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					    8th International Conference of Modeling and Simulation - MOSIM’10 - May 10-12, 2010 - Hammamet - Tunisia
                  “Evaluation and optimization of innovative production systems of goods and services”


                    Daniel THIEL                                               Vincent HOVELAQUE
    CEPN, UMR CNRS 7115/Université de Paris 13,                     UMR 1302 SMART/ AGROCAMPUS OUEST
          99 avenue Jean-Baptiste Clement,                                   65 rue de Saint-Brieuc, CS 84215
             93430 Villetaneuse - France                                   35042 Rennes Cedex - France

                                                  Thi Le Hoa VO
                                      CREM, UMR CNRS 6211/IGR-IAE de Rennes
                                           11 rue Jean Macé, CS 70803
                                         35708 Rennes Cedex 7 - France

ABSTRACT: This article focus on the behaviour of a multi-product batch production line with fixed capacity which is
scheduled according to inaccurate inventories (IRI). We assume an unlimited supply of raw materials and a constant
demand for the different finished goods. The ordering policy of this production line is based on a (Q,R) continuous
review, lost-sales inventory model and on given priority for each product using the same production line. Simulation
modelling is proposed to investigate the relationship between the quality of service, safety stock and inventory
inaccuracy under demand variations for each product. It is shown that the service-level quality is a non-monotone
function of the inaccuracy rate, i.e. the service-level quality increases twice up to an IRI’s level and decreases after.
This unusual phenomenon has been observed which goes against certain empirical practices in the SMEs that safety
stock is only necessary for certain intervals of data inaccuracy rate.

KEYWORDS: Multi-product production line, continuous review inventory system, inventory inaccuracy, continuous
model, discrete-time simulation.

                                                               et al., 1999; Simchi-Levi et al., 2000). ECR initiative has
1   INTRODUCTION                                               tried to redefine how grocery supply should work (Lee et
                                                               al., 1997). According to the authors, one motivation for
The objective of this paper is to undertake the study of       the initiative was the excessive amount of inventory in
influence of inventory record inaccuracy (IRI) on ser-         the supply chain. The result showed that distorted infor-
vice-level quality of a multiproduct manufacturing line.       mation has led every entity in the supply chain to stock-
IRI notion was introduced by Schrady (1970) as a dis-          pile because of the high degree of demand uncertainties
crepancy between the recorded inventory quantity and           and variability. In addition, VMI is an important strategy
the actual inventory quantity physically present on the        to share information both demand and inventory. Bene-
shelf. According to other authors, such errors are also        fits of using VMI systems include lowered inventory
due to replenishment errors, shoplifting, improper han-        levels, faster inventory turns, increased sales, and re-
dling of damaged merchandise, imperfect inventory au-          duced out-of-stock costs (Angulo et al., 2004). Using a
dits, transaction errors, misplaced products and incorrect     simulation model, Disney and Towill (2003) show that
recording of sales. The effects of this dysfunction are        VMI implementation can help to eliminate two sources
numerous and for instance, in one of their recent pro-         of the Bullwhip Effect, i.e. rationing and gaming (Houli-
jects, ECR Europe (2003) found that the value of lost          han Effect) and the order batching effect (Burbidge Ef-
inventory due to shrinkage in 2000 was €13.4 billion for       fect) and to reduce the impact of other sources of
retailer and €4.6 billion for manufacturers in Europe          Bullwhip Effect. The authors also propose that VMI can
(Kök and Shang, 2009).                                         be of great benefit to the vendor or supplier in a VMI
                                                               relationship if they correctly use inventory and sales in-
Organizational and/or technical improvements have been         formation in the production and inventory control deci-
proposed to address this recurring problem. Automatic          sion-making process.
replenishment programs (ARPs) such as Efficient Con-
sumer Response (ECR) or Vendor-Managed Inventory               Therefore, the main goal of this paper is to develop a
(VMI) represent an inventory management tool designed          simulation model in order to analyze the impact of IRI
to improve efficiency across the supply chain (Daugherty       on the quality of service of a multi-product assembly line
                                  MOSIM’10 - May 10-12, 2010 - Hammamet - Tunisia

with lot priority. To achieve this aim, a simulation model    echelon inventory system with multiple item types and
of a (Q,R) continuous review lost-sales inventory model       the use of cycle counting as the corrective action. The
with different products according to product priority and     results show that the correct application of cycle count-
resource constraints has been completed by an analytical      ing will increase record accuracy and provide significant
approach aiming at studying the relationship between          amount of savings for the entire supply chain. The au-
IRI and the volume of products out of stock during a          thors also demonstrate the ability of simulation models
long period of time.                                          to simulate more than one item type within a multi-
                                                              echelon inventory system as well as a more general de-
The paper is then organized as follows. At first, a litera-   mand amount process. Nevertheless, none of these au-
ture review shows that few researches deal with the im-       thors focuses on the problems of IRI in a multi-product
pact of IRI on service-level quality subjected to demand      manufacturing system.
fluctuations and particularly in a multiple product multi-
echelon inventory system. Second, a simulation model is       From a theoretical point of view, many papers consider
described and based on a (Q,R) policy taking into ac-         such problems with inventory policy approaches. To our
count inaccuracies in inventory records. At third, the        knowledge, works on optimizing safety stock (e.g. Shin,
simulation results will be analyzed in order to show the      1999; Ross, 2002; Atali et al., 2005) never take into con-
impact of inventory inaccuracy on the quality of service      sideration the risk induced by inventory inaccuracy.
in this particular system. Finally, discussion and out-       Most researchers do indeed introduce the fluctuation of
looks are proposed focusing on both service-level quality     demand and shipment delay, but few of them take IRI
and safety stock calculation in case of inventory inaccu-     into account. Their research usually focuses on (Q,R)
racy.                                                         system optimization models under uncertainties in lead-
                                                              times, demand, supply, machine breakdown, etc., but
2   LITERATURE REVIEW                                         rarely emphasize the effect of inventory inaccuracy upon
                                                              service-level quality. For example, Sahin et al. (2009)
Research on IRI has been taking place since the 1960s         propose a newsvendor type model which analytically
with the report by Rinehart (1960) on a case study of a       derives the optimal policy in the presence of records
Federal government supply facility. The author stated         errors of evenly distributed inventory and demand in the
that this inaccuracy produces a “deleterious effect” on       supply chain. Rekik et al. (2008) have also developed an
operational performance. Following this, Iglehart and         analytical model of a single-period store inventory
Morey (1972) reported that this divergence between            model subject to misplacement errors and compare it to a
stock record and physical stock results in “warehouse         RFID implemented inventory system.
denials”. Their research took into consideration the fre-
quency and depth of inventory counts and stocking pol-        Even though most of the current research focusing on
icy to minimize total cost per time unit. Studying a simi-    (Q,R) policy often propose models of operational re-
lar problem, Kök and Shang (2004) have suggested im-          search, simulation modelling is becoming an effective
plementing a cycle count program and carefully adjust-        and timely tool and is capturing the cause and effect rela-
ing base-stock levels across periods to minimize total        tionship in this field. For example, Kang and Gershwin
inventory and inspection costs. Moreover, focusing on         (2004) use analytical and simulation modelling to inves-
the significance of measuring IRI, DeHoratius and Ra-         tigate the problems caused by information inaccuracy in
man (2008) show that inventory counts may not impact          inventory systems. By applying the (Q,R) policy, they
record inaccuracy and additional buffer stock may not be      suggest that a small rate of stock loss can disrupt the
equally necessary across all items in all stores. They also   replenishment process and create severe shortages of
suggest that inventory density and product variety have       stock. According to these authors, the IRI problem can
substantial implications for identifying and eliminating      be effectively controlled if the stochastic behaviour of
the source of inventory record inaccuracy. However,           the stock loss is known. Fleisch and Tellkamp (2005) use
their study is only based on the retail stores of one firm    simulation and variance analysis to study the individual
and does not include all factors that might impact varia-     impacts of different types of IRI on the performance
tion in IRI from one store to the next or across manufac-     measurements of a three-echelon inventory system with
turing plants with product variety and inventory levels.      on product. Their results show that eliminating inventory
                                                              inaccuracy can reduce supply chain cost and out-of-stock
Product variety and inventory levels are analogous to         level even if the level of process quality, stolen and un-
environmental complexity in information processing            saleable items remains unchanged. Besides, the supply
theory (Flynn and Flynn, 1999; Vachon and Klassen,            chain performance increases further if at the same time
2002). Particularly, increasing product variety is akin to    as inventory inaccuracy is eliminated; the factors that
increasing the organizational “complexity cost” (De-          cause inventory inaccuracy are improved.
Horatius and Raman, 2008). In manufacturing such cost
include reduced manufacturing efficiency, frequent
                                                              3   THE MODEL
changeovers, and the activities need to track and support
each variant (Yunes et al., 2004). In addition, Gumruk-
                                                              Following our previous work (Thiel et al., 2010)
cua et al. (2008) present a simulation model of a two-
                                                              concerning the influence of inaccuracies in (Q,R)
                                                           MOSIM’10 - May 10-12, 2010 - Hammamet - Tunisia

models, we choose here to study the influence of
inventory record inaccuracies of quality of service of                                        Then, the inventory shortage in period k for the product i
different products according to a given priority and a                                        is defined by:
unique shared resource (one production line for different                                                      {
                                                                                              Kr k , i = max δ k , i − ( X k , i + Q i × S k , i ); 0   }     (2)
products, see Figure 1).
                                                                                              Following Kang and Gershwin (2004), the inventory
                                                                                              records X1,i, X2,i… of product i suffer from inaccuracy
                                       Inaccurate                                             information which would lead to shortages. For the
                                                                                              supply decision process, it is assumed that the manager
                                                                                              has an approximate knowledge of the stock level.
          Multiproducts line
          Limited capacity                             1                  Retailer 1 Orders

                                                                                              A supply order is placed if the on-hand estimated stock
              Batch    production    by                i                  Retailer i Orders
                                                                                               X k ,i is less than Ri and if there is no inventory on-order;
              product priority
                                                                                   .          that is, there is no supply delivered between k and (k+Li-
                                                                                              1). Then the supply order process is defined as follows:
                                                       n                  Retailer n Orders

                                                                                                             ~                                k −1
                                                                                                       1 if X k − Li , i < Ri and
                                                                                              S k ,i =                                        ∑ S j ,i = 0   (3)
                                                                                                                                             j = k − Li
                                                                                                       0 otherwise
   Production Orders
   with priority 1, ...i..., n

                                    (Qi,Ri) inventory management policy
                                                                                              Finally, this model is based on two inventory level
                                                                                              comparisons: demand and the real inventory levels, and
                                           Figure 1                                           the approximate inventory with the reorder point levels.

Nomenclature                                                                                  As referred in introduction, the research objective is not
δk,i    Demand for period k (mean µi and standard                                             to define an optimal policy for inventory management
                                                                                              but to analyze the service-level evolution for the
        deviation σ i )
                                                                                              different products under different model parameters. In
Li      Delivery time                                                                         the following, Qi and Ri are fixed and assumed to be the
Qi, Ri Inventory policy for product i                                                         best responses to the classical optimization problem
Xk,i    Real stock level at the beginning of period k for                                     (Thiel et al, 2009).
        product i
 ~      Estimated inventory level at the beginning of
 X k ,i                                                                                       In this lost-sales case, the service-level is defined by
        period k for product i                                                                cumulating the number of inventory shortages Krk,i de-
εk,i    Error of inventory level for period k                                                 fined in (2) during a definite period of time (there is no
Sk,i    Binary variable (equals 1 if a packaging order                                        order backlog). To consider an inaccuracy in the inven-
        was placed at k-Li                                                                    tory level, εk,i is defined as an error of inventory estima-
                                                                                              tion at each period k. When reporting inventory accuracy
Model process                                                                                 or variance many companies talk about the net results of
                                                                                              the actual physical inventory against the book balance; in
Consider a retailer’s warehouse which follows a conti-                                        other words, the net sum of all the overstocks and short-
nuous review (Qi,Ri) policy for each finished good prod-                                      ages is close to 0. This may be acceptable for financial
uct i. This policy consists in supplying a fixed quantity                                     purposes but not acceptable for managing inventory.
Qi when the inventory level becomes lower as a given                                          Under these rules, one SKU could have an overage of
threshold Ri (Ri < Qi). For each period k, the demand δk,i                                    100 pieces while another has a shortage of 100, but the
is assumed to be independent and normally distributed                                         net result would be perfect. According to these empirical
random variable with mean µi and standard devia-                                              observations, inventory inaccuracy will be considered as
tion σ i .                                                                                    a Gaussian continuous random variable independently
                                                                                              and identically distributed with mean 0 and finite stan-
At the beginning of a period k, the real inventory level
for each product i is equal to Xk,i. If a supply is delivered                                 dard deviation σ ε , i . This assumption has been chosen by
during this period k, the on-hand stock is Xk,i+Qi. Thus,                                     Iglehart and Morey (1972), Morey (1985), Kök and
the demand δk,i is compared either to Xk,i or to (Xk,i+ Qi).                                  Shang (2004), Sahin et al. (2008) or Uçkun et al. (2008)
The inventory evolution can be described by the follow-                                       in the form of additive random variables. Many authors
ing relationship:                                                                             also consider two main errors which can occur, stock-
 X k +1, i = max {X k , i + Qi × S k , i − δ k , i ,0}                                        loss error and transaction error at the retailer level. For
                  1 if an order wasplaced at k − Li     (1)                                  example, Gumrukcua et al. (2008) consider the amount
            with S k ,i =                                                                    of the stock-loss error as a Poisson distribution with a
                          0 otherwise
                                          MOSIM’10 - May 10-12, 2010 - Hammamet - Tunisia

mean proportional to the demand rate. Kang and                                       {              }
                                                                         X t , i = max 0, X t , i + ε t , i
Gershwin (2004) suggest that overall in the retail indus-
try, the inventory record error tends to have nonzero                   Ori = 0
mean.                                                                   If (OIPt,i = 0 and X t ,i < Ri and π i > max (π j ) ∀j ≠ i )
                                                                        then Ori = µι z.
Thus, the sequence at each period and for each product is               If OIPt,i > 0 then OAt+L,i = µι z else 0.
assumed to be as follows:                                               Xt+d,t,i = Xt,i + ( OAt,i – min[Xt,i, δt,i] ) dt
- The real component inventory is adjusted to                           Krt+dt,i = Krt,i + max[0, (µι - Xt,i )] dt
Xk,i + Sk,iQi , with Sk,i defined in equation (3).
- The demand δk is revealed. Either the demand is totally
satisfied (if Xk,i + Sk,i Qi ≥ δk,i) or not (loss-sales of          4   IMPACT OF THE INVENTORY RECORD
δ k ,i − X k ,i − S k ,i Qi )                                           INACCURACY ON THE QUALITY OF
- The         inventory           level  is  approximated  by
 X k +1,i = X k +1,i + ε k +1,i and  a supply order is placed
                                                                    Fleisch and Tellkamp (2005) propose to define inventory
if X k +1,i < Ri .                                                  inaccuracy as “the absolute difference between physical
                                                                    and information system inventory, divided by the aver-
                                                                    age physical inventory”. For each product i, it is chosen
Simulation translation
                                                                    here an inaccuracy rate IRi =  σ ε  varying from 0% to
                                                                                                   
This analytical formulation is now translated into a con-                                          Ri 
tinuous model with discrete-time simulation. This model             90% which corresponds to a variation of σ ε between 0
is simulated using Euler integration method during a                and 5,000.
period T with a time step dt.
                        ~                                           We consider a manufacturer which produces a specific
Variables: δt,i , Xt,i, X t ,i , OIPt,i, OAt,i, Krt,i Ori,          product for each retailer using the same production line.
Model parameters: σ ε i , σ i , πi                                  To just focus on the effect of inventory errors, we as-
                                                                    sume that the demand and inventory policy for each
Constant:, z, CP, L, Ri, Qi                                         product are the same.
δt,i Demand of product i at time t normally distributed             Simulation were run one hundred times using iThink®
z Order quantity inventory coverage time                            software and default random noise seed for generating
Xt,i Inventory level at time t with X0,i = µι z                     different inaccuracies in the inventory data. The data
 X t , i Inaccurate inventory record                                were collected after a run-in period of 1,000 hours fol-
L Production lead-time (assumed to be the same for                  lowed by a recording period of T = 32,000 hours and
         each product i using the shared production line)           with a time step dt = 1 hour.
Ri Reorder point with safety stock for a 97.5% service
         level Ri = µι L + 1.96 σ i                                 For each running time, the service-level quality for each
Qi Fixed quantity order Qi = µι z                                   product is evaluated by recording the value of Krt,i ac-
OIPt,i Order quantity in process not delivered at time t
                                                                    cording to each value of the inventory inaccuracy rates.
OAt,i Order quantity arrived at time t+L when launching
                                                                    The values of Krt,i have been defined by average values,
         an order at time t                                         standard errors, confidence intervals, skewness and kur-
Ori Ori = 0 when no order is launching (else Ori = Qi)              tosis. Each simulation is based on a constant demand
Krt,i Cumulated number of products out-of-stock at time t           µ of 300 per hour for each product i, a delivery time
πi Priority given for each product i                                L = 18 hours, an order quantity inventory coverage time
CP Fixed capacity of the production line                            z = 64 hours, a reorder point Ri = µ L = 300 x 18 = 5,400
                                                                    and a fixed order quantity Qi = µ z = 300 x 64 = 19,200.
Preliminary comments

If no order OIP is in process during the lead-time L and
if the inaccurate inventory level X t , i is under the reorder
                                                                    4.1. Service-level quality with production capacity
point Ri, then one orders a fixed quantity Ori.                     variation
The quantity OAi is available at time t+L when an order
has been launched at time t.                                        We propose to study the product service-level quality
                                                                    according to different levels of the production capacity.
OIP0,i = 0; OA0,i = 0; X0,i = µι z; Kr0,i = 0;
For t = 0 to T step dt
                                                                 MOSIM’10 - May 10-12, 2010 - Hammamet - Tunisia

The first hypothesis considers a production line with a
minimum production capacity defined so that there are
no shortages if there are no inventory inaccuracies.

The figure 2 shows a case with three products using the

                                                                                                     Number of shortages
                                                                                                     during 32000 hours
same production line with the highest priority for prod-
uct 1, a medium priority for product 2 and lowest priori-                                                                  30000
ty for product 3.
For each product, a non-monotone relationship between
the number of shortages Kr,i cumulated after a total simu-                                                                 10000
lation time of 32,000 hours and the inventory inaccuracy
rate IRi. Two peaks are observed for low and high val-                                                                        0
                                                                                                                                   0%   20%        40%          60%         80%    100%
ues of IRi. For high IRi values the peak amplitudes are                                                                                        Inventory inaccuracy rat e
higher for low priority products which confirm that the
priority policy rules are kept whatever inaccuracy level.                                                    Product 1                              Product 2
                                                                                                             Product 3                              P1 Only two products
We also simulated the case of one product                                                                    P2 only two products
( µ 2 = µ3 = 0 ) and we observed only one peak which
                                                                                                Figure 3: Evolution of service-level quality Kr,i with IR,i
confirms our previous work (Thiel et al, 2009).
                                                                                                inventory inaccuracy rate (constant demand).

                                                                                                Some empirical explanations can be provided. When the
                        90000                                                                   inaccuracy rate is between 10% and 40%, it seems that
                        80000                                                                   in case of a high level of inaccuracy, the decider more
                                                                                                frequently supposes that the stock level is not enough
                                                                                                and consequently, anticipates more orders. Nevertheless,
  Number of shortages

  during 32000 hours

                                                                                                when the inaccuracy rate is greater than 50%, the ser-
                        50000                                                                   vice-level quality decreases again and the same phe-
                        40000                                                                   nomenon can be observed after 70% with an improve-
                        30000                                                                   ment of the service-level quality.

                        10000                                                                   4.2. Service-level quality in VMI context
                                0%   20%       40%         60%         80%   100%
                                           Inventory inaccuracy rate
                                                                                                We consider now that the manufacturer develops a VMI
                         Product 1     Product 2             Product 3       Only one product   with one of the retailer. In that case, we make the hypo-
                                                                                                thesis that the retailer’s stock is fully accurate. We de-
Figure 2: Evolution of service-level quality Kri with IRi                                       velop two simulations: the VMI relationship with the
inventory inaccuracy rate (constant demand).                                                    first retailer (that is the high level priority in the produc-
                                                                                                tion line) and the VMI relationship with the second one.

The second hypothesis corresponds to the case of a very
high level of the production line capacity >> 3Q. The                                           Same as before, we simulate the model for different val-
figure 3 shows the evolution of the service-quality level                                       ues of stock error (Ei) for each product i.
of each product according to different inventory
inaccuracy rates in case of three or just two products
using the same production line.                                                                                                               H1                             H2
Compared to the previous case with shorter capacity,                                                   E1                                     0                             50%E
two peaks are also observed but are more tightened.                                                    E2                                50%E                                 0
Obviously, the shortages levels are lower with a higher
capacity.                                                                                              E3                               100%E                               100%E

                                                                                                The results are shown in Figure 4 (hypothesis H1) and
                                                                                                Figure 5 (hypothesis H2).
                                                                                                On each figure are also presented the standard deviations
                                                                                                of total shortages.
                                                                                                  MOSIM’10 - May 10-12, 2010 - Hammamet - Tunisia

                                                                                                                               The relationship between these two variables is quite
                                                                                                                               complex. In fact, the service-level initially declines as
                                                                                                                               the inaccuracy rate increases and then it improves at or
                                                                                                                               after a threshold and again the same phenomenon has
                                                                                                                               been observed for high inaccuracy rates. This observa-
                                                                                                                               tion has been validated in different cases of n products,
                                                                                                                               n>1. Even though the results in this study are based on
    Number of shortages
    during 32000 hours

                                                                                                                               simulation modeling, the observed phenomenon will
                              30000                                                                                            further theoretically analyzed by defining the shortage
                                                                                                                               probabilities in the case where the real stock level is be-
                                                                                                                               low the replenishment threshold and also the measured
                                                                                                                               inventory exceeds the same threshold.

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                                                    0%            20%          40%         60%           80%         100%
                                                                        Inventory inaccuracy rat e (E)
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                                                Product 1         Product 2       Product 3                                      Supply chain information sharing in a vendor-
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