Objective Effect on the Performance of a Multi- Period ... · profit maximization. Revenues and costs are related, maximizing profit can be achieved by maximizing revenues and/or

International Journal of Mechanical & Mechatronics Engineering IJMME-IJENS Vol:16 No:03 88

162803-5858-IJMME-IJENS © June 2016 IJENS I J E N S

Objective Effect on the Performance of a Multi-

Period Multi-Product Production Planning

Optimization Model

M. S. Al-Ashhab1, 2

, Nahid Afia 1 and Lamia A. Shihata

1 1 Design & Production Engineering Dept. Faculty of Engineering, Ain-Shams University, Egypt

2 Dept. of Mechanical Engineering Collage of Engineering and Islamic architecture, UQU, KSA

Abstract-- This paper introduces a multi objective

optimization model to solve production planning problems for a

multi products, multi period, and multi echelon manufacturing

chain to minimize the total cost and maximize the overall

service level of customers. The model is formulated using mixed

integer linear programming optimization form.

The obtained results are compared with the results of a similar

model which maximizes the total profit. It was proved that the

configuration of the network and consequently its performance

differs with the corresponding objectives and constraints taken

into consideration when designing the network. Analysis of

results prescribed that cost minimization is not always lead to

maximizing profit.

Index Term-- Production planning; MILP; multi-products,

multi echelon, multi-objective; multi-periods; cost

minimization; and profit maximization.

1. INTRODUCTION

One of the most important supply chain decisions is how to

design the network as its implication is significant and long

lasting. The existing literature concerning SCN design

problems are strongly dissimilar, different researchers

include different objectives in their proposed models.

Most researches dealt with minimizing the sum of

various cost components that depend on the set of decision

modeled. Jayaraman and Ross (2003) provided a robust and

practical approach for solving a multiple product, multi-

echelon problem. The objective function minimizes fixed

costs to open warehouses and cross-docks, costs to transport

products from warehouses to cross-docks and costs to supply

products from cross-docks to satisfy the demand of

customers. This approach obtained optimal solution using

the LINGO software for small datasets and near-optimal

solutions. Bidhandi et al. (2009) reconsidered the

mathematical formulation provided by Cordeau et al. for

logistics network design. They developed a multi-

commodity single-period integrated SCND model with two

levels of strategic and tactical variables to minimize the sum

of all fixed and variable costs.[

Similarly, Davoudpour and Sadjady (2012) approached

the minimization of total variable and fixed costs of the

network by designing a two-echelon supply chain network,

which allows multiple levels of capacities for the facilities of

both stages.

Successive research activities evolved accordingly

dealing with minimizing the sum of various cost components

that depend on the set of decision modeled [Jeung Ko et al.-

Wang et al.} while some others dealt with the objective of

maximizing profit to determine the network [Costa et al.,-

Melo et al.]. Akbari & Behrooz Karimi (2015) considered a

multi-echelon, multi-product, multi-period supply chain

including manufacturing plants, distribution centers, and

retailers at customer zones with the objective to minimize

the sum of location, allocation, transportation, and inventory

carrying costs which can be formulated as a mixed integer

linear programming problem.

Ryanb et al. (2016) formulated a novel profit

maximization model using mixed-integer linear

programming for a multi-period, single-product and

capacitated CLSCN design problem to maximize the

expected profit. Their major contribution is developing a

hybrid robust-stochastic programming approach to model

qualitatively different uncertainties. Historical data for

transportation costs was assumed and used to generate

probabilistic scenarios by a scenario generation and

reduction algorithm.

One of the earliest researches that approached the multi-

objective method for supply chain network was Weber and

Current JR. in 1993. They proposed a multi-objective

approach for vendor selection, considering three objectives

including the purchases cost, number of late deliveries, and

rejected units. (Sabria et al. 2000). Guillen et al. (2005)

introduced three objectives in his research, maximizing net

present value, maximizing demand satisfaction and

minimizing financial risks in a stochastic supply chain

setting to choose numbers, location and capacities of plants

and warehouses. They mention that generating different

configurations of SCN can help decision makers to

determine the best design according to the chosen objectives.

The authors stated that the main objective of the supply

chain management is to achieve suitable economic results

together with the desired consumer satisfaction levels.

In the following decade larger numbers of multi-

objective optimization problems have been presented

[Guilléna et al.- Al-Ashhab et al.]. Lately, Chen et al. (2016)

developed a multi-echelon, multi-item supply network

model with various replenishment policies under volume (or

weight) discounts on transportation costs. The rates of

demand and lead time are both uncertain. The study

compares two multi-item replenishment policies: single-

cluster replenishment and joint cluster replenishment. It was



demonstrated that single-cluster replenishment is generally

superior to joint cluster replenishment. However, based on

transportation cost discounts, joint cluster replenishment

may be superior to single cluster replenishment. The results

showed that single-item replenishment is inferior to multi-

item replenishment under volume (weight) discounts on

transportation costs. Choudhary et al. (2016) introduced a

multi-objective problem for supply chain network design by

incorporating the issues of social relationship, carbon

emissions, and supply chain risks such as disruption and

opportunism. The proposed MOP included three conflicting

objectives: maximization of total profit, minimization of

supply disruption and opportunism risks, and minimization

of carbon emission considering a number of supply chain

constraints. An illustrative example was presented to

manifest the capability of the model and the algorithm. The

results obtained revealed the robust performance of the

proposed MOP.

Pazhami et al. (2013) developed a bi-objective supply

chain network design model. The objective of their research

was minimizing the total supply chain network cost and

maximizing the service level. In order to measure the service

level they used Multiple Criteria Decision Making

techniques and established an efficiency score for each

warehouse and hybrid facility. As a second objective they

have tried to maximize the total efficiency score.

Most of researches reduce their optimization models to

single objective either to minimize the total cost of the

supply chain or to maximize the total profit. However

modeling may require more than single objective such as

maximizing profit, maximizing service level, minimizing

cost, maximize the utilization of resources. The multi

objectives models represent reality more than the single

objective ones. Usually, these objectives may cause

conflicts. For example, in most cases; increasing service

level usually causes a growth in costs while it may maximize

profit. Similarly, minimizing the supply chain network total

cost may lead to lower level of customer satisfaction due to

usage of cheaper resources. The aim of a multi objective

supply chain network design is to find trade off solutions in

order to satisfy the conflicting objectives which must be

optimized by the decision maker.

The above review of supply chain models shows the

importance of assessing the impact of more than one

objective while designing a SCN, but as far as the

researchers of this paper went, there was no comparative

study performed to support the tradeoff decision that should

be reached by the decision maker. This research in addition

to introducing a model with the objective of minimizing cost

and maximizing the overall service level, it compares the

results obtained those results when applying the same model

after changing the model objective of profit maximization to

a cost minimization one.

In general, the configuration of the supply chain depends

on the total costs associated with the various operational

supply chain network activities, the existing capacities of

suppliers, factories and distributors, the quantities transferred

between echelons through the determined links, storage cost

and transportation cost values so that the demand is satisfied

with associated penalties if the demand is not met in the

form of shortage cost as well as the non-utilized capacity

cost if it is optimal not to produce with the full capacity.

Cost minimization is one of the necessary conditions for

profit maximization. Revenues and costs are related,

maximizing profit can be achieved by maximizing revenues

and/or minimizing cost. In the domain of supply chain

network design, minimizing costs may also minimize

revenues and therefore will not maximize profit.

In this paper, a model is formulated using mixed integer

linear programming optimization form. This model solves

the production planning problem for a multi products, multi

period, and multi echelon manufacturing chain. The

proposed model attempts to simultaneously minimize total

cost and maximize the overall service level of the customers.

A case study is used to show the ability of the proposed

model in solving the problem. The obtained results is

compared with the results mentioned in Al-Ashhab et

al.(2016)where the objective was maximizing profit and the

overall service level of the customers.

The remainder of this paper is organized as follows: the

model description is described in Section 2. The model

assumptions and limitations are introduces in section 3. The

detailed mathematical formulation is shown in Section 4.

Section 5, presents and discusses the computational results

of the model and the case study. Concluding remarks are

made in Section 6. Finally, Future Work and

Recommendations are presented in Section 7

2. MODEL DESCRIPTION

The proposed model assumes a set of customer locations

with known and time varying demands and a set of candidate

suppliers of known, limited and time varying capacity, and

distributor’s locations of known, limited and time varying

capacity. It optimizes locations of the suppliers, distributors

and customers and allocates the shipment between them to

minimize the total cost while maximizing the overall

customer service level taking their capacities, inventory and

shortage penalty and other costs into consideration.

Suppliers are responsible for supplying of raw materials

to the facility. Facility is responsible for manufacturing of

the three products and supplying some of them to the

distributors and storing the rest for the next periods; if it is

profitable. Distributors are responsible for the distribution of

products to the customers and/or storing some of them for

the next periods, and customers’ nodes may represent one

customer, a retailer, or a group of customers and retailers.

The model considers fixed costs for all nodes, materials

costs, transportation costs, manufacturing costs, non-utilized

capacity costs for the facility, holding costs for facility and

distributors’ stores and shortage costs.

3. MODEL ASSUMPTIONS AND LIMITATIONS

The assumptions of the model are assumed to be the same as in M. S. Al-Ashhab, (2016) except that the current model minimizes the total cost



4. MODEL FORMULATION

The current model involves the same sets, parameters and

variables where:

Sets:

S: potential number of suppliers, indexed by s.

D: potential number of distributors, indexed by d.

C: potential number of first customers, indexed by

c.

T: number of periods, indexed by t.

P: number of product, indexed by p.

Parameters:

Fs, Ff, Fd: fixed cost of contracting supplier s, the

facility, and distributor d

DEMANDcpt: demand of customer c from product p

in period t,

Ppct: unit price of product p at customer c in period

t,

Wp: product weight.

MHp: manufacturing hours for product.

Dij: distance between location I and j.

CAPst: capacity of supplier s in period t (kg),

CAPMft: capacity of the facility Raw Material Store

in period t.

CAPHft: capacity in manufacturing hours of the

facility in period t,

CAPFSft: storing capacity of the facility in period t,

CAPdt: capacity of distributor d in period t (kg),

MatCostt: material cost per unit supplied by

supplier s in period t,

MCft: manufacturing cost per hour for facility in

period t,

MHp: Manufacturing hours for product (p)

NUCCf: non utilized manufacturing capacity cost

per hour of the facility,

SCPUp: shortage cost per unit per period,

HFp: holding cost per unit per period at facility

store (kg),

HDp: holding cost per unit per period at distributor

d store (kg),

Bs: batch size from supplier s

Bfp& Bdp: batch size from the facility and distributor

d for product p.

TCperkm: transportation cost per unit per

kilometer.

Decision Variables:

Li: binary variable equal to 1 if a location i is

opened and equal to 0 otherwise.

Qsft: number of batches transported from supplier s

to the facility in period t,

Qfdpt: number of batches transported from the

facility to distributor d for product p in period t,

Ifpt: number of batches transported from the facility

to its store for product p in period t,

Ifdpt: number of batches transported from store of

the facility to distributor d for product p in

period t,

Qdcpt: number of batches transported from

distributor d to customer c for product p in

period t,

Rfpt: residual inventory of the period t at store of the

facility for product p.

Rdpt: residual inventory of the period t at distributor

d for product p.

OSLc: Overall Service Level of customer c.

4.1. Objective Function

The objectives of the model are to minimize the total cost

while maximizing the overall service levels of the four

customers.

Total cost = fixed costs + material costs + manufacturing

costs + non-utilized capacity costs + shortage costs +

transportation costs + inventory holding costs.

Pp

cpt

Dd Pp

dcptc DEMAND /Q Level Service OverallTtTt

(1)

4.1.1. Costs

(1)

Total cost = fixed costs + material costs + manufacturing

costs + non-utilized capacity costs + shortage costs +

transportation costs + inventory holding costs.

d

Dd

d

Ss

ss LFFfLF

costs Fixed (2)

(2)

Ss Tt

stssft MatCost B Qcost Material (3)

(3)

Pp TtDd Pp Tt ...2

ftpfpfptftpfpfdpt Mc MH B IMc MH B Qcosts ingManufactur (4)

Pp

fNUCCD d

pfpfptpfpfdpt

D dTt

fft )))MH B (I)MH B Q(L )((CAPH( cost capacity Utilized-Non (5)

p

1

dpdcpt

Tt

t

1

cpt SCPU )))B QDEMAND(((cost Shortage

t

DdCcPp

(6)

)D T WB QD TWB I

D T WB Q(DS T B Q coststion Transporta

dcdpdpdcpt

2

fdfpfpfdpt

fdfpfpfdpt

Tt

sfsssft

Dd Cc Tt

T

t Dd

Tt DdPpSs

(7)

Dd TtTtPp

)HD WRHF WR( costs holdingInventory dpdptfpfpt (8)



4.1.2. Total Revenue

Dd Cc Pp

pctdpdcpt P B Q revenue TotalTt

(9)

Total Profit = Total revenue – Total cost

4.2. Constraints

Model constraints are categorized as follows:

4.2.1. Balance constraints:

Pp

pfpfptpfpfdpt

DdSs

ssft TtWBIWBQBQ , (10)

PpTtBIBRBRBIDd

fpfdptfpfptfptfpfpfpt

,,)1( (11)

DdTtBQBRBRBIQPp Cc

dpdcptdpdptdptdp

Pp

fpfdptfdpt

,2,)( )1( (12)

PpCcTtBQBQt

dp

Dd

tdcptcp

Dd

cptdpdcpt

,,,DEMANDDEMAND1

)1()1( (13)

4.2.2. Capacity constraints:

SsT,t ,L CAPB Q sstssft (14)

Tt ,L CAPMB Q fftssft Ss

(15)

PpT,t ,L CAPH MH )B IB Q(Dd Dd

fftpfpfptfpfdpt

(16)

Tt ,L CAPFSWBR fftpfpptf Pp

(17)

PpD,dT,t ,L CAPWB RWB )I (Q ddt

T

pfp1-dptpfpfdptfdpt t

(18)

5. RESULTS AND DISCUSSION

This section illustrates the behavior of the proposed model with the objective of minimizing cost and maximizing the overall service level. The obtained results are compared with the results obtained in M. S. Al-Ashhab, (2016) when applying the same model after changing the model objective of profit maximization to

a cost minimization one. To facilitate the comparison, the same case study is solved using the same parameters’ values given in Table 1. Identical demand pattern of all customers is assumed for all the 12 planning periods as shown in Figure 1.



Table I

Verification model parameters

Parameter Value Parameter Value

Number of potential suppliers 3 Manufacturing hours for product 1 1

Number of facilities 1 Manufacturing hours for product 2 2

Number of potential Distributors 3 Manufacturing hours for product 3 3

Number of Customers 4 Transportation cost per kilometer

per unit 0.001

Number of products 3 Facility holding cost 3

Fixed costs for supplier &

distributor 20,000 Distributor holding cost 2

Fixed costs for facility 50,000 Capacity of each suppliers in

each period 4,000

Weight of Product 1 in Kg 1 Supplier batch size 10

Weight of Product 2 in Kg 2 Facility Batch size for product p 10

Weight of Product 3 in Kg 3 Distributor Batch size for product p 1

Price of Product 1 100 Capacity of Facility in hours 12,000

Price of Product 2 150 Capacity of Facility Store in

each period 2,000

Price of Product 3 200

Capacity of each Distributor

Store in

each period

4,000

Material Cost per unit weight 10 Capacity of each Facility Raw

Material Store in each period 4,000

Manufacturing Cost per hour 10

Fig. 1. Demand Pattern

The behavior of the model under the condition of

minimizing the cost is initially illustrated. Thereafter a

comparison is carried out between the behaviors of the

model with the other of maximizing profit.

5.1. Cost minimization model behavior

In this section, the results of applying the proposed model

with the objective of minimizing cost are introduced. The

results were discussed to show the optimal production plan

in the design of manufacturing chain operating under a

multi-product, multi-period with the objective of cost

minimization and to select the partners as well. The resulted

optimal network configuration that minimizes the total cost

is as shown in Figure 2.

Fig. 2. The resulted optimal network

The number of batches transferred from suppliers to the facility is illustrated in Table 2 where it is noticed that while applying the model to design the network over 12 periods, the optimal production plan determined that the quantities transferred between the partners are just over only10 periods. This also can be easily shown in Tables 3a, 4a, 5, 6 and 7.

0

200

400

600

800

0 1 2 3 4 5 6 7 8 9 10 11 12 13

De

ma

nd

Period

Demand Pattern



Table II

Number of batches transferred from suppliers to the facility

Cost minimization Profit maximization

Period S1F S2F S3F S1F S2F S3F

1 160 400 0 0 400 160

2 400 440044 200 200 400 400

3 400 400 200 400 400 200

4 400 400 200 200 400 400

5 400 400 200 400 400 200

6 200 400 400 200 400 400

7 400 400 200 200 400 400

8 400 400 200 200 400 400

9 400 400 200 200 400 400

10 399 399 202 400 400 200

11 0 0 0 400 400 200

12 0 0 0 400 400 200

Table IIIa

Number of batches transferred from the facility to distributors (min. Cost)

Period QFD1 QFD2 QFD3

P1 P2 P3 P1 P2 P3 P1 P2 P3

1 20 0 20 40 100 20 20 20 40

2 30 0 120 30 50 60 60 30 40

3 52 39 0 40 42 92 80 79 44

4 38 100 0 50 49 58 100 51 66

5 100 60 60 0 61 26

120 89 34

6 70 70 1 70 69 60 70 70 63

7 70 70 61 69 71 63 0 0 69

8 0 60 93 61 60 54 0 129 0

9 0 50 34 50 50 83 180 51 39

10 149 40 18 38 40 66 40 40 93

11 0 0 0 0 0 0 0 0 0

12 0 0 0 0 0 0 0 0 0



Table IIIb

Number of batches transferred from the facility to distributors (max. profit)

Period To distributor 1 To distributor 2 To distributor 3

P1 P2 P3 P1 P2 P3 P1 P2 P3

1 0 0 1 60 41 66 20 40 39 2 0 30 61 60 70 20 65 117 33 3 134 40 29 42 0 92 78 22 53

4 0 74 7 48 76 57 53 50 81

5 97 60 61 20 40 36 115 116 13

6 70 69 46 9 71 69 1 143 0

7 68 5 41 0 176 5 279 60 0

8 62 85 56 248 67 4 60 70 2

9 50 49 23 50 105 46 100 95 31

10 39 41 27 80 80 22 40 46 88

11 31 30 40 58 56 72 30 32 102

12 20 20 47 42 39 93 20 22 112

Table IVa

Number of batches transferred from facility store to distributors (min cost)

Period IFD1 IFD2 IFD3

P1 P2 P3 P1 P2 P3 P1 P2 P3 2

0 0 0 0 0 0 0 0 0 3

0 0 0 0 0 0 0 0 0 4

0 0 0 0 0 0 0 0 0 5

0 0 0 20 0 60 0 0 0 6 0 0 0 0 0 0 0 0 0 7 0 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 9

0 0 0 0 0 0 0 0 0 10 0 0 0 2 0 0 0 0 0 11 0 0 0 0 0 0 0 0 0 12

0 0 0 0 0 0 0 0 0

Table IVb

Number of batches transferred from the facility store to distributors. (max. profit)

Period

To distributor 1 To distributor 2 To distributor 3

Product 1 P2 P3 Product 1 P2 P3 Product 1 P2 P3

2 0 0 1 0 0 12 0 0 0

3 0 0 0 0 0 0 0 0 0

4 0 0 0 0 0 8 0 0 0

5 0 0 0 0 21 50 5 0 3

6 0 0 0 6 0 1 0 0 0

7 0 0 0 0 0 11 0 0 0

8 0 0 0 0 0 0 0 0 0

9 0 0 0 0 1 0 0 0 0

10 0 0 0 0 0 31 0 0 1

11 0 0 1 0 0 0 0 0 0

12 0 0 0 0 0 0 0 0 0



Table V

Number of batches transferred from the distributor #1 to customers (min cost)

Period D1C1 D1C2 D1C3 D1C4

P1 P2 P3 P1 P2 P3 P1 P2 P3 P1 P2 P3

1 200 0 200 0 0 0 0 0 0 0 0 0

2 300 0 300 0 0 0 0 0 0 0 0 0

3 400 390 400 0 0 0 0 0 0 0 0 0

4 500 500 500 0 500 0 0 0 0 0 0 0

5 600 600 600 400 0 0 0 0 0 0 0 0

6 700 700 10 0 0 0 0 0 0 0 0 0

7 700 700 610 0 0 0 0 0 0 0 0 0

8 0 600 930 0 0 0 0 0 0 0 0 0

9 0 500 340 0 0 0 0 0 0 0 0 0

10 1490 400 178 0 0 0 0 0 0 0 0 2

11 0 0 0 0 0 0 0 0 0 0 0 0

12 0 0 0 0 0 0 0 0 0 0 0 0

Table VI

Number of batches transferred from the distributor#2 to customers (min cost)


P1 P2 P3 P1 P2 P3 P1 P2 P3 P1 P2 P3

1 0 200 0 200 200 200 200 200 0 0 0 0

2 0 300 0 300 300 300 0 300 300 0 0 0

3 0 10 0 400 400 400 0 10 260 0 0 0

4 0 0 0 500 0 500 0 490 340 0 0 0

5 0 0 0 200 600 600 0 10 260 0 0 0

6 0 0 100 700 690 500 0 0 0 0 0 0

7 0 0 0 690 710 630 0 0 0 0 0 0

8 0 0 0 610 600 540 0 0 0 0 0 0

9 0 0 0 498 500 830 0 0 0 0 0 0

10 0 0 0 398 400 400 0 0 260 2 0 0

11 2 0 0 0 0 0 0 0 0 0 0 0

12 0 0 0 0 0 0 0 0 0 0 0 0



Table VII

Number of batches transferred from the distributor#3 to customers (min cost)


P1 P2 P3 P1 P2 P3 P1 P2 P3 P1 P2 P3

1 0 0 0 0 0 0 0 0 200 200 200 200

2 0 0 0 0 0 0 300 0 0 300 300 300

3 0 0 0 0 0 0 400 390 140 400 400 400

4 0 0 0 0 0 0 500 10 160 500 500 500

5 0 0 0 0 0 0 600 590 340 600 300 0

6 0 0 0 0 0 0 700 700 630 0 0 0

7 0 0 0 0 0 0 0 0 690 0 0 0

8 0 0 0 0 0 0 0 1290 0 0 0 0

9 0 0 0 0 0 0 1800 510 390 0 0 0

10 0 0 0 0 0 0 400 400 930 0 0 0

11 0 0 0 0 0 0 0 0 0 0 0 0

12 0 0 0 0 0 0 0 0 0 0 0 0

Table VIII

Number of batches transferred from distributors to customers. (max. profit)

Period 1 2 3 4 5 6 7 8 9 10 11 12

D1-

C1

P1 0 0 395 500 600 700 680 620 500 390 310 200 P2 0 300 400 500 600 690 50 850 490 410 300 200 P3 0 300 165 500 600 460 410 560 230 270 410 470

D1-

C2

P1 0 0 0 445 370 0 0 0 0 0 0 0 P2 0 0 0 240 0 0 0 0 0 0 0 0 P3 0 0 0 25 10 0 0 0 0 0 0 0

D1-

C3

P1 0 0 0 0 0 0 0 0 0 0 0 0 P2 0 0 0 0 0 0 0 0 0 0 0 0 P3 0 0 0 0 0 0 0 0 0 0 0 0

D1-

C4

P1 0 0 0 0 0 0 0 0 0 0 0 0

P2 0 0 0 0 0 0 0 0 0 0 0 0 P3 0 0 0 0 0 0 0 0 0 0 0 0

D2-

C1

P1 200 300 5 0 0 0 0 0 0 0 0 0 P2 200 0 0 0 0 10 400 0 0 0 0 0 P3 200 0 235 0 0 0 0 0 0 1 0 0

D2-

C2

P1 200 300 400 55 200 150 0 1880 500 400 300 200 P2 200 300 400 260 600 700 679 51 1060 410 280 220 P3 200 300 400 475 590 691 160 37 460 514 720 818

D2-

C3

P1 200 0 1 439 0 0 0 600 0 400 280 220

P2 0 0 10 500 10 0 681 619 0 390 280 170

P3 12 268 273 187 270 9 0 3 0 15 0 112

D2-

C4

P1 0 0 0 0 0 0 0 0 0 0 0 0

P2 0 0 0 0 0 0 0 0 0 0 0 0

P3 0 0 0 0 0 0 0 0 0 0 0 0

D3-

C1

P1 0 0 0 0 0 0 0 0 0 0 0 0 P2 0 0 0 0 0 0 0 0 0 0 0 0 P3 0 0 0 0 0 0 0 0 0 0 0 0

D3-

C2

P1 0 0 0 0 0 0 0 0 0 0 0 0 P2 0 0 0 0 0 0 0 0 0 0 0 0 P3 0 0 0 0 0 0 0 0 0 0 0 0

D3-

C3

P1 0 300 399 61 600 0 1400 0 500 0 0 0

P2 200 300 390 0 590 700 0 0 500 10 20 30 P3 188 32 127 313 160 0 0 14 310 890 1020 1120

D3-

C4

P1 200 300 400 500 600 10 1390 600 500 400 300 200 P2 200 300 400 500 570 730 600 700 450 450 300 190 P3 200 300 400 500 0 0 0 6 0 0 0 0



It can be concluded from Figure 3 that the facility capacity

in hours are sufficient and exceeds the equivalent required

hours both in the first four periods from T1 to T4 and the last

four ones from T9 to T12. Moreover, it is not used for the

last two periods T11 and T12. At the first four periods, the

equivalent given hours is equal to the required hours and it is

equal exactly to the facility capacity at period T4. This

illustrates that all of the manufactured batches are delivered

directly to the distributors without storing any inventory in

the facility store. It is remarkable that the equivalent required

hours exceed the facility hour’s capacity from T5 to T8, but

it doesn’t matter as the optimal production plan is to

manufacture equal or less than the facility capacity hours as

shown in Figure 3.

Fig. 3. Relationship between the equivalents required manufacturing hours

and the equivalent given hours

Considering capacity of material supply; Figure 4 illustrates

the relationship between the equivalents required weight,

supplying material and the equivalent given weight. The

supplying capacity of the suppliers is 12,000 Kilograms as

three suppliers were opened; the capacity of each is 4000

kilograms. This will exceed the raw material store capacity

which is 10,000 kilograms. The required weights have not to

be exceeded by both of them. It is evident that in the first

three periods, the supplied material is more than the

required; consequently the required weights are delivered to

customers while the excess is stored in the distributor’s

stores to be available as compensation in the following

periods when needed.

It is notable that, the equivalent given weight exceeds the

facility capacity as shown in periods T4 and T5. The

difference can be compensated from the facility store as it is

less than or equal 2000 kilograms which represent the

maximum capacity of the facility store. The required

material is more than the supplied from period T6 to period

T9 and exceeds the facility capacity. Consequently, the

facility cannot manufacture more than its capacity and

customer demand cannot be satisfied. Shortage in demand is

faced in the coming periods in the form of backorders. In

spite of the supplied material is more than the required in

period T10, but unfortunately the difference may not be

sufficient to face or cover the shortage as no equivalent

given weights can be delivered in the last two periods T11

and T12 for the purpose of respecting the objective of

minimizing the total cost. The resulted overall service level

of the customers are shown in Figure 5

Fig. 4. Relationship between the equivalents required weight, supplying

material and the equivalent given weight

Fig. 5. The resulted Overall Service Level of the customers

Table 9 represents the results obtained from applying the proposed model on the case study. The total revenue, cost elements, total cost and total profit can be seen. A pie chart, on which the cost shares percentages are mentioned, can be shown in Figure 6.

Table IX

The resulting Cost /Revenue values

Cost/Revenue Value Cost/Revenue Value

Total Revenue 7203000 Shortage Cost -778020

Fixed Cost -170000 Transportation Costs -83704

Material Cost -956000 Inventory Holding

Cost -25008

Manufacturing Cost -996400 Total Cost -3,452,732

Non Utilized Cost -443600 Total Profit 3750268

Fig. 6. Cost Shares

86.17% 90.72% 90.74%

31.51%

C 1 C 2 C 3 C 4

OSL

4.8%

32.8%

35.1%

5.7% 17.8%

3.0% 0.7% Costs Shares

FixedCost

MaterialCost

ManufacturingCost

NonUtilizedCost

ShortageCost

TransportationCosts

InventoryHoldingCost



5.2. Comparison between the obtained results in both cases

of minimizing the total cost and maximizing profit

This section introduces a comparison between the results

mentioned in the above section concerning applying the

proposed model on the case study with the objective of

minimizing the total cost and the results mentioned in M. S.

Al-Ashhab, (2016) when applying the model on the same

case study but with the objective of maximizing profit.

5.2.1 The supply chain network design

The same resulted optimal network which is shown in Figure

2 is obtained in both cases, but with different number of

batches to be transferred between partners. This explains

why the fixed cost is equal as shown in Table 10.

Table X

The resulting Cost /Revenue values in both cases

Cost/Revenue Minimizing

total cost

Maximizi

ng profit

Percentage

of change%

Total Revenue 7,203,000 8,786,500 18 %

Fixed Cost -170,000 -170,000 0 %

Material Cost -956,000 -

1,156,000 17.3 %

Manufacturing

Cost -996,400

-

1,238,400 19.5 %

Non Utilized

Cost -443,600 -201,600 -120 %

Shortage Cost -778,020 -628,000 -23.9 %

Transportation

Costs -83,704 -106,002 21 %

Inventory

Holding Cost -25,008 -25, 000 0 %

Total Cost -3,452,732 -

3,500,002 1.4 %

Total Profit 3,750,268 5,261,498 28.7 %

5.2.2 Cost/ Revenue values

Figure 7 depicts the total revenue, costs and profit for the

both cases. The following can be concluded:

Fig. 7. Comparison between cost/ revenue values and total profit

1) The first set of bars represents the total revenue. It is

clear that, the total revenue with the objective of

maximizing profit is greater than that of minimizing

cost. It can be seen from Figure 8 that the resulting

overall service level OSL at each customer with the

objective of maximizing profit is greater than that of

minimizing cost. As a result this will lead the total

revenue to be increased.

Fig. 8. The resulting Overall Service Level percentage in both cases

2) The set of bars in between represents the different cost

elements in both cases

The following can be concluded from Figure 7 and Table 10:

Replacing the objective of profit maximization by the other

of cost minimization in this case resulted in:

a) No change in the fixed cost because the resulted

networks are configuration similar

b) Decreasing in material cost. This is as a result that

the supplying material weight is greater through the

12 periods as obtained in M. S. Al-Ashhab, (2016).

Consequently, it is obvious that the manufacturing

cost will be smaller in this case as well.

c) Decreasing in transportation cost as the transferred

number of batches decreases.

d) Inventory holding cost is almost the same. The

produced batches in most of the cases are transferred

directly as it is less than or equal to the equivalent

required weight in most of the periods.

e) Increasing in non-utilized capacity cost. The reason

of that is clear when comparing the results in both

tables 3a with 3b, Table 4a with 4b and Tables 5, 6

and 7 with Table8. Mainly, the last two periods are

off which means greater non-utilized capacity cost.

f) Increasing in shortage cost as well. This is because

the equivalent given weight is less than the required.

3) The set of bars before last represents the total cost. It is

evident that the total cost with the objective of

minimizing cost is smaller than that of maximizing

profit as it is the main objective in the second case.

4) The last set of bars represents the total profit. It is

evident that the total profit with the objective of

maximizing profit is greater than that of minimizing

cost as it is the main objective of the first case and equal

to the difference between the total revenues and the sum

of total mentioned costs.

5) It can be seen from Table 10 that, the revenue decreased

by about 18% while the total cost increased by 1.35%.

This will lead to a decrease in profit by 28.7%. This

means that a relatively little percentage increase in total

cost results in a reasonable greater increase in profit.

From another point of view, the percentage increase in

revenue is less than the percentage increase in profit.

Consequently, the decision maker should not build the

0.E+001.E+062.E+063.E+064.E+065.E+066.E+067.E+068.E+069.E+06

Minimizing total cost

Maximizing profit

0.00%

20.00%

40.00%

60.00%

80.00%

100.00%

120.00%

C 1 C 2 C 3 C 4

Se

rvic

e L

ev

el

Customers

OSL MinimizingcostOSL MaximizingProfit



decisions based on the traditional relations between

revenue, cost and profit.

6. CONCLUSIONS

The difference in the performance of the supply chain is

studied under two different cases. The first case is to

minimize the total costs of designing and managing the

network beside the objective of maximizing the overall

service level of customers. The second case is the same but

with maximizing the profit instead of minimizing the total

cost.

A case study is solved by the proposed model

considering multi products, multi periods, and multi echelon

to achieve optimal configuration network with optimal

operation performance and detailed production planning for

multiple planning horizons as well. There are many

circumstances where the structures of the maximum profit

and minimum cost solutions will be different, their facility

number, locations, and quantities transferred between

echelons which affect the overall service level of customers.

The comparison of the two models results revealed that

the performance of the manufacturing chain affected

drastically by the objective of the model. So, deciding the

objective is a very critical decision. Although minimizing

the total cost is an important performance metric in supply

chain management but the overall service level of customers

should be respected to certain reasonable levels in order to

have profit. The decision of minimizing the total costs is

accompanied by sacrificing some profit. Maximizing profit

and minimizing costs are conflicting. The decision makers

have to highlight the tradeoff between objectives.

Conflicting may occur when a supply chain is supporting

multiple products with capacity constraints and varying

profit margins. Maximizing profit should be the objective of

designing the profit organization where minimizing cost

should be the objective of designing the non-profit or service

organization with assigned minimum overall customer

service level.

7. FUTURE WORK AND RECOMMENDATIONS

Further research can be done considering uncertain

conditions to study the performance of the model under

uncertainty. If product demands are highly variable, the

minimum cost solution may not lead to the maximum profit.

From this research it can be recommended that, in all

profit business networks; the objective of minimizing cost is

not the good decision where it does not respect both revenue

and profit.

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