Coordinated Location, Distribution, and Inventory Decisions in Supply Chain Network Design
Read this article. The goal is to understand optimum product allocation and distribution locations so products are delivered at the lowest possible cost. As you read Part 2, what are some other problems associated with supply chain allocation and distribution?
Introduction
The distribution planning decision (DPD) is one
of the most comprehensive strategic decision issues that need to be
optimised for the long-term efficient operation of a whole supply chain
(SC). The DPD involves optimising the transportation plan for allocating
goods and/or services from a set of sources to various destinations in a
supply chain. An important strategic issue related to the
design and operation of a physical distribution network in a supply
chain system is the determination of the best sites for intermediate
stocking points, or warehouses. The use of warehouses provides a company
with flexibility to respond to changes in the marketplace, and can
result in significant cost savings due to economies of scale in
transportation or shipping costs.
The major task of DPD is the
determination of distribution costs, customer service level (safety
stock holding), resource (warehouse space) utilisation, and the total
delivery time, with reference to multiple warehouse capacities and
uncertain forecast demands.
In
previous studies, both deterministic and stochastic customers' demands
have been considered, but more attention has been paid to the
deterministic cases.
Generally, the applied
constraints in modelling DPDs are the capacity limitation and single
source constraints. In some cases, in
addition to the capacity constraints, some other restrictions on the
number of covered demands and the service levels of the warehouses are
also defined.
Recently some authors have incorporated inventory
control decisions into DPD models. For example, Miranda & Garrido, Daskin et al., and Shen et al. present similar versions
of the DPD model incorporating the inventory control decisions.
Erlebacher
& Meller present a location-inventory model for designing a
two-level distribution system serving continuously represented customer
locations. They develop a stylised analytical model to provide some
intuition and basic results for the problem. The stylised model also
motivates bounds for the problem, which they use to develop a heuristic.
They show that the heuristic performs very well on test problems that
considered variation in customer demand and spatial dispersion.
In
these works, the ordering decisions are based on the classic economic
order quantity (EOQ) model, and a normal distribution is assumed for the
demand pattern.
Additionally, researchers have developed various
methods to solve multi-objective DPD problems. Liang develops an
interactive fuzzy multi-objective linear programming method for solving
the fuzzy multi-objective DPD problem with piecewise linear membership
functions. Selim & Ozkarahan suggest an interactive fuzzy goal
programming (FGP) for the supply chain distribution network design. The
goal of their model is to select the optimum numbers, locations, and
capacity levels of the plants and warehouses to deliver the products to
the retailers at the least cost while satisfying the preferred customer
service level.
In most of the past research studies like Gourdin
et al., Jayaraman, Pirkul & Jayaraman, and
Tragantalerngsak et al., one major drawback is that they limit the
number of capacity levels available to each facility to just one.
However, in real case studies, there are usually several capacity levels
to choose for each facility. This flexibility in capacity levels makes
the problem more realistic and, at the same time, more complex to solve.
Another major drawback in some previous studies is that they limit the
number of opening facilities to a pre-specified value. Moreover, these
studies fail to describe how this value can be determined in advance.
Amiri represents a significant improvement over previous research
by presenting a unified model of the problem that includes the numbers,-
locations, and capacities of both warehouses and plants as variables to
be determined in the model. In addition, he develops an efficient
heuristic solution procedure based on Lagrangean Relaxation (LR) of the
problem, and reports extensive computational tests with up to 500
customers, 30 potential warehouses, and 20 potential plants.
In
this paper we develop a new non-linear multi-objective DPD model,
consisting of one manufacturer and multiple distribution centres
(warehouses), that integrates the location/allocation and distribution
plans. In this model, to improve over previous research, we also
incorporate tactical/operational decisions - such as inventory control
decisions -into the DPD problem. Then we propose an efficient goal
programming approach to solve the developed model. We consider three
important objective functions:
- investment in opening distribution centres/warehouses (location costs);
- total cost of logistics, such as the costs of transporting products from the plant to the opened warehouses, and from the opened warehouses to the retailers, and holding costs (inventories and safety stocks); and
- total delivery time.
The
problem is particularly motivated by consulting work that was done for a
large food industry company owning one production site and multiple
distribution centres. Since the transportation cost constitutes the main
part of the unit cost, and since delivery time and limited storage
capacity are also very important, implementing the distribution planning
system for the DCs' location and inventory control decisions is of
particular interest.
The paper has two important applied and
theoretical contributions. First, it presents a new comprehensive and
practical, but tractable, optimisation model for distribution network
designing. Second, it introduces a novel solution procedure for finding
more non-dominated and efficient compromise solutions to a stochastic
multi-objective mixed-integer programme. In our literature survey we
have found a lack of studies in this field, which is understandable,
given that large mixed integer programming is known to be complex even
when all data is certain and precise.
The remainder of this paper
is organised as follows. In Section 2 we consider a summary of key
challenges in agro-food supply chains. In Section 3 we define our
notation, state our assumptions, and propose a new multi-objective
stochastic non-linear program (MOSNLP) for the proposed DPD problem.
After applying appropriate strategies for converting the stochastic
model into a multi-objective nonlinear model (MONLP), in Section 4 we
propose a novel interactive payoff approach to solve this MONLP and find
an efficient compromise solution. The proposed model and the solution
method are validated through numerical tests in Section 5. The data for
these numerical computations have been inspired by a real life food
industrial case study, as well as randomly generated data. Concluding
remarks on computational results and further research directions are the
subject of Section 6.