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Operations Management of DistributionCenters for Vegetables and Fruits

ROB A.C.M. BROEKMEULEN*

Eindhoven University of Technology, P.O. Box 513, Pav. E10, 5600 MB Eindhoven, The Netherlands

We present a tactical decision model that improves the eectiveness of the operations of a distributioncenter for vegetables and fruits. The operations are complicated in the case of vegetables and fruits dueto the seasonal uctuations in production and demand and the need for special storage conditions fordierent products. Using the decision model we determine an assignment plan, based on historicaldata. The assignment plan is used at the operational level for storage advice. We used local search tech-

niques to nd an assignment plan. The eect of the assignment plan on several storage policies wasexamined with a simulation model of the operations in the distribution center. The developed modeland algorithms are integrated in a PC-based decision support system. # 1998 IFORS. Published byElsevier Science Ltd. All rights reserved

Key words: Distribution center, local search, perishables, simulation, decision support system.

1. INTRODUCTION

The characteristics of vegetables and fruits make the operations management of a distribution

center more complex than that of an average distribution center. According to Hoogerwerf et

al. (1990), the share of distribution cost in the consumer price of vegetables and fruits is nearly

twice as high as the distribution cost of non-perishables. This dierence is due to two complicat-ing factors, i.e., fast handling and special storage conditions. Chung and Norback (1991) notice

that vegetables and fruits are distributed in a relatively short time to minimize the keeping qual-

ity loss. Meert (1990) describes the trade-o between conditioning and fast handling, and

remarks that it is dicult to improve the current speed of handling because it is already high.

A distribution center is a building with two main functions: warehousing and distribution.

Warehousing includes all activities concerned with storage and retrieval of products. The distri-

bution function concentrates on the activities groupage and shipment of customer orders. The sto-

rage accommodation is the part of the distribution center where products can be stored. The

storage equipment, such as racks and shelves, creates locations and storage space in the storage

accommodation where products can be stored.

An important activity in a distribution center for vegetables and fruits is the conditioning of

products. Vegetables and fruits are products that are susceptible to keeping quality loss, such as

aging and breakdown. Fu and Labuza (1993) dene keeping quality or shelf life as the average

period of time that a product is `t for use', if it is kept under constant storage conditions.

Adequate storage conditions such as relative humidity and temperature minimal handling

and avoidance of product interactions such as odor and hormone transmission can reduce

keeping quality loss as is illustrated in Ryall and Lipton (1979) and Petropakis (1989). An area

in the storage accommodation with specic storage conditions is called a zone. The following

items are examples of factors that inuence the keeping quality in the zones of a distribution

center; see also Ryall and Lipton (1979).

. Storage time. Short storage times reduce the keeping quality loss.

Int. Trans. Opl Res. Vol. 5, No. 6, pp. 501508, 1998# 1998 IFORS. Published by Elsevier Science Ltd

All rights reserved. Printed in Great Britain0969-6016/98 $19.00 + 0.00PII: S0969-6016(98)00038-0

Paper presented at the Seventh International Special Conference of IFORS: `Information Systems in Logistics and

Transportation', Gothenburg, Sweden, 1618 June 1997.

*Corresponding author. Tel.: 0031-40-2473974; fax: 0031-40-2464531; e-mail: [email protected].

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. Temperature. Each product has its own optimal storage temperature. Many vegetables and

fruits that now or in the past originated from tropical or subtropical climates are susceptible

to low-temperature breakdown.

. Odors. Products like onions and garlic produce odors that are adsorbed by fruits such as mel-

ons. Spatially separating the products or suitable packaging of the products can prevent keep-

ing quality loss by odors.

. Ethylene. The gas ethylene, a plant hormone for ripening, plays a role in the interaction

between products. High concentrations of ethylene accelerate the ripening and decay of a

large number of products. According to Abeles et al. (1992), products that produce ethylene

are susceptible to ethylene at the same time. The eect of the hormone ethylene can be

reduced by ventilation of the zone. The production of ethylene, as well as the inuence of this

product interaction on the keeping quality, is dependent on the storage temperature.

The quality change models used in this research describe for each product the keeping quality

under specic storage conditions. The concept for the used quality change models is based on

work from Kopec (1983), Woltering and Harkema (1987) and van Doorn and Tijskens (1991).The development and validation of these models are open research topics.

The assortment of a distribution center is a list of the products that are handled or in stock

during a specic period of time. A year can be divided into one or more planning periods. The

supply of many perishables depends on the seasons. The numerous changes in the assortment

during the year make the activities in a distribution center non-repetitive.

On the operational level, a storage policy determines where a product can be stored and a

retrieval policy determines which product can be retrieved. For the planning and control of sto-

rage and retrieval operations in distribution centers in general, a large number of methods are

now available. For retrieval, we only consider the First In First Out (FIFO) retrieval policy due

to the perishable nature of the products. Alternative retrieval policies such as Last In First Out

(LIFO) result in longer durations of stay for the products and therefore leads to much keeping

quality losses. The stock location assignment problem (SLAP), introduced by Hausman et al.(1976), concerns the assignment of incoming stock to storage locations in order to reduce the

mean travel time for storage and retrieval. The proposed class-based storage policy assigns the

products, based on the turnover rate, to a number of classes within the storage accommodation.

Each class has a specic storage space requirement. An incoming load is stored at an arbitrary

open location in the assigned class. When all the locations in the assigned class are occupied,

the closest and most suitable class with open locations is taken. The analytic results for the

SLAP with the class-based storage policy of Hausman et al. (1976) were veried by Schwarz et

al. (1978) with simulation. Graves et al. (1977) found that the storage space requirements

increase with the number of classes when an incoming load may only be stored in its assigned

class. The algorithm of van den Berg (1996) determines the optimal class-partition by imposing

a risk level on stock overow. Frazelle (1989) extended the SLAP for products that are often

ordered together. To our knowledge, the eect of keeping quality loss on stock location has not

been studied yet. For an exhaustive literature review we refer to van den Berg (1996).

1.1. Problem denition

The management of a distribution center for vegetables and fruits has to deal with questions

concerning operations management such as the ones below:

. How much storage space is needed?

. What kind of storage conditions are needed in each zone?

. Where should the products be located in the distribution center?

. What kind of storage policy should be applied?

The problem associated with answering these questions can be modeled in a quantitative way in

terms of the decision quantities, the objectives, and the constraints. An instance of the problem

R.A.C.M. BroekmeulenOperations Management of Distribution Centers502

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can be dened by a dataset that describes the building, the expected customer orders, and the

properties of the products in the assortment.

The customer orders determine the ow of products through the distribution center. The

minimal required information about the expected customer orders should include the expected

stock levels for each individual product in each planning period. This information can be

obtained by analyzing the historical transaction data of the distribution center.

The decision quantities at the tactical level are the assignment of products to zones. The

assignment of storage conditions to the zones and the selection of a storage policy are con-

sidered long-term decisions. The following constraints must be met when the management

makes decisions by assigning values to the decision quantities.

. Each product must be assigned to one zone.

. The storage capacity of a zone may not be exceeded.

. The keeping quality loss of the products may not exceed more than a predened level agreed

in the distribution chain.

The objective is, given an instance of the problem, that we nd values for the described decisionquantities such that the sum of the keeping quality loss cost is minimal, and that the constraints

are met.

An assignment of products to zones is called an assignment plan. We check with a simulation

model if the assignment plan with the chosen storage policy minimizes the keeping quality loss.

A distribution center may use an assignment plan for several years if the yearly turnover

remains constant over the years.

We have developed a decision support system that incorporates the developed models and al-

gorithms. With the decision support system, the management can handle the specic problems

of a distribution center for vegetables and fruits.

1.2. Overview of the article

In our research we concentrate on the eect of an assignment plan on the operations of a distri-

bution center for vegetables and fruits. We state the developed model for assignment planning

in Section 2. In Section 3, the simulation model to analyze the eect of an assignment plan is

described. Finally, the results of the experiments with a real-life dataset from a wholesaler of

vegetables and fruits are discussed.

2. ASSIGNMENT OF PRODUCTS TO ZONES

We will dene the assignment problem for vegetables and fruits (APVF) as a general assignment

problem (GAP) with constraints on the storage capacity and the keeping quality loss.

We use the following notation:

set of products

set of zones

set of planning periods

qijt expected keeping quality loss of product i in zone j in planning period t

sit peak stock level of product i in planning period t

eijt ethylene production of product i in zone j in planning period t

Sj storage capacity of zone j

Ej threshold ethylene concentration in zone j

Qi maximum allowed keeping quality loss of product i

Furthermore, we make the following assumptions:

1. The required storage space of a product in a planning period is equal to the expected peakstock level in that planning period.

2. The storage time, the temperature, and the ethylene concentration are the only storage con-

ditions that inuence the keeping quality loss of the products in the distribution center.

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3. The storage time is the same for all products.

4. The storage temperature is dependent on the zone.

5. The ethylene production of a product in a zone depends on the type of product, the over-

night stock level, the storage temperature, and the eective storage volume of a zone. The

eective storage volume of a zone is the physical storage volume increased by the ventilation

rate.

6. The eect of ethylene on keeping quality is neglectable below a threshold concentration. The

threshold concentration is dependent on the storage temperature.

7. The occupied storage location with the worst storage conditions for that product determines

the keeping quality loss.

8. The keeping quality loss of all products in the assortment is equally important.

9. The stock levels and the quality change models are known for all products.

The keeping quality loss qijt is equal to the fraction of the initial keeping quality that is lost

every day compared to the storage at the ideal conditions for that product. Note that the keep-

ing quality loss qijt is 0 when the stock level sit is 0. For the assignment plan we dene decision

variables x ij for all i$ and j$ .

x ij 1 if product i is assigned to zone j,

x ij 0 otherwiseX

The problem is to nd an assignment plan that minimizes the cost function

CAPVF

iP

jP

tP

qijt x ij 1

and satises the following constraints.

1. A product may be assigned to exactly one zone, i.e., for all i $ ,

jP

x ij 1X 2

2. The storage capacity of the zone may not be exceeded, i.e., for all j$ and t $ ,

iP

sit x ijSjX 3

3. The ethylene concentration in a zone may not exceed the threshold concentration, i.e., for all

j $ and t $ ,

iP

eijt x ijEjX 4

4. The maximum allowed keeping quality loss of a product may not be exceeded, i.e., for all i $

, j $ , and t $ ,

qijt x ijQiX 5

Fischer et al. (1986) proved that the GAP is NP-hard. Cattrysse and van Wassenhove (1992)

published a survey of models and algorithms for the GAP. Because of the large number of ad-

ditional constraints, we decided to use local search to nd solutions for the APVF. Local search

is a solution process that tries to improve a given solution by making relatively small changes in

several steps. Popular local search techniques are reviewed by Aarts and Lenstra (1997). The

quality of the solutions is determined with the cost function of the problem. We have chosen for

multi-start iterative improvement as our local search technique. Experiments with other localsearch techniques are discussed by Broekmeulen (1998).

To apply local search on a highly constrained problem, we transformed the constrained

APVF to the unconstrained LAPVF by associating a cost or penalty with all constraint viola-


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tions. These costs are included in the modied cost function of the following problem formu-

lation of LAPVF.

Find an assignment plan that minimizes the cost function

CLAPVF a

iP

jP

tP

qijt x ij b

iP

Uj g

iP

Fj d

iP

Ri 6

and satises the following constraints.

iP

x ij 1 Vi P , 7

iP

sit x ijSi Uj Vj P,t P, 8

iP

eijt x ijEj Fj Vj P,t P , 9

qijt x ijQi Ri Vj P ,t P , 10

where a is the weightfactor for keeping quality, Uj the additional required capacity in zone j, b

the penalty for capacity violations, Fj the excess ethylene produced in zone j, g the penalty for

exceeding the ethylene threshold, Ri the excess keeping quality loss of product i and d the pen-

alty for keeping quality violations. We use the following values for the weightfactor and the

penalties in all problem instances: a 1ajj jj,b 106ajj,g 104ajj, and d 100ajj.

The relative value of the penalties reects the priority of the associated constraints.

The initial solutions for the local search are constructed by a greedy heuristic that assigns pro-

ducts with high peak stock levels before products with lower peak stock levels to the zones. In

the iterative improvement the following cycle is carried out several times. In the rst step, candi-date solutions are derived from the current solution based on a neighborhood function. We

allowed the following types of moves in our neighborhood: a product is assigned to a dierent

zone or two products swap their zone assignments. These moves obey constraint (7). In the sec-

ond step, an acceptation criterion selects the new current solution for the next cycle. We accept

the rst candidate solution in the neighborhood that has a better object value than the current

solution. A local optimum has been reached if the object value of the last accepted solution is

better than all its neighbors. If such a local optimum is reached, a new initial solution is gener-

ated by assigning random values to the decision variables. After a limited amount of compu-

tation time the search is stopped.

We can calculate the following lower bound when we set b, g, and d to 0.

LB a

iP

tP

minjP qijtX 11

The assignment that can be derived from this lower bound can be seen as the relaxed solution

of the assignment problem with regard to storage capacity and ethylene concentration. The

upper bound for a feasible solution of APVF can be calculated as follows:

UB a jj

iP

QiX 12

3. SIMULATION MODEL OF THE OPERATIONS

The inuence of the daily requests for storage and retrieval during a whole year is studied with

a simulation model that assigns incoming loads of products to zones. The daily putaways and

retrievals follow the seasonal production and demand of the products. All requests are handled


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on a rst come rst served basis. We examined the following three storage policies with the

simulation model.

1. Free zone policy. The product is stored in the rst zone with enough unoccupied storagespace to satisfy the request.

2. Temperature zone policy. The product is stored in a zone where the storage temperature is

closest to the optimal storage temperature of the product.

3. Preferred zone policy. The preferred zone to store the product is determined by the assign-

ment plan. If the preferred zone has not enough unoccupied storage space, we store the pro-

duct in a zone with available storage space where qijt is minimal.

All three storage policies are derived from the class-based storage policy. The rst two are

based on existing practices in distribution centers for perishables. The free zone policy focuses

only on storage capacity utilization. The temperature zone policy requires only a little amount

of additional information about the keeping quality characteristics to reduce the keeping quality

loss compared to the last policy. In the case of a retrieval, we only follow the First In First Outrule when no alternative zones are occupied with the product. Stock in alternative zones with

harmful storage conditions for the product has priority over stock in the assigned or default

zone and is therefore used rst for a retrieval.

We measure the eectiveness of the operations with the cost function of LAPVF, as stated in

(6), where is redened as the set of working days and x ij equals 1 if product i is stored over-

night in zone j, 0 otherwise.

4. COMPUTATIONAL RESULTS

To test the solution strategy, we derived instances of the APVF based on real-world data from

a wholesaler of vegetables and fruits in the Netherlands.

4.1. Assignment plan

The wholesaler distribution center handles 180 dierent products during a year. The maximum

allowed relative loss of keeping quality Qi for each product i is set to 0.6. We divided the year

in 13 planning periods of four weeks each. The distribution center consists of six zones with a

storage capacity Sj of 300 pallets each. The ventilation rate in the rst zone is 20 times higher

than in the other zones.

The ve instances that we studied varied in the storage conditions in the zones. The storage

temperatures in the zones for each instance are described in Table 1. The threshold ethylene

concentrations depend on the storage temperature in the following way.

Ej 1X5 if the temperature in zone j is greater than 78C

Ej 8X0 if the temperature in zone j is less than 38C

Ej 5X0 otherwise

13

Table 1. The storage temperatures in the zones j $ of the distribution center for the dierent problem instances

A, F F F, E

j A B C D E

1 12 12 8 12 122 12 8 8 4 8

3 1 1 1 1 44 1 1 1 1 15 1 1 1 1 16 1 1 1 1 1


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The instances that we studied were highly capacitated because the sum of the total storage space

requirement in a planning period was on an average 80% of the total storage capacity of the

distribution center. Martello and Toth (1991) showed that instances of comparable generalized

assignment problems are dicult from a computational point of view.

The results for assignment planning of the APVF instances with dierent storage tempera-

tures using the multi-start iterative improvement heuristic are given in Table 2: The rst value

gives the lower bound LB. The second value gives the minimal value over ve runs. The thirdcolumn gives the average value over ve runs. Each run took a computation time of 1000 sec-

onds on a Pentium processor running under MS-DOS. According to (12) and with

a 1a jj jj, the upper bound for a feasible solution of APVF is equal to 0.6, since the

maximum allowed relative loss of keeping quality Qi is equal to 0.6 for each product i.

The results of the tests presented in Table 2 show that we only nd feasible solutions for

APVF for instance B and C. The other instances still have violations of constraint (5). We did

not nd optimal solutions, since all solutions stayed well above the lower bound LB. The dier-

ence in cost between three temperatures in instance B and two temperatures in instance C is

small. Unpublished experiments indicate that these results are dependent on the assortment and

the storage capacities of the zones.

4.2. Simulation of the operations

The turnover of the wholesaler is about 400 pallets per day. Six days a week the distribution

center buys vegetables and fruits on order at auctions and directly from growers for about 20

customers. These customers are large supermarket chains. Every sunday the distribution center

is almost empty. We simulated the operations of the wholesaler at the product level with gener-

ated daily purchases and shipments based on the wholesaler dataset of a whole year. The opti-

mal slot plans of APVF are found with local search, as presented in Table 2.

The results of the simulation are shown in Table 3. The cost of the best found assignment

plan for a problem instance is presented in the `Plan' column. The next three columns represent

the cost for each storage policy over ve simulation runs of a whole year.

The simulation results presented in Table 3 clearly show that the preferred zone policy hasthe best performance compared to the other two policies. Since not all products with a peak

stock level sit greater than 0 are present each day during a planning period t, we can nd a

lower cost of some simulation runs compared to the cost of the assignment plan. Ignoring the

Table 2. The results of the APVF instances with dierent storage temperatures. The column `LB' presents the lower

bound for the instance, the column `min' the minimal cost, and the column `avg' presents the average cost over ve runs

Instance LB min avg

A 0.1685 1.4469 1.9906B 0.1240 0.1517 0.1549C 0.1399 0.1518 0.1579D 0.1645 0.8527 0.9911E 0.1232 1.2349 2.0524

Table 3. The results of the simulation of storage and retrieval with three dierent storage policies. The cost of the best

found assignment plan for a problem instance is presented in the `Plan' column. The next three columns represent the

cost for each storage policy over ve simulation runs of a whole year

Storage policy

Instance Plan Preferred zone Temperature zone Free zone

A 1.4469 0.2759 0.5826 29735.1680

B 0.1517 0.1517 1228.7596 19052.3359C 0.1518 0.1517 0.3695 18981.7539D 0.8527 0.2295 1103.2052 4010.1765E 1.2349 0.2584 1098.2590 20171.7012


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need for specic storage conditions in the free zone policy results in excess unnecessary keeping

quality loss in the distribution center. The costs found for this policy indicate that the ethylene

concentration in the zones is sometimes above the threshold. The use of an assignment plan

compared to a simple quality oriented assignment rule in the temperature zone policy reduces

the keeping quality loss cost with at least 50% and avoids exceeding of the maximum allowed

keeping quality loss.

5. CONCLUSIONS

The use of an assignment plan seems useful for the operations of a distribution center of veg-

etables and fruits. The additional eort to make such a plan is relatively small compared to the

benets on keeping quality. The assignment rules used in the currently used storage policies are

not enough to ensure specic conditions for the products.

The proposed solution strategy for the assignment problem for vegetables and fruits seems to

work for problem sizes, such as in the case of the wholesaler of vegetables and fruits. The expertknowledge contained in the quality change models play an important role in the acceptance of

the presented solutions. In practice, better assignment plans and storage policies alone are not

enough. Personnel must follow the guidelines for storage and retrieval to avoid that products

suer from unnecessary keeping quality loss.

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182221, 294296.Broekmeulen, R.A.C.M., 1998. Layout and operations management of distribution centers for perishables. Ph.D. thesis,

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