H have the same qic , the first one has to be stored in pallets while the second one on racks, since they have a significant difference in the number of cartons required per time (resulting in, respectively, a high and a low
The case study presented in the previous section can offer some interesting insights about the results obtained as well as on the general application of the method. First of all, it has turned out that, due to their characteristics, for 3,355 out of 7,683 products it is more suitable to store them on racks with respect to a direct storage on pallets (Table 6). These products could then be placed in a separated picking area, organized in racks or with other smart solutions instead of with pallets (Battini, 2016). Hence, considering the number of pallet stock locations (3,355) that are no longer needed, it derives that the distances travelled on average by the operators are very reduced (Table 6). From the analysis of the graphs reported in Figs. 4 and 6, it can be highlighted that a great number of the items analysed, with a weight Wic < 5 kg , are characterised by a Qi / Zi < 1.5, meaning that every time the warehouse operators pick such products the number of picked cartons is very low, typically 1 or 2. Many products (2,989 items) even have exactly Qi / Zi = 1. This also represents an important confirmation of what has been pointed out as a common and recent trend in picking warehouses, in which customers are requiring ever smaller quantities per product (De Koster et al., 2007; Lu, McFarlane, Giannikas, & Zhang, 2016). 96
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Fig. 8. Warehouse configuration comparison: before and after CPCC method application.
terms of the volume occupied by the items, avoiding useless waste of warehouse space. As a consequence, this reduction leads to a decrease of the average distances that are travelled by the picking operators, with an important positive impact on the overall warehouse performance (Tompkins et al., 2010; Battini et al., 2015).
value of Qi / Zi ). Similar differences are reported in Fig. 7: although the average number of cartons picked per picking tour Qi / Zi is very similar for almost all the proposed products, the way they have to be stored for picking is different, considering their qic , and hence, their volume. Nevertheless, it is fundamental to underline that the CPCC frontier and the two consequent areas of the graph that have been identified depend strongly on the input times tR , tTp and tPp , which can normally be considered as general parameters of the warehouse. As shown in the parametric analysis of Section 3.2, provided that the time needed to perform a pallet refilling is substantially higher than the single order line processing time, the carton from rack picking area is interesting and can involve a significant number of storable items. If this ratio decreases, however, the carton from rack picking convenience turns out to affect only few items. In fact, although the presented method proves to be very effective as well as easily applicable, it requires particular attention to the way the input data are obtained and managed. This is especially true in the case of the refill time tR of the single order line processing time tTp and of the unitary picking time tPp . Furthermore, the convenience study presented in this paper could be applied also in another interesting way. In fact, once all the other characteristics of the warehouse and of a certain analysed product are known, from the CPCC formula (16) it is possible to calculate a socalled threshold qic , qtic , representing the minimum number of cartons that have to be put in the forward area to make the carton from rack picking more convenient than the carton from pallet picking:
qtic =
Qi / Zi tPp Qi xi · · ·(1−Ric / p) Zi xi − 1 tR
+
tTp tR
6. Conclusions and further research The present paper has introduced a new decision-making methodology that can be used to understand how to store all the various products that are in a picking warehouse. In particular, it refers to the choice between storing a product in pallets or in racks. Starting from the times needed to perform both kinds of picking, which depend on simple and easily obtainable item and warehouse information, the socalled Carton Pick from rack Convenience Condition (CPCC) has been formulated. After having proposed a parametric analysis, the decisionmaking methodology has been described. Moreover, the application of the new method has been shown in a real industrial case study, dealing with a food and non-food picking warehouse of a big supermarkets supplier. The proposed procedure turns out to be particularly interesting since it is easy and fast to apply; furthermore, it can be suitable for several different contexts, concerning warehouse manual picking as well as assembly lines feeding picking. Future research concerning this topic is intended to extend the model and the method here proposed in order to allow the estimation of the actual saving obtainable through the storage of some items in racks instead of in pallets, in terms of reduction of the time needed to perform the picking tour and, as a consequence, in terms of reduction of the picking costs. Furthermore, this method will be applied to more case studies, in order to understand the possibility of always applying the simplified CPCC (Eqs. (17) and (18)) instead of the full one.
(19)
Finally, it is important to point out that the application of such a methodology in a picking warehouse can lead to important benefits in 97
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References
Frazelle, E. H., Hackman, S. T., Passy, U., & Platzman, L. K. (1994). The forward-reserve problem. In T. C. Ciriani, & R. C. Leachman (Eds.). Optimization in industry 2 (pp. 43– 61). New York: Wiley. Gu, J., Goetschalckx, M., & McGinnis, L. F. (2007). Research on warehouse operation: A comprehensive review. European Journal of Operational Research, 177(1), 1–21. Gu, J., Goetschalckx, M., & McGinnis, L. F. (2010). Research on warehouse design and performance evaluation: A comprehensive review. European Journal of Operational Research, 203(3), 539–549. Hackman, S. T., & Rosenblatt, M. J. (1990). Allocating items to an automated storage and retrieval system. IIE Transactions, 22(1), 7–14. Lu, W., McFarlane, D., Giannikas, V., & Zhang, Q. (2016). An algorithm for dynamic order-picking in warehouse operations. European Journal of Operational Research, 248(1), 107–122. Rouwenhorst, B., Reuter, B., Stockrahm, V., Van Houtum, G. J., Mantel, R. J., & Zijm, W. H. M. (2000). Warehouse design and control: Framework and literature review. European Journal of Operational Research, 122(3), 515–533. Thomas, L. M., & Meller, R. D. (2015). Developing design guidelines for a case-picking warehouse. International Journal of Production Economics in press. Tompkins, J. A., White, J. A., Bozer, Y. A., & Tanchoco, J. M. A. (2010). Facilities planning. NJ: John Wiley & Sons. Van den Berg, J. P., Sharp, G. P., Gademann, A. N., & Pochet, Y. (1998). Forward-reserve allocation in a warehouse with unit-load replenishments. European Journal of Operational Research, 111(1), 98–113. Walter, R., Boysen, N., & Scholl, A. (2013). The discrete forward–reserve problem – Allocating space, selecting products, and area sizing in forward order picking. European Journal of Operational Research, 229(3), 585–594. Waters, T. R., Putz-Anderson, V., Garg, A., & Fine, L. J. (1993). Revised NIOSH equation for the design and evaluation of manual lifting tasks. Ergonomics, 36(7), 749–776.
Bartholdi, J. J., & Hackman, S. T. (2017). Warehouse and distribution science. Release 0. 98, Atlanta, GA. Bartholdi, J. J., & Hackman, S. T. (2008). Allocating space in a forward pick area of a distribution center for small parts. IIE Transactions, 40, 1046–1053. Battini, D., Calzavara, M., Otto, A., & Sgarbossa, F. (2017). Preventing ergonomic risks with integrated planning on assembly line balancing and parts feeding. International Journal of Production Research, 1–21. Battini, D., Calzavara, M., Persona, A., & Sgarbossa, F. (2015). Order picking system design: The storage assignment and travel distance estimation (SA&TDE) joint method. International Journal of Production Research, 53(4), 1077–1093. Battini, D., Calzavara, M., Persona, A., & Sgarbossa, F. (2016). Dual-tray vertical lift modules for fast order picking. 14th International material handling research colloquium (IMHRC 2016), 12–16 June 2016, Karlsruhe, Germany. Bozer, Y. A. (1985). Optimizing throughput performance in designing order picking systems. PhD thesisGeorgia Institute of Technology. Calzavara, M., Glock, C., Grosse, E., Persona, A., & Sgarbossa, F. (2017). Analysis of economic and ergonomic performance measures of different rack layouts in an order picking warehouse. Computers & Industrial Engineering, 111, 527–536. Calzavara, M., Hanson, R., Sgarbossa, F., Medbo, L., & Johansson, M. I. (2017). Picking from pallet and picking from boxes: A time and ergonomic study. IFAC-PapersOnLine, 50(1), 6888–6893. Caron, F., Marchet, G., & Perego, A. (2000). Optimal layout in low-level picker-to-part systems. International Journal of Production Research, 38(1), 101–117. De Koster, R., Le-Duc, T., & Roodbergen, K. J. (2007). Design and control of a warehouse order picking: A literature review. European Journal of Operational Research, 182(2), 481–501.
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A method to choose between carton from rack picking or carton from pallet picking
T
⁎
Daria Battini, Martina Calzavara , Alessandro Persona, Fabio Sgarbossa Department of Management and Engineering, University of Padua, Stradella San Nicola, 3, 36100 Vicenza, Italy
A R T I C LE I N FO
A B S T R A C T
Keywords: Warehouse picking Picker-to-parts Items storage Design methodology
In a manual picker-to-parts picking warehouse, a usual approach is to divide the whole stocking area in two different zones, the reserve and the forward areas. The dimensioning of the forward area, which is dedicated to picking activities, has an important impact on the overall performance of the picking system. Indeed, its size as well as the item allocation deeply influence the travel time of the operators on one side and the frequency of the refilling activities on the other. The present paper aims to provide a new method that can be easily used to assess the most suitable way of storing a product in the forward area, considering the possibility of keeping a product directly in a pallet or storing it in racks. Starting from simple data, such as the picking orders of the items to pick and their physical dimensions, as well as the characteristics of the warehouse, the method focuses on the comparison of the total times to define the Carton Pick from rack Convenience Condition (CPCC). The CPCC formulation and its application methodology allow to quickly establish which items should be stored on pallets and which on racks, with interesting impacts on space and time savings. This is shown also in the reported case study, the results of which prove the effectiveness as well as the easy and full applicability of the methodology, also in different warehouse contexts.
1. Introduction and background Warehouse manual picking is the activity performed within a warehouse by a human operator to retrieve products required by one or more customers. Due to its characteristics, the picking activity is often the target of several studies and debates, which propose various methods that can be used to solve its main issues (Thomas & Meller, 2015). In particular, one of the main topics dealt with in the literature concerns warehouse performance improvement, through the reduction of the time needed to process the picking orders, and, as a consequence, of the time spent travelling from one stock location to another one (De Koster, Le-Duc, & Roodbergen, 2007; Tompkins, White, Bozer, & Tanchoco, 2010). Strictly linked to the question of performance increase and distance reduction is the problem of the dimensioning and allocation of the forward and reserve areas. The forward picking area is generally a subregion of the warehouse dedicated to the pick and the order activities; such activities are often concentrated in a small physical space, in order to warrant more processing efficiency. On the other hand, the reserve area is the part of the warehouse designed for storage of bulk pallets, which are also used for the replenishment of the forward area
(Rouwenhorst et al., 2000; De Koster et al., 2007; Bartholdi & Hackman, 2017). The forward area and the reserve area can also be located in the same zone of the warehouse: in this case, the stockkeeping units (SKUs) of the forward area are on the lower floor of the shelving (ground floor), while on the other upper racks there are the SKUs for bulk storage and replenishment. In such a configuration, also called low-level picker-to-parts system, the SKUs of the forward area are usually pallets, with one pallet for each one of the different product codes that are needed for order picking (Caron, Marchet, & Perego, 2000). The allocation and dimensioning issues for these two warehouse zones have been studied by many researchers, with several proposed models and methods. In general, most of the authors underline that during the design of such zones a fundamental trade-off has to be considered. This deals with the fact that by enlarging the forward area through the introduction of more stock keeping units, there is a saving due to a faster picking and to a reduction in the number of restocks; however, such benefits are inevitably accompanied by an increase of the distances travelled to process the picking orders, leading to a reduction (and in some cases also a nullification) of the first possible saving (Gu, Goetschalckx, & McGinnis, 2007). Hence, it follows that the
⁎
Corresponding author. E-mail addresses: [email protected] (D. Battini), [email protected] (M. Calzavara), [email protected] (A. Persona), [email protected] (F. Sgarbossa). https://doi.org/10.1016/j.cie.2018.09.017 Received 27 January 2017; Received in revised form 9 June 2018; Accepted 7 September 2018 Available online 08 September 2018 0360-8352/ © 2018 Elsevier Ltd. All rights reserved.
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Fig. 1. Carton from pallet picking and carton from rack picking.
space reduction, it is demonstrated that there could be also time savings and ergonomics benefits. The present paper proposes a design methodology that can be used to understand the best way of storing goods in a warehouse forward picking area. Starting from simple information referring to the stored item, including also the characteristics of the carton and pallet employed, together with some typical warehouse times, it allows to establish, for every single product, whether this is more suitable for carton picking from a rack or from a pallet. The proposed method considers a typical picking low-level picker-to-parts warehouse configuration, where the forward area is on the ground level of the shelving, and the various items are stored on pallets, with only one stock location dedicated to each item. Then, the procedure allows to evaluate if this configuration is the most suitable one for a certain item, or if it is better to stock it in a specific warehouse aisle, in which the cartons are stored on racks. Fig. 1 shows the comparison of the two alternatives under study: on the left, the carton from pallet picking configuration; on the right, the carton from rack picking one. Also in this latter case, each stock location is dedicated to one product code. Moreover, according to the depth of the shelving, there could be the possibility of storing more than one carton of the same item in the same stock location, one behind the other. In order to give a clear exposition of the proposed methodology, the remainder of the paper is structured as follows. The following section reports the mathematical modelling of the problem, leading to the introduction of the so-called Carton Pick from rack Convenience Condition (CPCC). Subsequently, two individual cases are presented, referring to as many circumstances that are observable in practice and that can lead to a simplification of the CPCC formula. The same formula is then studied through a parametric analysis, to help understanding which parameters mainly influence the storage decision of a certain product code. Once the mathematical formulation has been described and proved, Section 4 introduces the full decision-making procedure, reporting also an example of application of the method in a real industrial case study. Furthermore, Section 5 comments upon the results obtained, while in the concluding paragraph some final considerations and ideas for further research are suggested.
design of the forward area has to consider both these conflicting aspects: some authors propose models that can be used to assess the most suitable dimensions, while others are focused on the choice of which SKUs should be stored within. The first contribution on the so-called forward-reserve problem is by Bozer (1985), in which it is acknowledged the usefulness of splitting the warehouse shelving into an upper reserve area and a lower forward picking area. Hackman and Rosenblatt (1990) start from this idea proposing a heuristic based on the knapsack problem. The objective is to decide which SKUs have to be assigned to a forward area of a fixed dimension, minimizing the total material handling costs of order picking and refilling. Frazelle, Hackman, Passy, and Platzman (1994) extend this method, modelling the investment costs and the material handling costs and considering the dimension of the forward area as a variable. Van den Berg, Sharp, Gademann, and Pochet (1998) focus on the storage replenishment from the reserve area to the forward one, minimizing the impact of this activity from a time perspective. Bartholdi and Hackman (2008, 2017) deeply study the dimensioning of the forward area, from various points of view, taking into account the trade-off between the number of items to store, the number of restocks and the occupied space. Walter, Boysen and Scholl (2013) propose to investigate discrete forward-reserve problems, comparing them with the fluid ones. The focus is the sizing of the forward area, taking into account space allocation and products selection. 2. Description and aim of the study An interesting question concerning the forward-reserve problem, that until now has received very little attention, concerns the decision on how to store a certain item in the forward area. This problem is typically not often addressed, either in the literature or in industrial contexts, since in many cases the products stocking mode is defined a priori, referring only to people’s experience or common sense and considering only a limited number of the aspects that can, in fact, come into play. For example, warehouse managers could decide to store all the products in a pallet in order to warrant easier warehouse management and maintenance. Alternatively, they could establish that small dimension items have to be stored in cartons and picked directly from racks, without considering how frequently they are ordered. However, an indepth study in this field, leading to an understanding of the possible convenience of storing a certain item in a certain way with respect to another one can bring relevant benefits. Among others, establishing that some product codes are more conveniently picked from racks than from a pallet implies a potential reduction of the space needed for storing such items in the forward area, with a subsequent decrease of the distances travelled by the pickers to process the picking orders and of the overall picking time (Tompkins et al., 2010). A very similar problem has already been addressed successfully in assembly systems design. Various methods and models have been proposed to evaluate and compare the feeding and the picking activity, when these are done with pallets or from boxes (Battini, Calzavara, Otto, & Sgarbossa, 2017; Calzavara, Hanson, Sgarbossa, Medbo, & Johansson, 2017). Besides to a
3. The carton pick from rack convenience condition (CPCC) As far as manual warehouse picking is concerned, there are several factors that can usually influence the outcomes of a picking tour. One of the most widespread and proven ways of describing and evaluating a manual warehouse picking system is to consider the time spent in processing a picking order. In fact, such time is indicative of the overall performance of the picking system, and it can be used as a reference to understand the effectiveness of any change that can be introduced. If a certain change leads to a decrease of the picking time, it means that probably this change deserves to be implemented (Gu, Goetschalckx, & McGinnis, 2010; Tompkins et al., 2010). For the study presented in this paper, the various time components involved in the picking process, in the case of cartons from both pallet 89
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to restore the storage in the reserve area, for both stocking alternatives. In fact, for carton from pallet picking, once a full pallet is moved to the forward area, there is the need of taking another pallet, to fill the empty stock location in the reserve area for that product code. For carton from rack picking, since in the forward area only a part of the full pallet can be stored, there is the need of replacing in the reserve area the remaining pallet. The total time for this activity depends on the average time for performing a single refill activity tR and the refill frequency, obtained by dividing the number of cartons of item i picked in the considered time period Qi (Battini, Calzavara, Persona, & Sgarbossa, 2015) by the maximum number of cartons storable in the forward area (qic in the case of picking from a rack, qi p in the case of picking from a pallet). 2. Cartons refill from pallet to rack: the warehouse operators put the cartons in the racks to restore the forward area for subsequent picking. The time needed depends on the frequency of this action, obtained dividing the number of cartons picked in the considered time period Qi by the number of cartons that can be refilled simultaneously Bi . Of course, this activity is needed only for carton from rack picking. 3. Carton picking: the pickers do the actual physical pick of the carton while processing the picking orders; again, the time needed is proportional to the number of cartons picked in the considered time period Qi . 4. Travel: the pickers move from one stocking location to another while processing the manual picking orders. The corresponding total time depends on the time for processing a single order line in a forward area with pallets, tTp , and the number of times the pickers have to visit the same storage location of item i during the considered time period. This corresponds to Zi , the number of picking lines (and, then, picking orders) requiring item i. Moreover, for carton from rack picking, it is assumed that the travel distance and, then, the travel time, is reduced by a factor that takes into account the different dimensions of a pallet and of a carton. In fact, considering the same space in a forward area, in case of carton from rack picking the different items that can be stored are more than in case of carton from pallet picking, as shown in Fig. 1.
Table 1 Notations. Notation
Description
i Qi Zi Tic
Item index Number of cartons of item i picked in the considered time period Number of picking lines of item i in the considered time period Total time for item i in the case of carton from rack picking
Tip tR tHc Bi tPc
Total time for item i in the case of carton from pallet picking
tPp
Unitary picking time in the case of carton from pallet picking
tTp
Lic
Single order line processing time in the case of carton from pallet picking Carton frontal dimension
Unitary pallet refill time, from reserve area to forward area Unitary carton refill time, from pallet to rack Number of cartons refilled simultaneously from pallet to rack for item i Unitary picking time in the case of carton from rack picking
L ip
Pallet frontal dimension
Dic
Carton depth
Dip
Pallet depth
Hic
Carton height
Hip
Pallet height
Vic
Carton volume
Vip
Pallet volume
Wic
Carton weight
Wtc Dr qic
Threshold for carton weight
qtic
qip
Rack depth Maximum number of cartons storable in the forward area for item i in the case of carton from rack picking Minimum number of cartons to put in the forward area for item i to make the carton from rack picking more convenient than the carton from pallet one Maximum number of cartons storable in the forward area for item i in the case of carton from pallet picking
picking and rack picking, have been considered and compared. It has also been considered that each product code can occupy at maximum one stocking location, both in case of carton from pallet picking and carton from rack picking. Table 1 reports the notations that are used in the formulations. Table 2 shows the different time elements that have been proposed for the analysis. All these time factors refer to a certain time period (e.g. one day, or one month) which is considered to be representative for the analysis and are calculated for each item i. The considered activities and, then, the corresponding times, are:
Considering the time factors introduced, as reported also in Table 2, it can be derived that the total time in the case of carton picking from pallet turns out to be the sum of three time factors:
Tip = tR·
1. Pallet refill from reserve area to forward area: the pallet is moved with a forklift from the reserve area to the forward area. In case of carton from pallet picking, this action is needed to refill the empty storage location with a full pallet. On the other side, in case of carton from rack picking, it is needed to refill the shelving with a part of a pallet, that has then to be replaced in the reserve area. The formulation refers to an average refill time tR , that includes the time to move the pallet from the reserve area to the forward area and the time needed
Qi + tPp·Qi + tTp·Zi qi p
(1)
In the case of carton picking from rack, instead, the times considered lead to the following formula for the total time:
Tic = tR·
L c Hc Dc Qi Q + tHc · i + tPc ·Qi + tTp· ip ip ip ·Zi c qi Bi Li Hi Di
(2)
In order to estimate the possible convenience of picking a product from a rack compared with picking it from a pallet, the two considered global times, Tic and Tip , can be put in a ratio, obtaining the so-called
Table 2 Carton picking time factors.
Carton from pallet picking Carton from rack picking
① Pallet refill from reserve to forward
② Carton refill from pallet to rack
③ Carton picking
④ Travel
Qi p qi Qi tR· c qi
–
tPp·Qi
tTp·Zi
tR·
tHc ·
tPc ·Qi
Qi Bi
90
tTp·
Lic Hic Dic p p p ·Zi Li Hi Di
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After some further mathematical elaborations, the following final relation is obtained:
Carton Pick from rack Convenience Index (CPCI), calculated for a certain product code i:
Tic Tip
CPCIi =
qic tp Qi ⩽ T· p c q q tp Zi tR ⎛ 1− pi i c · tP ·(1−Ric / p ) ⎞ qi − qi R ⎝ ⎠
(3)
In this way, it is easy to assess whether it is more convenient to pick a certain product from a rack than from the pallet, since it is sufficient to verify the following condition:
Tic Tip
CPCIi =
⩽1
in which qi , considering (10), can be substituted with c
Q
i
i
tR·
Qi qip
Lic Hic Dic Z Lip Hip Dip i
+ tPp·Qi + tTp·Zi
⩽1 (5)
At this stage, it is possible to make some algebraic elaborations. First of all, it is possible to define
Dr Dic
qic =
(6)
that is the maximum number of storable cartons in the forward area in case of carton from rack picking, which can be obtained by dividing the depth of the rack Dr by the depth of the carton Dic . On the other side, the maximum number of storable cartons in the forward area in case of carton from pallet picking is:
Vip L p · H p· D p = i c ic ic c Vi Li ·Hi ·Di
qi p =
3.1. Specific cases Starting from the CPCC obtained in the previous section (Eq. (16)), some particular but realistic cases can be presented, leading to a simplification of this formula. The first simplification refers to the case when the carton picking times are comparable (or even equal) for the two alternatives (tPc ≅ tPp or
(7)
Then, the ratio between the terms qic and qi p turns out to be:
qic qi
p
Dr Lic ·Hic ·Dic · Dic Lip ·Hip·Dip
=
tPc = tPp ) and
(8)
qi
p
Lic ·Hic Lip ·Hip
=
Here, by defining x i =
qic ·x i
= qi
qip
(10)
Another simplification is possible when the two picking and tPp , in addition to being equal to each other, are equal also to the unitary carton refill time from pallet to rack (tPc = tPp = tHc ), and when the specific item is refilled from pallet to rack a carton at time (Bi = 1). In fact, in this case the Ric / p ratio is equal to 2, and the CPCC (16) consequently turns out to be
(11)
tp Qi ⩽ T· Zi tR ⎛ 1+ ⎝
t Z qip· H + qip·tPc + tTp· i ·qic Bi Qi
tR Z qip·tPp + tTp· i ·qip Qi
1+
⩽1
tR
which can be elaborated as follows:
qi
qic
qi ·tPp p
p
−1 ⩽
+
Z tTp· Qi ·qi p−(qi p ·tPc i
+
tc qi p · BH i
+
Ric / p =
tR
+
(13)
Hence, Z
qi p ·tPp·(1−Ric / p) + tTp· Qi ·(qi p−qic )
qi
tR
−1 ⩽ c
⎠
(18)
Since formula (16) of the Carton Pick from rack Convenience Condition (CPCC) puts into relation the average number of cartons picked per picking line in the considered time period Qi / Zi to the number of cartons storable in the forward area for that product code qic , it is possible to display this mathematical expression also in a graph. In fact, considering a generic warehouse, in which several different products are stored in pallets in the lower level of the shelving, with various physical and commercial characteristics, it can be useful to have a unique report that shows the items’ different features in order to understand how to
Bi
qi p
tp xi ·q c · P ⎞ xi − 1 i tR
3.2. Parametric analysis
(12)
c tH
tPp
qic
Z tTp· Qi ·qic ) i
At this point, one can introduce the ratio
tPc
(17) times tPc
c
+
Bi
tp Qi ⩽ T ·qic Zi tR
Then, Eq. (5) becomes qic
tc
≪ tPc ( H is negligible). Knowing that tPc refers to the actc
it can also be obtained that
p
Bi
of putting a set of Bi cartons on a rack, all together, BH ≪ tPc is true for i Bi ≫ 1 and for tPc ≅ tHc , expressed in the same time unit. Then, it derives c/p that Ri = 1. Hence, the CPCC formula (16) becomes
(9) Lip Hip , Lic Hic
c tH
tion of picking a single carton from a rack, while tHc refers to the action
And, by assuming that the racks for the cartons have the same depth of the shelving used for pallet storage (Dr = Dip) , the previous equation becomes:
qic
(16)
This last expression represents the general convenience condition for a carton from rack picking with respect to a carton from pallet picking, here called CPCC, the Carton Pick from rack Convenience Condition. This is a comparison that involves the average number of cartons picked for a single order Qi / Zi , the number of cartons stored in the forward area for the product i in the case of cartons from rack picking qic , the refill time tR , the single picking line processing time in the case of pallet storage tTp , the actual pick from pallet time tPp and the ratios Ric / p and x i . This formula represents an easy and effective way of evaluating the possibility of storing a certain item for carton from pallet picking versus carton from rack picking. In particular, assuming such a comparison is true, the corresponding item can be stored on racks; otherwise, it is more suitable to consider storage of the product on pallets.
By substituting the proposed times (1) and (2) and by imposing the CPCI condition (3), the previous formula becomes: Q
x i ·qic :
qi tp Qi ⩽ T· tp Zi tR ⎛ xi 1− ·qic · tP ·(1−Ric / p) ⎞ R ⎝ xi − 1 ⎠
(4)
tR· q ci + tHc · Bi + tPc ·Qi + tTp·
(15)
p
i
(14)
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Table 3 Ric / p values varying tPc , tPp and Bi . tPp
Fig. 2. Example of CPCC frontier.
Bi
tPc
8
12
16
1
8 12 16
2.00 3.00
2.00
1.00 1.50 2.00
8 12 16
1.50
2
1.20
5
8 12 16
3.00
1.00 1.50 2.00
0.75 1.50
1.20 1.20
threshold is represented by a straight line (indicating a linear relationship between qic and Qi / Zi ). For this reason, the following analysis shows some of the possible behaviours that can characterize the CPCC frontier according to the values that can be assumed by the different parameters (Fig. 3). The y-axis of the graphs starts from Qi / Zi = 1 since this parameter, representing the average number of picked cartons for item i, is always at least equal to 1. In fact, this means that the picker picks minimum one carton of the product i per picking tour (so each time the picker stops in front of the corresponding picking location he/ she picks no less than one carton of that product). The analysis shown considers the variation of the three variable parameters that characterize the CPCC formula (16): tR, tTp and Ric / p . In
store all these products. In particular, the graph has to report the CPCC as a convenience threshold, and hence as a line on the plot area. Then, products that are placed below the CPCC line should be stored on racks, while those that turn out to be above this line should be stored in pallets (Fig. 2). As can be seen from (16), the profile and the position of the convenience threshold depend on the values of the times (tTp , tR , tPp ) and on the value of xi and Ric / p . For example, when Ric / p = 1 (corresponding xi − 1 to one of the specific cases presented in Section 3.1), the CPCC
Fig. 3. CPCC frontier parametric analysis, varying tR , tTp and Ric / p . 92
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• if W
particular, for Ric / p the displayed values refer to the values of tPc , tPp and Bi as reported in Table 3. Fig. 3 shows that changing the single order line processing time in the case of cartons from pallet picking tTp leads to a shift of the CPCC threshold: by increasing tTp the CPCC threshold moves upwards. In fact, if the time needed to retrieve a general product code from a warehouse in which the items are stored in pallets is higher, it is logical that the convenience of picking cartons from the rack area becomes greater. On the contrary, the increase of the unitary pallet refill time from the forward area to the reserve area tR makes picking the cartons from pallets more convenient, with a lowering of the CPCC threshold. Finally, by varying Ric / p , it is possible to see that with the increase of this parameter the CPCC threshold moves down, always becoming flatter when Ric / p > 1. In fact, for these values of Ric / p the carton from rack convenience area becomes very small and refers only to products that are picked with a few cartons per time (low values of Qi / Zi ). Moreover, from Fig. 3 it can be seen that for Ric / p = 1 the CPCC threshold is represented by a straight line. Then, considering Ric / p as a fixed value, it can be observed that the position of the threshold is influenced more by the change in the values of tR than of tTp .
c i
⩽ Wtc , the procedure can continue with the following steps 3
and 4
4.1.3. CPCC calculation In order to compute the Carton Pick from rack Convenience Condition (CPCC), the parameters qic (Eq. (6)), qi p (Eq. (7)) and, then, x i , have to be calculated for each item i. These are, respectively: the maximum number of cartons storable in the forward area in the case of carton from rack picking, in the case of carton from pallet picking, and their ratio. Moreover, it is necessary to determine the value of the ratio Ric / p with (13). Once all these factors are known, the CPCC (Eq. (16)) can be applied, comparing the way item i is usually picked (Qi / Zi ) with a ratio that depends on its physical characteristics and some general standard times of the warehouse.
4.1.4. Stock mode decision The CPCC (Eq. (16)) allows to establish the best storage and, then, the best picking mode for each item i:
• if
4. Carton picking convenience decision-making methodology
Qi Zi
⩽
tTp
qic
·
p tR ⎛ xi c/p ⎞ c tP ⎜1 − xi − 1 ·qi · tR ·(1 − Ri ) ⎟ ⎝ ⎠
, the cartons of item i should be stored
on a rack and picked from it, with a carton from rack picking approach
4.1. Decision-making methodology description
• if
Starting from the Carton Pick from rack Convenience Condition (16) introduced and studied in the previous section, a decision-making procedure is proposed here. This is composed of four subsequent steps, which lead to the final decision on the storing mode for all items i under study, comparing the carton from pallet picking with the carton from rack picking.
Qi Zi
>
tTp
qic
·
p tR ⎛ xi c/p ⎞ c tP ⎜1 − xi − 1 ·qi · tR ·(1 − Ri ) ⎟ ⎝ ⎠
, item i should be stored on a pallet
and picked directly from it, with a carton from pallet picking approach
• the carton information for each item i: frontal dimension L , depth D , height H , weight W and volume V ; the • orders information for each item i: number of picking lines for
The application of the methodology to all the items under study allows to have a general overview of the different stock modes that are required in the warehouse. This is useful to get a proper dimensioning of the whole stocking area, distinguishing between the picking area with pallets and the one with racks. The here proposed procedure stops with this result, considering the trade-off between reducing the movements of the pallets from the reserve area to the forward area and reducing the distances travelled by the operators, for all the stored items. For now, it is assumed that each item has only one stock location in the forward area, represented by a pallet place or by a place in the rack. The further dimensioning and the design of the picking area is left to a following study (see, for example, Bartholdi & Hackman, 2017).
•
4.2. Decision-making methodology application in a case study
4.1.1. Data collection The application of the decision-making process starts with the retrieval of all the data that are needed for the subsequent computations. These deal with some physical information of all items i, with their picking orders in a certain time period and with some standard times that describe the warehouse configuration in which the items are stored. In particular, they are: c i
c i
•
c i
c i
c i
item i Zi processed in the analysed time period and number of cartons Qi picked in the same time range; the pallet information for each item i: frontal dimension Lip , depth Dip , height Hip , as well as Bi , the number of cartons that are eventually packed together and that can be handled together, corresponding to the number of cartons refilled simultaneously for item i; the standard times data: unitary refill time tR , single order line processing time tTp , picking times tPp and tPc and unitary carton refill time from pallet to rack tHc .
The proposed case study deals with a low-level picker-to-parts manual warehouse of a major supermarkets supplier, where various kinds of food and non-food products are stored. The analysis concerns the picking mode decision for 11,342 different product codes that initially were all stored in EUR-pallets, with a total stocking length of 9,074 m. Seventy pickers are employed on two work shifts per day, for 30 days per month, for a total time of 14,481 h.
4.1.2. Weight threshold application Once all the needed data are known, the next step to perform is a check of the weight. In fact, if the weight of the carton of item i is greater than the carton weight that has been chosen as a threshold Wtc , for example, taking as a reference a specific ergonomic requirement (Waters, Putz-Anderson, Garg, & Fine, 1993), it is suggested to pick the corresponding item directly from pallets. In fact, putting its cartons on the racks would require a double movement of heavy objects, to refill the racks and then to process the picking orders (Calzavara, Glock, Grosse, Persona, & Sgarbossa, 2017). Hence, for each item i it has to be checked:
•
Table 4 Input values (* the same for all items i). Parameter
Value
tR tTp
120 s 30 s
tPp
10 s
L ip Di
if Wic > Wtc , item i has to be stored on pallets, for carton from pallet picking, and the procedure stops here
p
Wtc
93
800 mm* 1200 mm* 5 kg
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Table 5 Classification of the products according to Ric / p and xi xi − 1
they influence the trend of the CPCC frontier. It follows that the various products cannot be studied all together; however, the items can be grouped exactly according to their values of Ric / p and xi . A summary xi − 1 of the results obtained for these two parameters is given in Table 5, reporting a classification of the various product codes according exactly to their Ric / p and xi . It can be observed that most of the product codes
xi . xi − 1
Ric / p 1.0–1.1
1.1–1.2
1.2–1.3
1.3–1.4
1.5–1.6
1.9–2.0
Total
1–2 2–3 3–4 4–5
403 1
59
21
3
9
7,187
7,682 1 0 0
Total
404
59
21
3
9
7,187
7,683
xi − 1
x
have 1 ⩽ x −i 1 < 2 , meaning that x i is often much higher than 1. Then, i there are two main groups of items: one group of 404 items having c/p 1 < Ri ⩽ 1.1 and another one of 7,187 codes having 1.9 < Ric / p ⩽ 2 . As a consequence, the proposed analysis continues with the focus on these two main groups of product codes.
4.2.4. Stock mode decision Fig. 4 shows the application of the CPCC to the first group made up of 404 items, having 1.0 < Ric / p ⩽ 1.1. For each product code, characterised by a specific value of qic and of Qi / Zi , there is a corresponding point on the graph. The figure is focused on the area of the graph that includes the CPCC frontier, which is the line shown. It can be seen that, since Ric / p ≅ 1, the CPCC frontier is very similar to a straight line. The 212 products that turn out to be positioned under the CPCC frontier are those that can be stored for carton from rack picking, while the other 192 that are positioned above the line are more suitable to be picked directly from the pallet. In Fig. 5 some examples of both kinds of products (for pallet picking and for rack picking) are reported: besides their qic and Qi / Zi values, their position on the plot and a generic description are shown. Fig. 6 reports the same analysis, performed for the group of 7,187 products having 1.9 < Ric / p ⩽ 2.0 . In this case, too, the figure is focused on the area of the graph with the CPCC frontier. The products whose results are above the CPCC frontier and that can be picked directly from the pallet number 4,671, while the products that can be stored on the racks and picked from them total 2,516. Some of these products are proposed as an example in Fig. 7. A final comparison useful to understand the potential of such a study is reported on Table 6. This shows the number of items and the total time factors in hours (refill time, picking time, travel time and
4.2.1. Data collection Table 4 reports all the general data that have been calculated and measured for the application of the method introduced before. The data of the picking orders refer to one month, with a total of 1,160,821 picking lines for all codes. The corresponding total time for processing these orders is 14,481 h. 4.2.2. Weight threshold application The weight threshold limit that has been chosen is Wtc = 5 kg . After the application of this filter, the number of items that have to be put directly in a carton from pallet picking mode is 3,659, while those that can be further analysed total 7,683. 4.2.3. CPCC calculation For each of these 7,683 items, the parameters qic and qi p can be calculated with (6) and (7). For qic , it is considered that the carton depth Dic can be approximated with 3 Vic , since at this level of the study it is not important to know exactly how the item is stored on the rack (i.e. which dimension of the carton corresponds to Dic ). Then, in order to continue the study, the ratios Ric / p and xi have to xi − 1 be calculated for each product. In fact, both these parameters vary according to the characteristics of the product but, at the same time,
Fig. 4. Application of the method to the products having 1 ⩽
94
xi xi − 1
< 2 and 1.0 < Ric / p ⩽ 1.1.
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Fig. 5. Examples of products having 1 ⩽
xi xi − 1
< 2 and 1.0 < Ric / p ⩽ 1.1.
Fig. 6. Application of the method to the products having 1 ⩽
xi xi − 1
< 2 and 1.9 < Ric / p ⩽ 2.0 .
picking from racks (18,161 h). In particular, this led to a reduction of the workers employed in the picking activity of about 3%. Moreover, it allows to reach an interesting compromise also in terms of stocking length, with a warehouse length reduction of 2,701 meters compared to the case in which all items are stored on pallets. Finally, Fig. 8 shows the comparison of the starting configuration of the warehouse with the one obtained after the application of the CPCC method, referring to some of the items under study. As can be seen on the left of the figure, some of the items that were stored in pallets are stored in pallets also after the application of the methodology, due to their weight and/or to their picking frequency. On the contrary, on the right of Fig. 8 it is reported the case of some items that have been moved from a carton from pallet picking approach to a carton from rack picking one.
total time) required to process all the considered picking lists for three different cases. The first case deals with the starting configuration, with all items stored in pallets on the ground floor of the warehouse, the second one considers all items stored on a shelving with various levels, while the last one refers to the CPCC method proposed here, with a certain combination of items stored on pallets and items stored on racks. The same table also shows the total stocking length (in meters) resulting from the three different scenarios. This parameter roughly specifies the length of the whole warehouse, and it is calculated considering Lip = 0.8 m for all items and the various Lic , which have also been divided by the number of possible levels of the shelving. It can be seen that the CPCC method leads to a reduction on the total time (14,207 h), both compared to picking from pallets (14,639 h) and 95
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Fig. 7. Examples of products having 1 ⩽
xi xi − 1
< 2 and 1.9 < Ric / p ⩽ 2.0 .
Table 6 Number of items, stocking length and total time factors comparison for all in pallets stocking, all in racks stocking and CPCC method. All in pallets
All in racks
CPCC method
Number of items
On pallets On racks
11,342 –
– 11,342
7,079 4,263
11,342
Stocking length [m]
On pallets On racks
9,074 –
– 1,890
5,663 710
6,373
Total pallet refill time [h]
On pallets On racks
791 –
– 12,627
735 2,107
2,842
Total carton refill time [h]
On pallets On racks
– –
– 835
– 196
196
Total picking time [h]
On pallets On racks
4,175 –
– 4,175
3,193 982
4,175
Total travel time [h]
On pallets On racks
9,673 –
– 524
6,924 70
6,994
Total time [h]
On pallets On racks
14,639 –
– 18,161
10,852 3,355
14,207
5. Discussion of results
As far as the CPCC frontier is concerned, it can be seen that in the case of 1.0 < Ric / p ⩽ 1.1 it intersects the x-axis for qic ≅ 4 , while for 1.9 < Ric / p ⩽ 2.0 the intersection is for qic ≅ 6. Since qic is the maximum number of cartons storable in the forward area, it follows that the products that are more suitable for carton from rack picking are those that have a medium-small carton volume, hence, medium-small average carton physical dimensions and that are picked in small quantities per picking list (right-bottom area of the graph). Then, the convenience threshold has an increasing trend, since the convenience of putting the product in racks with respect to pallets increases if the item has a higher qic . Hence, it has a smaller volume and it occupies a smaller space in the warehouse, even if it is averagely picked at a higher number of cartons per time (higher values of Qi / Zi ). Considering the cases reported in Fig. 5, it emerges, for example, that the products E and F, having a very similar Qi / Zi , are more suitable to be stored in two different ways: the nylon ladle, with a lower qic , can be picked from the pallet, the pencil with eraser (qic = 5.24 ) from the rack. On the other hand, although the products A and H have the same qic , the first one has to be stored in pallets while the second one on racks, since they have a significant difference in the number of cartons required per time (resulting in, respectively, a high and a low
The case study presented in the previous section can offer some interesting insights about the results obtained as well as on the general application of the method. First of all, it has turned out that, due to their characteristics, for 3,355 out of 7,683 products it is more suitable to store them on racks with respect to a direct storage on pallets (Table 6). These products could then be placed in a separated picking area, organized in racks or with other smart solutions instead of with pallets (Battini, 2016). Hence, considering the number of pallet stock locations (3,355) that are no longer needed, it derives that the distances travelled on average by the operators are very reduced (Table 6). From the analysis of the graphs reported in Figs. 4 and 6, it can be highlighted that a great number of the items analysed, with a weight Wic < 5 kg , are characterised by a Qi / Zi < 1.5, meaning that every time the warehouse operators pick such products the number of picked cartons is very low, typically 1 or 2. Many products (2,989 items) even have exactly Qi / Zi = 1. This also represents an important confirmation of what has been pointed out as a common and recent trend in picking warehouses, in which customers are requiring ever smaller quantities per product (De Koster et al., 2007; Lu, McFarlane, Giannikas, & Zhang, 2016). 96
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Fig. 8. Warehouse configuration comparison: before and after CPCC method application.
terms of the volume occupied by the items, avoiding useless waste of warehouse space. As a consequence, this reduction leads to a decrease of the average distances that are travelled by the picking operators, with an important positive impact on the overall warehouse performance (Tompkins et al., 2010; Battini et al., 2015).
value of Qi / Zi ). Similar differences are reported in Fig. 7: although the average number of cartons picked per picking tour Qi / Zi is very similar for almost all the proposed products, the way they have to be stored for picking is different, considering their qic , and hence, their volume. Nevertheless, it is fundamental to underline that the CPCC frontier and the two consequent areas of the graph that have been identified depend strongly on the input times tR , tTp and tPp , which can normally be considered as general parameters of the warehouse. As shown in the parametric analysis of Section 3.2, provided that the time needed to perform a pallet refilling is substantially higher than the single order line processing time, the carton from rack picking area is interesting and can involve a significant number of storable items. If this ratio decreases, however, the carton from rack picking convenience turns out to affect only few items. In fact, although the presented method proves to be very effective as well as easily applicable, it requires particular attention to the way the input data are obtained and managed. This is especially true in the case of the refill time tR of the single order line processing time tTp and of the unitary picking time tPp . Furthermore, the convenience study presented in this paper could be applied also in another interesting way. In fact, once all the other characteristics of the warehouse and of a certain analysed product are known, from the CPCC formula (16) it is possible to calculate a socalled threshold qic , qtic , representing the minimum number of cartons that have to be put in the forward area to make the carton from rack picking more convenient than the carton from pallet picking:
qtic =
Qi / Zi tPp Qi xi · · ·(1−Ric / p) Zi xi − 1 tR
+
tTp tR
6. Conclusions and further research The present paper has introduced a new decision-making methodology that can be used to understand how to store all the various products that are in a picking warehouse. In particular, it refers to the choice between storing a product in pallets or in racks. Starting from the times needed to perform both kinds of picking, which depend on simple and easily obtainable item and warehouse information, the socalled Carton Pick from rack Convenience Condition (CPCC) has been formulated. After having proposed a parametric analysis, the decisionmaking methodology has been described. Moreover, the application of the new method has been shown in a real industrial case study, dealing with a food and non-food picking warehouse of a big supermarkets supplier. The proposed procedure turns out to be particularly interesting since it is easy and fast to apply; furthermore, it can be suitable for several different contexts, concerning warehouse manual picking as well as assembly lines feeding picking. Future research concerning this topic is intended to extend the model and the method here proposed in order to allow the estimation of the actual saving obtainable through the storage of some items in racks instead of in pallets, in terms of reduction of the time needed to perform the picking tour and, as a consequence, in terms of reduction of the picking costs. Furthermore, this method will be applied to more case studies, in order to understand the possibility of always applying the simplified CPCC (Eqs. (17) and (18)) instead of the full one.
(19)
Finally, it is important to point out that the application of such a methodology in a picking warehouse can lead to important benefits in 97
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