Mixed integer linear programming model for dynamic supplier selection problem considering discounts
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Mixed integer linear programming model for dynamic supplier selection problem considering discounts
Purnawan Adi Wicaksono 2
I Nyoman Pujawan 1
Erwin Widodo 1
Sutrisno 0
Laila Izzatunnisa 2
0 Department of Mathematics, Diponegoro University , Semarang 50275 Indonesia
1 Department of Industrial Engineering, Sepuluh Nopember Institute of Technology , Surabaya 60111 Indonesia
2 Department of Industrial Engineering Diponegoro University , Semarang 50275 Indonesia
Supplier selection is one of the most important elements in supply chain management. This function involves evaluation of many factors such as, material costs, transportation costs, quality, delays, supplier capacity, storage capacity and others. Each of these factors varies with time, therefore, supplier identified for one period is not necessarily be same for the next period to supply the same product. So, mixed integer linear programming (MILP) was developed to overcome the dynamic supplier selection problem (DSSP). In this paper, a mixed integer linear programming model is built to solve the lot-sizing problem with multiple suppliers, multiple periods, multiple products and quantity discounts. The buyer has to make a decision for some products which will be supplied by some suppliers for some periods cosidering by discount. To validate the MILP model with randomly generated data. The model is solved by Lingo 16.
1 Introduction
In a highly competitive industry today, firms must realize
the importance of supplier selection that meet the required
quality and time. Firms are now facing increased
consumer demand, shorter product life cycles, and sharper
price cuts. This condition causes firms to cut costs and
improve supply chain. Supply chain improvements
become critical in rising the competitiveness of the firm.
It can be done through supplier selection process
(Sagar,
2012)
.
Fluctuative and dynamic demand make it difficult for
firms to determine the order quantity and and when the
order must be made to fulfill the demand and minimize
the inventory costs. Suppliers are also expected to be
dynamic as well. This can happen because a firm usually
has a demand regarding supplier capacity, quality level,
lead time, unit cost part, and time-varied fixed
transportation cost.
(Ware et al., 2014)
. Supplier selection
problems are usually classified in terms of multi-echelon,
multi-product, multi-supplier and the time period’s nature
(Lin & Lei, 2009)
. Firm’s requests always fluctuate so
that time value requirements are considered dynamic, not
with short or long-term agreements. Therefore, this paper
will discuss Dynamic Supplier Selection Problem
(DSSP). In DSSP which a set of suppliers is selected
supplier for each period.
(Ware et al., 2014)
.
Most of the models that have been developed for
supplier selection problems ignore transportation
elements that significantly impact the total procurement
costs.
(Wicaksono et al., 2016)
. However, there are
already some researchers who consider transportation
costs in the selection of single product suppliers such as
(Burke et al., 2007; Liao & Rittscher, 2007; Aguezzoul,
A., & Ladet, 2007; Choudhary & Shankar, 2011;
Choudhary & Shankar, 2013)
. Some researchers are
choosing suppliers with multi-period, multi-product and
multi-supplier
(Rezaei & Davoodi, 2011; Ware et al.,
2014; Wicaksono et al., 2016)
. In another case, the
supplier provides discounts for each purchase in large
quantities to increase sales of a product goods / services.
With discounts, buyers may be interested to buy a product.
In practice, ordering in large amount with far distance can
reduce transportation costs per unit
(Shinn et al., 1996)
.
Therefore, this study will develop a model that integrates
procurement decisions with transportation costs and
discounts.
To minimize procurement expenditures, purchasing
and transportation costs need to be considered. Suppliers
offer total cost discount and transportation costs based on
trucking rates. The goal is to select several suppliers in
fulfilling the demand of the product with a minimum total
cost. In this paper, the researcher will make a model to
solve supplier selection problem with multi-period,
multiproduct and multi-supplier condition based on the
development of the previous model
(Ware et al., 2014)
with discount consideration. The method used is Mixed
Integer Linear Programming (MILP). Random data used
for model validation. This model then solved using
LINGO 16 software.
Furthermore, in part 2 of this paper, a brief literature
review of models or techniques related to the dynamic
supplier selection will be presented. Section 3 will present
the model and its mathematical formulation. Section 4
will present a case study to test the proposed model.
Finally, section 5 will provide conclusions and
suggestions for further research.
2 Literature Review
In supplier selection, there are two categories: quantitative
model and qualitative model. Q (...truncated)