Algorithms for Supplier Selection and Order Quantity Allocation
Date Issued
2020
Author(s)
Advisor(s)
Mendoza Andrade, Abraham
Olivares Benitez, Elías
Type
text::thesis::doctoral thesis
Abstract
Supply chain management is particularly important because of its influence on a
compan\¶s profitabilit\ and competitiYeness. Among the different actiYities inYolYed in
supply chain management, purchasing decisions, supplier selection, and order quantity
allocation have a direct impact on the cost of the produced items.
The cost function usually deals with non-linear equation systems with an infinite number
of possible solutions. The result is an optimal inventory policy with a minimum cost per time
unit.
This research addresses the supplier selection and order quantity allocation problem. The
objective is to allocate the corresponding order quantities over time to the selected suppliers,
while minimizing inventory and transportation costs, simultaneously. In selecting suppliers,
two feasibility constraints are considered: capacity and quality (perfect rate). Typically, in
the literature, the acceptable perfect quality rate of raw materials is ensured with a
mathematical inequality in the model constraints. Therefore, this research first addresses the
desired perfect rate by including it as part of the order cycle parameters calculation and not
as an individual constraint. The main advantages of doing so are: (i) it leads to lower-cost
solutions compared to previously proposed literature, (ii) it effectively faces the so-called
low perfect rate situations, by providing feasible solutions when the perfect rate of suppliers
is smaller than the minimum perfect-rate required by the customer. A sensitivity analysis was
carried out on the proposed model to analyze the effect of some parameters on the total cost
per time unit. Results showed that transportation costs have an important effect on the order
quantity and that the price levels do not necessarily affect the number of purchased units.
Hence the importance of considering transportation costs when making order quantity
allocation decisions.
Another challenge of the problem under study is that the model is non-linear and has an
infinite number of possible solutions because of the continuous nature of the variables.
Therefore, there is a need from the scientific and industry communities to find solutions in
an efficient and timely manner. Former studies introduced limits to the length of the order
cycle or to the number of orders in the order cycle in order to obtain a solution using
commercial software. However, computers still take many hours or days to provide optimal
solutions, if at all.
Therefore, second, this research applies different metaheuristic algorithms to solve the
problem, namely: particle swarm optimization (PSO), genetic algorithm (GA), and differential evolution (DE). With these algorithms, a larger solution space can be explored
while getting a solution in the order of seconds; this allows cheaper solutions to be found.
PSO, GA, and DE are well known metaheuristic algorithms in the optimization field and
have been used to solve lot-sizing, and supplier selection problems. New metaheuristic
methods are commonly proposed for particular circumstances, for example, converging to an
optimal solution faster than other strategies. A recently proposed metaheuristic algorithm,
the Grey Wolf Optimizer (GWO), was explored in this research. The algorithm was modified
and adapted to the supplier selection and order quantity allocation problem when the amount
of decision variables is too large. The improved GWO method, called iGWO, includes
weighted factors and a displacement vector to promote the exploration of the search strategy
avoiding the use of unfeasible solutions. The iGWO was tested and results showed that, in
addition to obtain optimal solutions, it performed a better search strategy, finding feasible
solutions in all instances of the tested problem.
Finally, based on the knowledge acquired through the previous contributions, a heuristic
algorithm to solve the problem under study is proposed. This heuristic algorithm allows to
extend the explored solution space to an exceptionally large limit. The solutions obtained
with the proposed heuristic algorithm were compared against the solutions obtained with
PSO and DE. Two numerical examples are solved. In the first one, it is shown that the
proposed heuristic performed best compared to other solutions previously published in the
literature, both in terms of computational time and total cost. In the second numerical
example, larger instances were studied. Our findings show that the proposed heuristic was
able to find a feasible solution, while PSO and DE were unable to find a solution. Therefore,
the proposed heuristic does not just lead to lower total cost solutions, but it also performs a
more exhaustive search in shorter computational times for larger instances of the problem.
compan\¶s profitabilit\ and competitiYeness. Among the different actiYities inYolYed in
supply chain management, purchasing decisions, supplier selection, and order quantity
allocation have a direct impact on the cost of the produced items.
The cost function usually deals with non-linear equation systems with an infinite number
of possible solutions. The result is an optimal inventory policy with a minimum cost per time
unit.
This research addresses the supplier selection and order quantity allocation problem. The
objective is to allocate the corresponding order quantities over time to the selected suppliers,
while minimizing inventory and transportation costs, simultaneously. In selecting suppliers,
two feasibility constraints are considered: capacity and quality (perfect rate). Typically, in
the literature, the acceptable perfect quality rate of raw materials is ensured with a
mathematical inequality in the model constraints. Therefore, this research first addresses the
desired perfect rate by including it as part of the order cycle parameters calculation and not
as an individual constraint. The main advantages of doing so are: (i) it leads to lower-cost
solutions compared to previously proposed literature, (ii) it effectively faces the so-called
low perfect rate situations, by providing feasible solutions when the perfect rate of suppliers
is smaller than the minimum perfect-rate required by the customer. A sensitivity analysis was
carried out on the proposed model to analyze the effect of some parameters on the total cost
per time unit. Results showed that transportation costs have an important effect on the order
quantity and that the price levels do not necessarily affect the number of purchased units.
Hence the importance of considering transportation costs when making order quantity
allocation decisions.
Another challenge of the problem under study is that the model is non-linear and has an
infinite number of possible solutions because of the continuous nature of the variables.
Therefore, there is a need from the scientific and industry communities to find solutions in
an efficient and timely manner. Former studies introduced limits to the length of the order
cycle or to the number of orders in the order cycle in order to obtain a solution using
commercial software. However, computers still take many hours or days to provide optimal
solutions, if at all.
Therefore, second, this research applies different metaheuristic algorithms to solve the
problem, namely: particle swarm optimization (PSO), genetic algorithm (GA), and differential evolution (DE). With these algorithms, a larger solution space can be explored
while getting a solution in the order of seconds; this allows cheaper solutions to be found.
PSO, GA, and DE are well known metaheuristic algorithms in the optimization field and
have been used to solve lot-sizing, and supplier selection problems. New metaheuristic
methods are commonly proposed for particular circumstances, for example, converging to an
optimal solution faster than other strategies. A recently proposed metaheuristic algorithm,
the Grey Wolf Optimizer (GWO), was explored in this research. The algorithm was modified
and adapted to the supplier selection and order quantity allocation problem when the amount
of decision variables is too large. The improved GWO method, called iGWO, includes
weighted factors and a displacement vector to promote the exploration of the search strategy
avoiding the use of unfeasible solutions. The iGWO was tested and results showed that, in
addition to obtain optimal solutions, it performed a better search strategy, finding feasible
solutions in all instances of the tested problem.
Finally, based on the knowledge acquired through the previous contributions, a heuristic
algorithm to solve the problem under study is proposed. This heuristic algorithm allows to
extend the explored solution space to an exceptionally large limit. The solutions obtained
with the proposed heuristic algorithm were compared against the solutions obtained with
PSO and DE. Two numerical examples are solved. In the first one, it is shown that the
proposed heuristic performed best compared to other solutions previously published in the
literature, both in terms of computational time and total cost. In the second numerical
example, larger instances were studied. Our findings show that the proposed heuristic was
able to find a feasible solution, while PSO and DE were unable to find a solution. Therefore,
the proposed heuristic does not just lead to lower total cost solutions, but it also performs a
more exhaustive search in shorter computational times for larger instances of the problem.
Subjects
License
Acceso Abierto
URL License
How to cite
Alejo Reyes, A. (2020). Algorithms for Supplier Selection and Order Quantity Allocation (Tesis de Doctorado). Universidad Panamericana.
Table of contents
Chapter 1. Introduction and Overview -- Chapter 2. Article 1 Inventory Replenishment Decisions Model for the Supplier Selection Problem Facing Low Perfect Rate Situations -- Chapter 3. Article 2 Inventory Replenishment Decision Model for the Supplier Selection Problem Using Metaheuristic Algorithms -- Chapter 4. Article 3 An Improved Grey Wolf Optimizer for a Supplier Selection and Order Quantity Allocation Problem -- Chapter 5. Article 4 A Heuristic Method for the Supplier Selection and Order Quantity Allocation Problem