An Algorithm for Production Planning Based on Supply Chain KPIs

Abstract

This paper observe multi-period multi-product production planning problem in make-to-stock production environment with limited production capacity. Such problem is identified in Fast Moving Consumer Goods industry. The goal was to develop an algorithm for supporting dynamic production triggering decisions in relation with two supply chain key performance indicators: stock cover and customer service level. The presented approach is applied to a real example in several scenarios based on different decision criteria.

Full text

INTERNATIONAL JOURNAL OF COMPUTERS COMMUNICATIONS & CONTROL
ISSN 1841-9836, 9(6):711-720, December, 2014.
An Algorithm for Production Planning Based on Supply Chain
KPIs
D. Makajić-Nikolić, S. Babarogić, D. Lečić-Cvetković, N. Atanasov
Dragana Makajić-Nikolić*, Sladjan Babarogić
Danica Lečić-Cvetković,Nikola Atanasov
University of Belgrade, Faculty of Organizational Sciences
Serbia, 11000, Belgrade, Jove Ilića 154
E-mail: gis@fon.bg.ac.rs, sladjan@fon.bg.ac.rs
danica@fon.bg.ac.rs, atanasovn@fon.bg.ac.rs
*Corresponding author
Abstract: This paper observe multi-period multi-product production planning prob-
lem in make-to-stock production environment with limited production capacity. Such
problem is identified in Fast Moving Consumer Goods industry. The goal was to de-
velop an algorithm for supporting dynamic production triggering decisions in relation
with two supply chain key performance indicators: stock cover and customer service
level. The presented approach is applied to a real example in several scenarios based
on different decision criteria.
Keywords: production planning, stock cover, customer service level, heuristic algo-
rithm.
1 Introduction
Manufacturing companies that operate in markets with changing demand are often faced
with the problem of insufficient supplies of finished products. Constant fluctuations in demand
and the required financial investments are influencing the decision concerning the expansion of
the production capacity. Until the production capacity is actually increased, the manufacturing
company has to meet the growing demand of the market with its existing production capacity.
As customer orders are received periodically and production capacities are often insufficient, it
is necessary to make a choice of products which will be produced in each period. In circumstances
of reduced uncertainty, it is possible to use exact methods for planning customer satisfaction by
cycle, when trends in demand are predictable over a longer period of time. However, in real
life this is not the case, as demand is a weekly phenomenon which requires dynamic decision-
making. Therefore, in this paper we propose an algorithm for production planning in which
decision on triggering new production is based on two supply chain key performance indicators
(KPI): customer service level and stock cover.
This paper is organized in six sections. Next section describes related work with conceptual
foundations. Problem description with relevant notation is presented in section tree. Heuristic
algorithm for inventory planning is given in fourth section. In fifth section, numerical results
with case study are described. Last section is dedicated to conclusions of the research.
2 Related Work
According to [5] uncertainty in production companies is categorized into environmental uncer-
tainty - based on demand and supply uncertainty and system uncertainty (within the production
process) - mainly related to production lead time, quality or failure of production process. Un-
certainty depends on level of information required to perform relevant business activity based
on efficient and effective management decision [4]. Responsive production planning and control
Copyright ©2006-2014 by CCC Publications

712 D. Makajić-Nikolić, S. Babarogić, D. Lečić-Cvetković, N. Atanasov
system according to [7] is the most important factor in achieving good delivery performance and
demand satisfaction in supply chain. This fact represents one of important reason to focus more
on customer service as external performance, once when internal performance is already achieved
on certain level.
As recognized by Shen and Daskin in [13] major cost factors associated with designing and
managing a supply chain are the facility location costs, the inventory management costs, and
the distribution costs, and always should be considered jointly and integrated with customer
service goals. Customer service was recognized as key measure of performances within production
companies according to [9] and very well described by [11]. Overall managerial question in
supply chain is to determine a cost-effective customer-service level in correlation with profits
and associated costs, what lead to question: Which service level will satisfy customers and what
level of inventory is required? Jeffery et al. identified a range of models for determining service
level and the appropriate level of inventory, process was carried out based on logistic regression
to understand how performance of delivery are dependent on three independent variables: order
lead time, errors in forecast, and variation in demand [6]. Further development of service level
and customers selection in make-to-stock production environment was evaluated by [8], while
authors in [1] evaluated possibilities for maximization of customer service with limited production
capacity and customer classification.
Stock cover is key performance indicator measuring length of time that available finished
goods will last if forecasted consumption happens. Available finished goods ready to be delivered
to customer according to identified demand are in direct correlation with customer service level.
Dellaert and Jeunet [2] evaluated stock cover in relation to behavior of lot-sizing rules in a
multilevel context, when forecast demand is subject to changes within the forecast window and
relevant lead time. According to [12], supply system needs to ensure adequate stock level to
satisfy customers need, despite that additional stock only generates unnecessary costs, which
customer has to absorb at the end. Managing customer service level and stock cover represents
highly complex problem of supply chain, taking into account that these two KPIs are leading
to opposite directions - high stocks assume high customer service level, and, at the same time,
stock need to be minimized to deliver working capital reduction and overall company efficiency.
Working capital reduction coupled with increase of sales and certain service level was evaluated
by [14] through results of horizontal collaboration between supply chain members. Combined
approach of managing in parallel customer service level and stocks cover was done by [3] who
evaluated main obstacles in increasing pressure to reduce working capital, growing variety of
products and the fulfillment of a demanding service level. Petri nets model of production planning
system based on supply chain KPIs: customer service level and stock cover was presented in [10].
3 Problem Description
In this paper we observe multi-period multi-product inventory planning problem in make-to-
stock production environment with limited production capacity. We started from a real example
of Fast Moving Consumer Goods (FMCG) in Serbia. Choice of products than will be produced
should be made in each period (cycle). This decision is based on two key performance indicators:
Customer service level (CSL) and Stock cover (SC). The basic assumptions of the observed
problem can be divided into three groups as follows.
•Customers orders assumptions:
–Customers place orders in all or almost all of the cycles;
–Demand for each product is uneven and is known only for one cycle in advance;

An Algorithm for Production Planning Based on Supply Chain KPIs 713
–Demand for each product represents the sum of all customers orders for delivery in
given cycle;
–Decision about fulfillment is done in given cycle when all orders are received;
–Demand is fulfilled from the stock, entirely or partially, depending on the inventory
level;
–Orders that have not been fully met in the reporting cycle shall not be compensated
in the subsequent cycles - no reordering policy;
•Inventory assumptions:
–If the incoming customer orders in a single cycle do not exceed the available stock of
finished goods, the allocation is complete and all customer orders are fulfilled, while
any surplus products are stored for the next cycle;
–Inventory holding costs are neglected;
–Total inventory capacity is not limited. Therefore, inventory planning problem be-
comes production planning problem;
•Production assumptions :
–The production capacity is limited and constant in the entire period;
–There is no possibility for production extension in medium term planing horizon;
–Due to specific production technology requirements, outscoring with acceptable costs
is not possible;;
–Lot sizes of products are different and fixed;
–Production time and costs are neglected due to homogeneity of the products;
In order to formulate the algorithm and based on the problem assumptions, the following
notation will be used in the remaining of the paper:
•n- number of products;
•m- number of periods in the observed time horizon;
•mcsl - minimally acceptable customer service level;
•msc - minimally acceptable stock cover;
•li- lot size of i-th product, i= 1, . . . , n;
•C- available production capacities in each period;
•Si- inventory level of i-th product at the beginning of the observed time horizon, i=1,. . . ,n;
•tij - demand for i-th product in j-th period, i=1,. . . ,n,j=1,. . . ,m;
•pij - forecast for i-th product in j-th period, i=1,. . . ,n,j=1,. . . ,m;
Forecasts are calculated using k-periods moving average:
pij =1
k
k
∑
u=1
tij−u(1)

714 D. Makajić-Nikolić, S. Babarogić, D. Lečić-Cvetković, N. Atanasov
4 Algorithm
The goal of the algorithm (Fig.1) is to support two-phased decision making process. The
result of the first phase is a list of products that should be produced in observed period, where
decision is made based on calculated KPIs (CSL and SC). In the second phase, the algorithm
forms a list of products that will be produced, applying one of four defined criteria: minimal
CSL, minimal SC, maximal capacity utilization and maximal number of products and taking
into account the available capacities. The proposed algorithm has polynomial complexity.
Figure 1: Algorithm represented as UML 2.0 Activity Diagram
Using parameters defined in problem description section, the following variables are calculated
in each period.
•sij is a stock level of i-th product in j-th period, i=1,. . . ,n,j=1,. . . ,m.
•qij - delivered quantity of i-th product in j-th period, i=1,. . . ,n,j=1,. . . ,m. The delivered

An Algorithm for Production Planning Based on Supply Chain KPIs 715
quantity of each product depends on demand and stock level as follows:
qij ={tij , sij ≥tij
sij ,otherwise , i = 1, . . . , n, j = 1, . . . , m
•cslij =qij /tij - customer service level of i-th product achieved in j-th period, i=1,. . . ,n,
j=1,. . . ,m, observed as fill rate, indicates ratio between delivered and ordered quantity;
•scij =sij /pij - stock cover for i-th product provided in j-th period, i=1,. . . ,n,j=1,. . . ,m.
Based on variables values, two decisions must be made sequentially for each product in each
period.
1. The first decision refers to the request for the production of the i-th product in j-th period
(dsij , i = 1, . . . , n, j = 1, . . . , m). Request for production is initiated if any of the indicators
(cslij or scij ) falls below the minimum value, i.e:
dsij ={1 (production requested) , cslij < mcsl or scij < msc
0 (production not requested),otherwise
for i= 1, . . . , n, j = 1, . . . , m.
As a result, a set of all products that should be produced during j-th period is obtained:
Dj={i|dsij = 1}.
2. Since the available production capacities are limited without possibilities of extension in
short term and often insufficient, the second decision is related to a choice of products
that will be produced. This choice can be made using several criteria: minimal CSL,
maximal number of product and maximal production capacities utilization. Let Pbe a set
of chosen product. In the following, each of the above criteria for generating the set Pwill
be described in detail.
Options 1 and 2 - minimal CSL and minimal SC
According to the first two criteria, the higher priority is given to the products with smaller
demand satisfaction or with smaller stock cover in the previous period. These criteria should be
used in the case of large variations in the customer service level or stock cover among products.
For each time period j, the following procedure is applied.
Initialization: P=∅.
Do
Find i∗such that csli∗j=min{kpiij |i∈D}.
If li∗≤Cthen i∗ → P,C:= C−li∗endif.
Dj:= Dj i∗
until C= 0 or Dj=∅.
Variable kpiij represents key performance indicator cslij (Option 1) or scij (Option 2) de-
pending on chosen criteria.
The output of the procedure is the set Pwhich contains the indexes of the products that will
be produced.

716 D. Makajić-Nikolić, S. Babarogić, D. Lečić-Cvetković, N. Atanasov
Options 3 and 4 - maximal number of products and maximal production capaci-
ties utilization
Maximal number of products can be used as criterion when company wants to cover the
market with wide variety of products. When there is a large lack of capacity, maximal production
capacities utilization should be used as a criterion. For each period j, these two criteria can be
modeled as following knapsack problem:
max ∑
u∈Dj
ai·xi
s.t.
∑
u∈Dj
li·xi≤C
where:
xi={1,if the productiis chosen to be produced
0,otherwise , i = 1, . . . , n
ai={1,if the criterion is number of products (Option 3)
li,if the criterion is capacities utilisation (Option 4), i = 1, . . . , n
After obtaining the optimal results, set of products that will be produced, P, contains all
products isuch that xi= 1.
5 Computational Results and Discussion
The algorithm has been applied on real data calculation based on 28 weeks observation,
made for four products of real, medium sized Fast Moving Consumer Goods (FMCG) company.
Installed production capacity is 290 units per period (week), while lot sizes are 120, 110, 170 and
50 units for products p1, p2, p3 and p4, respectively. Customers’ orders are shown in Table 1.
Forecast is calculated based on three-week moving average (equation 1).
Table 1: Customers’ orders for 28 weeks
Product w1 w2 w3 w4 w5 w6 w7 w8 w9 w10
p1 35 75 29 48 40 52 29 59 67 82
p2 50 122 55 129 40 346 70 102 112 16
p3 68 112 48 94 62 357 75 98 124 18
p4 6 23 27 57 0 30 45 38 56 69
Product w11 w12 w13 w14 w15 w16 w17 w18 w19 w20
p1 96 88 45 23 16 31 166 16 34 137
p2 83 28 40 28 53 100 70 36 49 292
p3 11 25 49 34 63 117 112 48 69 325
p4 14 67 171 27 4 66 5 8 15 110
Product w21 w22 w23 w24 w25 w26 w27 w28
p1 83 23 110 156 109 102 34 69
p2 95 119 447 56 154 34 112 107
p3 162 128 314 93 156 88 115 128
p4 3 86 153 1 1 1 0 25

An Algorithm for Production Planning Based on Supply Chain KPIs 717
Based on descriptive statistical analysis for the observed period, it can be concluded that
products p2 and p3 had the highest average demand (105.18 and 110.46, respectively) but also
the highest standard deviation of demand (99.81 and 87.69, respectively). In addition, these two
products had three major demand peaks in the same periods (w6, w20 and w23). These facts
lead us to the conclusion that production capacity will remain mean issue in the future.
Developed algorithm can be used at operational and strategic level. Operational level is
related to the decision of production requesting and launching. Table 2 illustrates the operational
decisions. It shows the decisions for the product p1 in the entire period when minCSL criterion
is used. The first column represents the weeks of the observed period. The second and third
columns give the orders and the forecasts per weeks for product p1. Columns labeled as SB
and SA shows the stock level before and after product delivery while the next column gives
the amount of delivered quantities. Columns CSL and SC show calculated values for customer
service level and stock cover per periods. The last three columns represent the decisions about
requested, confirmed and missed production, respectively. In the last row of the Table 2, the
values of total delivered quantities, average SCL and SC, and total number of production request,
conformation and missing are given.
Table 2: Production decisions for 28 weeks for p1 and minCSL criterion
Time Order Forecast SB SA delivered CSL SC PR PC PM
w1 35 36 110 75 35 1 2.083
w2 75 66 75 0 75 1 0 1 1
w3 29 95 120 91 29 1 0.958 1 1
w4 48 46 211 163 48 1 3.518
w5 40 51 163 123 40 1 2.428
w6 52 39 123 71 52 1 1.821 1 1
w7 29 47 71 42 29 1 0.9 1 1
w8 59 40 162 103 59 1 2.554
w9 67 47 103 36 67 1 0.771 1 1
w10 82 52 36 0 36 0.439 0 1 1
w11 96 69 120 24 96 1 0.346 1 1
w12 88 82 144 56 88 1 0.686 1 1
w13 45 89 176 131 45 1 1.477 1 1
w14 23 76 251 228 23 1 2.987
w15 16 52 228 212 16 1 4.077
w16 31 28 212 181 31 1 6.464
w17 166 23 181 15 166 1 0.643 1 1
w18 16 71 135 119 16 1 1.676 1 1
w19 34 71 119 85 34 1 1.197 1 1
w20 137 72 205 68 137 1 0.944 1 1
w21 83 62 68 0 68 0.819 0 1 1
w22 23 85 120 97 23 1 1.146 1 1
w23 110 81 97 0 97 0.882 0 1 1
w24 156 72 0 0 0 0 0 1 1
w25 109 96 120 11 109 1 0.114 1 1
w26 102 125 11 0 11 0.1080 0 1 1
w27 34 122 120 86 34 1 0.703 1 1
w28 69 82 86 17 69 1 0.208 1 1
Total 1533 0.902 1.346 21 13 8

718 D. Makajić-Nikolić, S. Babarogić, D. Lečić-Cvetković, N. Atanasov
Table 3 shows requesting for productions and decisions about confirmation or missing the
production for all four products in the entire observed period. Abbreviation used in the Table3
are the same as in the Table 2. In the last row total numbers of production request, conformation
and missing are given for all the products. Production requests for all four products appeared
in 9 out of 28 weeks and in 5 of them only two product were produced.
Table 3: Production decisions for 28 weeks for all products and minCSL criterion
p1 p2 p3 p4
Time PR PC PM PR PC PM PR PC PM PR PC PM
w1 1 1 1 1
w2 1 1 1 1
w3 1 1 1 1 1 1
w4 1 1 1 1
w5 1 1 1 1 1 1
w6 1 1 1 1 1 1
w7 1 1 1 1 1 1 1 1
w8 1 1 1 1 1 1
w9 1 1 1 1 1 1 1 1
w10 1 1 1 1 1 1
w11 1 1 1 1 1 1
w12 1 1 1 1 1 1
w13 1 1 1 1
w14 1 1
w15 1 1 1 1
w16 1 1 1 1 1 1
w17 1 1 1 1 1 1
w18 1 1 1 1 1 1
w19 1 1 1 1
w20 1 1 1 1 1 1 1 1
w21 1 1 1 1 1 1 1 1
w22 1 1 1 1 1 1 1 1
w23 1 1 1 1 1 1 1 1
w24 1 1 1 1 1 1 1 1
w25 1 1 1 1 1 1 1 1
w26 1 1 1 1 1 1 1 1
w27 1 1 1 1 1 1
w28 1 1 1 1 1 1
Total 21 13 8 25 20 5 20 15 5 19 14 5
At strategic level, a decision about the most appropriate criterion can be made using the
proposed algorithm. Computational results for all observed products and all four decision criteria
are given in Table 4. Column "Delivered" represents quantities which are delivered during entire
period per product. Columns "csl" and "sc" represents KPIs. The last column represents the
percent of launched production requests.
The percentages of capacity utilizations for options 1, 2, 3 and 4, are 0.863, 0.857, 0.872 and
0.817, respectively. After algorithm results presentation, management of the observed company
considers option 1 the most appropriate. Applying the first option (min CSL) in algorithm, the
highest level of CSL and the largest quantity of delivered products are provided. As positive
side effect, high level of capacity utilization is achieved even that was not included as criterion

An Algorithm for Production Planning Based on Supply Chain KPIs 719
Table 4: Summary results
Delivered csl sc card(P)/card(D)
Option 1 (min csl) p1 1533 0.90 1.35 0.714
p2 2263 0.91 0.98 0.800
p3 2538 0.89 1.29 0.750
p4 778 0.83 7.36 0.737
total 7112 avg 0.88 avg 2.75 avg 0.753
Option 2 (min sc) p1 1533 0.90 1.40 0.619
p2 2240 0.93 1.05 0.833
p3 2488 0.89 1.03 0.682
p4 728 0.77 7.30 0.684
total 6989 avg 0.87 avg 2.70 avg 0.709
Option 3 p1 1823 0.99 1.78 1
(max capacity utilization) p2 1687 0.67 0.67 0.600
p3 2940 0.98 2.44 1
p4 575 0.59 2.08 0.591
total 7025 avg 0.81 avg 1.74 avg 0.765
Option 4 p1 1823 0.99 1.78 1
(max number of product) p2 1690 0.73 0.76 0.625
p3 2263 0.80 1.32 0.619
p4 879 0.91 11.20 1
total 6655 avg 0.86 avg 3.76 avg 0.782
in option 1. Although the average results in the last column indicate the similar percentages
of launched production requests for all four options, detailed analysis by products shows that
even nearly 40% production requests for some products remain unrealized in options 3 and 4.
Considering this indicator in the last column, option 1 gives the most balanced values.
6 Conclusions
The aim of this paper was to develop a heuristic algorithm for multi-period production
planning based on supply chain KPIs: customer service level and stock cover. Analyzing FMCG
company with limited production capacities, two important decisions are recognized in each
period: which products should be produced (production requesting) and which product can be
produced (production launching). The proposed algorithm provides support for both decisions.
The first decision is based on two used KPIs, while the second decision can be made by using one
of four criteria: minCSL, minSC, maximal capacity utilization and maximal number of products.
Developed algorithm was applied in real FMCG where option 1 was chosen as the most
appropriate according to their business policy. However, the main advantage of the algorithm is
the fact that it offers a choice among four different decision criteria based on company’s business
policies. It can be extended in order to generate demand forecast based on different forecasting
techniques and adding new KPI: demand forecast accuracy, which will be used for evaluation of
the impact of forecast accuracy on customer service level and stock cover variations.

720 D. Makajić-Nikolić, S. Babarogić, D. Lečić-Cvetković, N. Atanasov
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