FIFO v LIFO

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Production, Manufacturing and Logistics

Two-warehouse inventory model with deteriorationunder FIFO dispatching policy

Chun Chen Lee *

Department of Accounting, Soochow University, 56, Sec. 1, Kuei-Yang Street, Taipei 100, Taiwan

Received 3 November 2004; accepted 21 March 2005Available online 3 January 2006

Abstract

In most of the literatures on two-warehouse inventory decision models, the last-in-first-out (LIFO) dispatching pol-icy has always been assumed. This presumption, however, is not in line with the actual practice of most business entities.To enhance the freshness of merchandise or goods, businesses commonly follow the first-in-first-out procedure (FIFO).This inconsistency forms the base and main motivation for our research. In this paper, Pakkala and Acharys two-ware-house LIFO model is first modified and then a FIFO dispatching two-warehouse model with deterioration is proposed.Comparison of the two models indicated that the FIFO model is less expensive to operate than LIFO, if the mixed

effects of deterioration and holding cost in RW are less than that of OW. Finally, numerical examples are providedto investigate and examine the impact that various parameters have on policy choice. 2005 Published by Elsevier B.V.

Keywords: Inventory; Deterioration; Two-warehouse; FIFO; LIFO

1. Introduction

The classical economic order quantity (EOQ) model is formulated by considering three inventory coststo achieve a minimum system cost. These costs are the procurement cost, carrying cost and shortage cost.

One of the unrealistic assumptions is that items are not perishable while in storage. However, there areitems such as highly volatile substances, radioactive materials, fresh goods, etc., in which the rate of dete-rioration is higher. Loss from deterioration should not be ignored. Ghare and Schrader [4] were the first to

0377-2217/$ - see front matter 2005 Published by Elsevier B.V.doi:10.1016/j.ejor.2005.03.027

* Tel.: +886 2225 38244.E-mail address: [email protected]

European Journal of Operational Research 174 (2006) 861873

www.elsevier.com/locate/ejor
mailto:[email protected]:[email protected]


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consider issues regarding on-going deterioration of inventory. Since then, research for deterioration ofinventory has been extensively examined by many researchers from time to time. Raafat [14] and Goyaland Giri [6] have made excellent reviews of these models.

In various situations, the degree of deterioration depends on the preservation of inventory in the facilityand its environmental conditions which are available in the warehouse. An interesting research topic incor-porating deterioration effect in inventory decision involves the situations in which there are two storagefacilities. Sarma [15] is the first to discuss the two-warehouse inventory model with deterioration. In hismodel, a single inventory item is first stored in the owned warehouse (OW), with limited capacity, andany additional quantity to be stored in the rented warehouse (RW). An infinite replenishment rate isconsidered in this model with uniform scheduling period and shortage allowance. Other authors, e.g.Benkherouf [2], Bhunia and Maiti [3], Goswami and Ghaudhuri [5], and Lee and Ma [8] proposed thetwo-warehouse models when demand is a function of time either with or without the consideration ofdeterioration. Pakkala and Achary [10] extended Sarmas model to the case of finite replenishment rate withshortage. All of the above mentioned research models are commonly referred to as continue release model,assuming that inventory is to be released directly and continuously in each warehouse. Murdeshwar and

Sathe [9], Pakkala and Achary [11] considered bulk release model which inventory in RW must first betransferred to OW before its release to the customer.

It is generally assumed that the RW offers better preserving facilities than the OW, therefore it charges ahigher holding cost. The two-warehouse models discussed above naturally adopt the LIFO (last-in-first-out) inventory flow. Under such circumstances, inventories are first stored in OW with overflows goingto RW. But when retrieving for consumption, it is always from RW when available before retrieving fromOW. However, we believe such rule needs to be further investigated when applying to a real world situation.First, in the RW, particular in a public warehouse, a professional vendor who specializes in the warehous-ing operation would carry a lower operating cost due to well equipped set ups, learning effect of trainedworker, and the economics of scale from high volume. Second, as competition increases between warehousefacilities in real world, their ability to offer valued added service with completive lower price is becoming

more and more necessary. Many businesses have gotten into or expanded their use of public warehousebecause of cheap shipping or other financial reasons (Anonymous, [1]). Finally, a critical point of inventorydecision for perishable products, to allow later stored inventory in RW to be dispatched last means agreater risk of deterioration of inventory. The cost of deteriorated inventory and related opportunity costmay far exceed the cost saving benefit derived from the warehouse rent. In the real world, maintaining aFIFO rule of inventory flow has been the common practice of most managers. In fact, Pierskalla and Roach[12] have shown that a FIFO issuing policy is optimal for perishable and deteriorating inventories in a sin-gle warehouse setting with unlimited capacity.

In this paper, Pakkala and Acharys [10] LIFO model with finite replenishment rate will be reconsidered.We propose a FIFO two-warehouse model that inventory in OW, which is stored first, will be consumedbefore those in RW based on the above considerations that the true holding cost in RW is not necessarily

higher than in OW. Before making comparisons between the two models, in Section 3.1, we made a mod-ification to Pakkala and Acharys model to allow their model to be more complete. Furthermore, the pro-posed assumption of a predetermined cycle time will also be relaxed to a more general approach which is tolet cycle time be part of decision and to determine both order level and backorder level simultaneously. Inthe final section, various parameter analyses are implemented to examine the impact on policy choice.

2. Notations and assumptions

The two-warehouse inventory models proposed in this research are based on the following notations andassumptions:

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D demand rate which is a constantP constant production rate, P > DC1 cost of a deteriorated item

C2 shortage cost per unit inventory per unit of time in shortageC3 unit set up costTi time period in a production cycle of stage i, i = 1, . . . , 6Ii(t) inventory level at time t during time period TiF, H holding cost held in the RW and OW respectivelyb, a deteriorating rates in RW and OW respectively, 0 < b, a < 1W capacity of the OWR maximum inventory level in RWB maximum shortages allowed

The following assumptions are adopted in this study:

1. Lead time is zero and shortages are allowed.2. The rented warehouse RW has unlimited capacity.3. Inventory items are stored in RW only after OW is fully utilized. Once stored, these items are assumed

not to be relocated.

For convenience to differentiate between the models, each time stage Ti under LIFO and FIFO policy isfurther denoted by TLi and TFi, i = 1, . . . , 6. Denote TL and TF as total production cycle time for the twopolicies, then TL

PiTLi, and TF

PiTFi. Also, inventory level during each stage ifor the two models are

set as ILi(t) and IFi(t).

3. The models

3.1. Modified LIFO inventory model

The inventory in a production system with LIFO dispatching policy is depicted in Fig. 2. The inventorycycle can be divided into six parts, named TLi, i = 1, . . . ,6. Initially, BL units of backorders are carried over

Time

BL

Inventory level

W

RL

Fig. 1. Inventory level of Pakkala and Acharys two-warehouse LIFO model.

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from the previous cycle. The production run starts at the beginning of TL1 and, while production anddemand happen simultaneous, backorders are made up within TL1 at the rate ofP D. During TL2, inven-tory items in OW are built from 0 up to W units with a deterioration rate ofa. Any production quantityexceeding this level must be stored in RW. During TL3, inventory items in RW are built from 0 to RL unitsbut with a deterioration rate ofb. Meanwhile, in OW, inventory level will be depleted because of deterio-ration in stock with a rate of a. In (11) of Pakkala and Achary [10], the available spaces in OW releasedfrom deteriorated inventory items during TL3 are assumed not to be reutilized (see Fig. 1). However, underthe proposed assumption that H < F, the system cost will obvious be higher if it is not reutilized, and viceversa. This short coming will be modified in this paper before making a comparison between FIFO andLIFO in the next section.

The production run stops at the end of TL3, and RL units of inventory items in RW are depleted in TL4.The remaining inventory items in OW are then depleted in TL5 by demand and deterioration. Finally, BLunits of backorders are accumulated at the end ofTL6 by a rare ofD, which completes the production cycle.In this system, the management seeks to find the optimal levels of both RL and BL.

The differential equations describing the inventory level at any time in the production cycle are given asfollows:

dIL1t=dt P D; 0 6 t6 TL1;

dIL2t=dt aIL2t P D; 0 6 t6 TL2;

dIL3t=dt 0; 0 6 t6 TL3;

dIL4t=dt bIL4t P D aW; 0 6 t6 TL3;

dIL5t=dt bIL5t D; 0 6 t6 TL4;dIL6t=dt aIL6t 0; 0 6 t6 TL4;

dIL7t=dt aIL7t D; 0 6 t6 TL5;

dIL8t=dt D; 0 6 t6 TL6.

Using the boundary conditions that IL1(TL1) = 0, IL2(0) = 0, IL4(0) = 0, IL5(TL4) = 0, IL6(0) = W,IL7(TL5) = 0, and IL8(0) = 0, the above equations can be solved respectively as follows:

IL1t P DTL1 t; 0 6 t6 TL1; 1

IL2t P D1 eat=a; 0 6 t6 TL2; 2

Time

IL8(t)BL

Inventory level

W

TL6

IL5(t)IL4(t)

IL1(t)

RL

IL2(t)

TL2TL1 TL5TL4TL3

IL3(t)IL6(t)

IL7(t)

Fig. 2. Inventory level of modified two-warehouse LIFO model.



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IL3t W; 0 6 t6 TL3; 3

IL4t P D aW1 ebt=b; 0 6 t6 TL3; 4

IL5t D ebTL4t 1 =b; 0 6 t6 TL4; 5

IL6t Weat; 0 6 t6 TL4; 6

IL7t D eaTL5t 1

=a; 0 6 t6 TL5; 7

IL8t Dt; 0 6 t6 TL6. 8

Now, the inventory items held in RW and OW for a production cycle are

G1

ZTL30

IL4tdt

ZTL40

IL5tdt P TL3 DTL3 TL4 aW TL3=b; 9

and

G2

ZTL2

0

IL2

tdt

Z

TL3

0

IL3

dtZ

TL4

0

IL6

tdt

Z

TL5

0

IL7

tdt

P TL2 DTL2 TL5 aW TL3=a. 10

Denote G3 the inventory items deteriorated per cycle, G3 = bG1 + aG2:

G3 PTL2 TL3 DTL2 TL3 TL4 TL5. 11

The total amount of shortages in the production cycle is

G4

Z0TL1

IL1tdt

Z0TL6

IL8tdt P DT2L1 DT

2L6

=2.

Denote TLB = TL1 + TL6, using IL1(0) = IL8(TL6), from (1) and (8), TL1 and TL6 can be expressed as

functions of TLB

:TL1 DTLB=P and TL6 P DTLB=P. 13

We then have

G4 D P D T2LB=2P.

The total system cost per unit of time for LIFO policy is

TCL 1=TLFG1 HG2 C1G3 C2G4 C3

1=TLfFP TL3 DTL3 TL4 aW TL3=b HP TL2 DTL2 TL5 aW TL3=b

C1PTL2 TL3 DTL2 TL3 TL4 TL5 C2DP DT2LB=2P C3g. 14

Now that IL2(TL2) = W, TL2, which is a constant can be derived from (2):

TL2 1

aln

P D

P D aW

. 15

Using IL4(TL3) = IL5(0), from (4) and (5), we get TL4 in terms of TL3:

TL4 1

bln

P aW P D aWebTL3

D

!. 16

Also, using IL7(0) = IL6(TL4) from (6) and (7), TL5 can be derived as a function of TL4 (also function ofTL3):

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TL5 1

aln 1

aWeaTL4

D

. 17

Therefore, the total cost per unit time can then be expressed explicitly in terms ofTL3 and TLB. The opti-mal value of TL3 and TLB must satisfy the following two necessary conditions: oTC/oTL3 = 0 and oTC/oTLB = 0. After rearrangement, we can obtain

W HaF

b

PD C1

F

b

D C1

F

b

dTL4dTL3

D C1 H

a

dTL5dTL3

TC 1 dTL4dTL3

dTL5dTL4

0

18

and

C2DP D

PTLB TC 0; 19

wheredTL4dTL3

P D aW

P aWebTL3 P D aW

and

dTL5dTL3

aWP D aWeaTL4

D aWeaTL4 P aWebTL3 P D aW.

The total system cost in (14) is a complicated nonlinear function in terms ofTL3 and TLB and not easy tosolve analytically. Through an enormous amount of numerical analyses, we have found that the total costfunction shows convexity with respect to TL3 and TLB. By applying numerical subroutine DNEQNF inIMSL, the optimal value of TL3 and TLB can be obtained from (18) and (19).

Now that IL1(0) = B, and that IL4(TL3) = RL from (1), (13) and (4),

BL DP D

PTLB; RL

P D aW1 ebTL3

b.

There the optimal production policy, i.e., BL and R

L, can be easily derived after the optimal solutions TL3

and TLB are obtained.

Theorem 1. Modified LIFO two-warehouse model always has a lower cost than Pakkala and Acharys LIFO

model if H aF/b > 0.

Proof. Denote TCP as average total cost of Pakkala and Acharys (11). Let TP1 = T t1, andTPi = ti1 ti2, for i = 2, . . ., 6. After variables and parameters transformation, Pakkalas (11) can

expressed as

TCP 1=TPfHP TP2 DTP2 TP5=a FP TP3 DTP3 TP4=b C1PTP2 TP3

DTP2 TP3 TP4 TP5 C2DP DTP1 TP62=2P C3g. 20

For our convenience and without loss of generality, assuming that TPi = TLi for i = 1, . . . ,6. From (14) and(20), cost difference between modified LIFO and Pakkala and Acharys LIFO model is given by

T CL T CP W TL3H aFb.

Since WTL3 > 0, ifa is not significantly less than b, modified LIFO model will have a lower cost than Pak-kala and Acharys LIFO model under their assumption that H < F. h



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3.2. FIFO model

In a system with FIFO dispatching policy, inventory items in OW that is stored first will first be released

for consumption before that of RW. After the end of TF3 (see Fig. 3), when production stops, inventoryitems in RW will remain in storage but with a deterioration rate b. Any demands are withdrawn fromOW until the inventory items in OW are completely consumed, thereafter withdrawing from RW. Otherinventory fluctuations and the decision objectives are all to be the same as those in a LIFO system.

The differential equations describing inventory behavior for IFi, for i = 1, 2 and 8, are the same as LIFOmodel and can be obtained from (1), (2) and (8). Inventory level IFi, for i = 3, . . .,7, are described asfollows:

dIF3t=dt aIF3t 0; 0 6 t6 TF3;

dIF4t=dt bIF4t P D; 0 6 t6 TF3;

dIF5t=dt bIF5t 0; 0 6 t6 TF4;

dIF6t=dt aIF6t D; 0 6 t6 TF4;

dIF7t=dt bIF7t D; 0 6 t6 TF5.

Using the boundary conditions that IF3(0) = W, IF4(0) = 0, IF5(0) = IF4(TF3), IF6(TF4) = 0, IF7(TF5) =0, one can obtain following inventory level functions:

IF3t Weat; 0 6 t6 TF3; 21

IF4t P D1 ebT=b; 0 6 t6 TF3; 22

IF5t P D1 ebTF3 ebt=b; 0 6 t6 TF4; 23

IF6t DeaTF4t 1=a; 0 6 t6 TF4; 24

IF7t DebTF5t 1=b; 0 6 t6 TF5. 25

The inventory holding in RW and OW are

S1 P TF3 DTF3 TF5=b and S2 P TF2 DTF2 TF4=a. 26

The total inventory deteriorated and shortages are

S3 bS1 aS2 PTF2 TF3 DTF2 TF3 TF4 TF5 and S4 DP DT2FB=2P; 27

where TFB = TF1 + TF6.

Time

TF6

IF8(t)BF

Inventory level

W

IF5(t)

IF4(t)

IF1(t)

RF

IF2(t)

TF2TF1 TF5TF4TF3

IF3(t)

IF7(t)

IF6(t)

Fig. 3. Inventory level of two-warehouse FIFO model.



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Finally, total system cost per unit of time under FIFO dispatching policy is

TCF 1=TFF S1 HS2 C1S3 C2S4 C3

1=TFfFP TF3 DTF3 TF5=b HP TF2 DTF2 TF4=a C1PTF2 TF3 DTF2 TF3 TF4 TF5 C2DP DTFB

2=2P C3g. 28

In (28), TF2 is a constant that should have no difference with TL2, we have

TF2 TL2 1

aln

P D

P D aW

. 29

By using IF3(TF3) = IF6(0) and IF7(0) = IF5(TF4), from (21), (23), (24) and (25), the value of TF4 and TF5can be derived respectively as

TF4 1

a ln 1 aWeaTF3

D !

and TF5 1

b ln 1 P D1 ebTF3 ebTF4

D

. 30

Let TF3 and TFB be the two decision variables of(28). The optimal value ofTF3 and TFB must satisfy thetwo necessary conditions: oTC/oTF3 = 0 and oTC/oTFB = 0. After rearrangement, we have

P D C1 F

b

D C1

H

a

dTF4dTF3

D C1 F

b

dTF5dTF3

TC 1 dTF4dTF3

dTF5dTF3

0; 31

and

C2DP D

PTFB TC 0; 32

wheredTF4dTF3

aW

DeaTF3 aW;

dTF5dTF3

P DaW DeabTF3

aW DeaTF3 DebTF4 P D1 ebTF3 .

Furthermore, BF can be derived as BF DPD

PTFB, and by using IF4(TF3) = RF, from (22)

RF P D aW1 ebTF3

b.

Therefore, the optimal production policy under FIFO dispatching, i.e., BF and RF, can also be derived after

the optimal solutions TF3 and TFB are obtained.

From (14) and (28), one interesting observation is shown between the two policies.

Theorem 2. If the two warehouses have the same deterioration rate, i.e., a = b, then TCF > TCL for H < F,otherwise TCF > TCL if H < F, or TCF < TCL if H > F.

Proof. Let T3 and TB be the decision objectives of the two models. We want to prove that if F < H anda = b, then TCF < TCL for any combinations ofTC(T3, TB). First, let TL3 = TF3, TLB = TFB. The follow-ing Lemmas will hold:

Lemma 1. TL4 + TL5 = TF4 + TF5.

Lemma 2. aWD

TL3 TF4 > TL5.

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Proof of Lemma 1

(i) Add TL4 to both sides of (17), we have

TL5 TL4 1a

ln 1 aWD

eaTL4

1a

lneaTL4 1a

ln aWD

eaTL4

.

Substitute the value of TL4 in (16) to above equation and after simplification

TL4 TL5 1

aln

P P D aWebTL3

D

!.

(ii) Add TF4 to both sides of (30), we have

TF5 TF4 1

bln 1

P D1 ebTF3 ebTF4

D

1

bln ebTF4

1

bln

DebTF4 P D1 ebTF3

D

.

Substitute the value of TF4 in (30) to above equation and after simplification

TF4 TF5 1

bln

P P D aW ebTF3

D

! TL4 TL5.

(iii) Note also that, from (29) TL2 = TF2, we hence have

TLB TL2 TL3 TL4 TL5 TFB TF2 TF3 TF4 TF5; i.e., TL TF.

Proof of Lemma 2. Denote r = aW/D > 0, and let T0F4 1a

ln1 r.Define fTF3 TF4 rTF3 T

0F4, from (30)

fTF3 1a

ln1 reaTF3 1a

ln1 r rTF3 1a

ln 1reaTF3

1r

rTF3,

where f(0) = 0, f0TF3 r1eaTF3

re

aTF3

1reaTF3h i

> 0 by eaTF3 < 1.

Which implies that f(TF3) > 0 for TF3 > 0. We hence have TF4 rTF3 > T0F4.

Furthermore, from (17) TL5 1a

ln1 reaTL4 , which impliesTL5 < T

0F4 < TF4 rTF3. h

Proof of Theorem 2. From (14), (28), and the two lemmas

TCF TCL 1

TF

F

bDTL4 DTF5 aW TL3

H

aDTL5 DTF4 aW TL3

!

1

TF

F

bDTL4 DTF5 aW TL3 DTL5 DTF4 aW TL3

H F

aDTL5 DTF4 aW TL3

!

D

TF

F H

a

aW TL3

D TF4 TL5

!> 0; provided that F > H.

The above theorem implies that, in facing policy choice, if the two warehouses have similar preservationconditions that the inventory deterioration are nearly the same, then the policy choice solely depends on thedifference in inventory holding cost, namely H and F. FIFO policy will be less expensive when HF, other-wise, LIFO is suggested. Undoubtedly, when the two warehouses have all the same parameters i.e., b = a,and F = H, these two policies should have no difference, i.e., TCF > TCL. h



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3.3. Choice from one-warehouse system (L1) and two-warehouse system (L2)

Let the two warehouses be utterly no difference, i.e., a = b, H = F, total cost of different dispatching

policy in (14) and (28) of L2 can both be reduced to the following expression:TCF TCL 1=TfC1 F=bPT2 T3 DT2 T3 T4 T5

C2DP DT1 T62=2P C3g. 33

After certain variable simplification, expression in (33) is the same as Raafat et al. [13], which is an eco-nomic production quantity model for deteriorating items with unlimited warehouse space. Denote TCL1to be the average total cost of L1 system, we have TCF = TCL = TCL1.

Furthermore, let W = 0 and RW be the sole warehouse under consideration. By using the fact thatTL2 = TL5 = 0 [substitute W = 0 into (15) and (17)], same result in (33) can also be obtained from (14)of our modified LIFO model. Or, similarly, from (28)(30), one can derive TCL1 from TCF.

Under the assumption that OW is to be utilized first, L2 system will not necessarily be used if it is eco-

nomically less than L1. The following algorithm can be employed to determinate between the systemschoices for the two policies.

Step 1. First solve L1 in (33).Step 2. Calculate and denote RL1 the optimal maximum inventory level of L1.Step 3. If RL1 is less than W, L1 will be used. Otherwise, when R

L1 > W, compare TC

L2 with the boundary

cost on L1 at W, i.e., TCL1(W). L2 will be used if TCL2 < TCL1W, otherwise L1(W) is the optimal

solution.

4. Illustrative example

The following parameters are used to illustrate the application of the two models. The production capac-ity is 32 000 units per year; the demand rate is 8000 units per year; other related factors are as follows: short-age cost is $8 per unit per year; deterioration cost is $20 per unit; OW capacity is 1200 units.

In Table 1, in order to make comparison of the deteriorating effect on policy selection, holding cost inthe two warehouses are assumed to be equal, i.e., (H, F) = (2, 2), deterioration rate in RW be fixed at 0.06.

Denoted r = a/b, by increasing the value r (increase a), total cost would increase under both policies.From Table 1, we can observe that, if r = 1, both policies will utterly bear no difference and have the samedecision as Theorem 2 has shown. In fact, the selection of policy depends on the value of r when there areno material differences in the holding cost between the two warehouses. If r < 1, when deterioration effect inOW is smaller than in RW, LIFO is suggested in order to avoid a higher cost in RW due to a higher inven-

Table 1Comparison of policy by varying deterioration rate

r FIFO LIFO

RF W BF TC

F R

L W B

L TC

L

0.1 2305.8 882.6 7061.3 2497.7 837.2 6697.50.5 2311.4 902.5 7219.9 2419.3 878.0 7024.11 2317.7 927.1 7416.7 2317.7 927.1 7416.72 2328.4 975.7 7805.2 2100.7 1018.5 8147.84 2342.1 1070.4 8563.3 1588.6 1170.8 9366.3



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tory deterioration. On the other hand, if r > 1, FIFO is preferred to LIFO. Defining cost penaltyDTC% = (TCL TCF)/TCF, in the case of relatively higher deterioration rate in OW, namely r = 2,and r = 4, the cost penalty of using LIFO policy are 4.39% and 9.37% respectively.

By letting (a,b) = (0.0625, 0.05), i.e., r = 1.25, other parameters remain the same, Table 2 shows theimpact that H and F have on the optimal policy. We have the following observations:

1. Under the L2 system, FIFO policy will always suggest a lower total cost than LIFO when F5 H. Whilefor H = 8, the optimal policy suggests the L1 policy, it is unnecessary to make any differentiation.

2. The higher the value of holding cost in H and F, the higher the value of TCF and TCL. While it is indi-cated that TCL is more sensitive to a change in H than a change in F, and vice versa, TCF is more sen-sitive to the change of F. When F increases, it is expected that FIFO has a higher increase in total costthan LIFO, as it implies higher holding cost in RW, since inventory items have to be carried longer thanthat of LIFO.

3. Under the assumption that OW is to be stored first, any changes in RW parameters ( F or b) will notchange the decision from L2 to L1, or vice versa, from L1 to L2 in both two models. From Table 2,

for example, for H = 2 (where RL1 > W), L2 is suggested as the optimal solution except when F= 8

Table 2Comparison of the difference in policy under varying holding cost combination

H F FIFO LIFO

RFW BF TC

F R

LW B

F TC

L

2 2 2417.7 915.8 7326.8 2370.2 926.0 7408.64 1715.9 925.6 8044.8 1957.1 961.7 7694.38 1200.0(W) 932.2 8365.7 1646.7 992.2 7938.1

4 2 2429.5 996.5 7971.7 1967.8 1073.9 8591.44 1721.3 1084.8 8678.2 1684.1 1089.9 8719.48 1200.0(W) 1091.2 8973.8 1481.3 1105.5 8820.7

8 2,4,8 1097.2(L1) 1268.9 10151.2 1097.2(L1) 1268.9 10151.2

Table 3Analysis of change in various parameters has on policy choice

TC0

L TC0

F DTC0% Policy suggest

W0/W 0.5 8075.2 7549.7 6.96% FIFO2 8729.7 8729.7 0% L1

P0/P 0.5 7100.9 6858.4 3.54% FIFO2 9223.3 8404.7 9.74% FIFO

D0/D 0.5 6668.3 6241.2 6.84% FIFO2 9792.3 9314.6 5.13% FIFO

C01=C1 0.5 8170.0 7462.7 9.48% FIFO2 9244.5 8792.9 5.14% FIFO

C02=C2 0.5 7360.4 7008.6 5.02% FIFO2 9456.7 8620.8 9.69% FIFO

C03=C3 0.5 6170.6 5936.9 3.94% FIFO2 11782.5 10908.3 8.01% FIFO



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where L1 is to be used but at full capacity (W). Similarly, in LIFO, when F increase (under H = 2 and 4where L2 is used) it would not reverses back to L1 system. In fact, only as F ! 1, L1(W) would be theoptimal solution of LIFO, a similar result has been shown in (1256) of Hartley [7].

The sensitivity analysis, with respect to other parameters on the total system cost is examined. Theresults are summarized in Table 3. The following inference may be drawn from Table 3.

1. The range ofDTC0% is from 3.54% to 9.74%. The average value ofDTC0% is about 6.68%.2. The value ofDTC0% is more sensitive to the parameter of subset P, C1, C2, C3, and less sensitive to

parameter D.3. The higher the value of subset W, D, C1, the smaller the value ofDTC

0%, but the higher the value ofsubset P, C 2, C3, the higher the value ofDTC

0%.4. Changes in the parameter subset W, P, D, C1, C2, C3 do not change the optimal dispatching policy.

5. Summary and conclusions

Previous literature on two-warehouse inventory model has always assumed that inventory holding costin RW is higher than OW. This resulted in a LIFO flow of inventory that items in RW must be consumedprior to OW to avoid higher holding cost. This assumption is not necessarily true in the real world becauseRW is a specialized operation faced with severe competition that the opportunity to gain lower holding costthan OW is higher. Most important for managers that deal with perishable products using FIFO, ratherthan LIFO, is a common accepted practice of making sure that the products are dispatched at its maximumfreshness. In this paper, a two-warehouse inventory model with the FIFO dispatching policy for deteriorat-ing inventory items was proposed. It has been proven that when deterioration rate is the same in the two

warehouses, FIFO is less expensive than LIFO provided that holding cost in RW will be lower than OW. Inaddition, Pakkala and Acharys two-warehouse LIFO model has been sufficiently modified to be morecomplete. The modified LIFO model has proven to have a lower cost than Pakkala and Acharys modelunder their assumption that H < F, when a is not significantly less than b.

Numerical analysis have indicated {a, b, H, F} are the key set of factors in choosing LIFO or FIFO.Particularly, when RW parameters {b, F} are superior to that of OW {a, H}, in this case FIFO wouldbe employed rather than LIFO. From the analysis, it was pointed out that TCL is more sensitive to a changein Hthan a change in F, and to the contrary, TCF is more sensitive to a change in F. Other parameters suchas {P, D, W, C1, C2, C3} would have impacted solely on the magnitude but not in the directions between thetwo policies.

References

[1] Anonymous, Public warehouse: Broadening service to meet new needs, Modern Materials Handling 39 (1984) 4851.[2] L. Benkherouf, A deterministic order level inventory model for deteriorating items with two storage facilities, International

Journal of Production Economics 48 (1997) 167175.[3] A.K. Bhunia, M. Maiti, A two warehouse inventory model for deteriorating items with a linear trend in demand and shortages,

Journal of Operational Research Society 49 (1998) 287292.[4] P.M. Ghare, G.F. Schrader, A model for an exponentially decaying inventory, Journal of Industrial Engineering 14 (1963) 238

243.[5] A. Goswami, K.S. Chaudhuri, An economic order quantity model for items with two levels of storage for a linear trend in

demand, Journal of Operational Research Society 43 (1992) 157167.



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[6] S.K. Goyal, B.C. Giri, Recent trends in modeling of deteriorating inventory, European Journal of Operational Research 134(2001) 116.

[7] V.R. Hartley, Operations Researcha Managerial Emphasis, Goodyear, Santa Monica, 1976.[8] C.C. Lee, C.Y. Ma, Optimal inventory policy for deteriorating items with two-warehouse and time-dependent demands,

Production Planning and Control 11 (2000) 689696.[9] T.M. Murdeshwar, Y.S. Sathe, Some aspects of lot size models with two levels of storage, Opsearch 22 (1985) 255262.

[10] T.P.M. Pakkala, K.K. Achary, A deterministic inventory model for deteriorating items with two warehouses and finitereplenishment rate, European Journal of Operational Research 57 (1992) 7176.

[11] T.P.M. Pakkala, K.K. Achary, Two level storage inventory model for deteriorating items with bulk release rule, Opsearch 31(1994) 215227.

[12] W.P. Pierskalla, C.D. Roach, Optimal issuing policies for perishable inventory, Management Science 18 (1972) 603614.[13] F. Raafat, P.M. Wolfe, H.K. Eldin, An inventory model for deteriorating items, Computers and Industrial Engineering 20 (1991)

8994.[14] F. Raafat, Survey of literature on continuously deteriorating inventory models, Journal of Operational Research Society 42 (1991)

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FIFO v LIFO