Page 305 - DMGT523_LOGISTICS_AND_SUPPLY_CHAIN_MANAGEMENT

Logistics and Supply Chain Management

Notes Mixed-integer programming is the other optimization solution technique successfully applied to
logistics problems. The formulation offers considerable flexibility, which enables it to incorporate
many of the complexities and idiosyncrasies found in logistics applications. The primary
advantage of the mixed-integer format is that fixed as well as different levels of variable cost can
be included in the analysis.

Example: Demand can be treated on a non-integer basis, thus allowing increments to
system capacity in specific step increases.
In other words, mixed-integer programming allows solutions to accurately reflect increased
fixed costs and economies of scale as larger distribution centres are employed. The mixed-
integer approach permits a high degree of practicality to accommodate restrictions found in
day-to-day logistics operations.
Historically, the major limitation of optimization has been constraints on problem sizes. Along
with other advances in mixed-integer programming, problem size constraints have been
overcome, for a considerable period of time, through the application of decomposition to the
solution techniques. Decomposition permits multiple commodities to be incorporated into
logistical system design. Most firms have a variety of products or commodities that are purchased
by customers in varied assortments and quantities. While such products may be shipped and
stored together, they are not inter-changeable from the viewpoint of servicing customers.

The decomposition technique provides a procedure for dividing the multi-commodity situation
into a series of single-commodity problems. The procedure for arriving at commodity assignment
follows an iterative process wherein costs associated with each commodity are tested for
convergence until a minimum cost or optimal solution is isolated.
These optimization approaches provide effective tools for analysis of location-related issues
such as facility location, optimum product flow, and capacity allocation. Mixed-integer approaches
are typically more flexible in terms of capacity to accommodate operational nuances, while
network approaches are more computationally efficient.

Did u know? Both types of linear programming optimization approaches are effective
techniques for evaluating situations where significant facility capacity limitations exist.

Simulation

A second location analysis method is static simulation. The term simulation can be applied to
almost any attempt to replicate a situation. Robert Shannon originally defined simulation as
“the process of designing a model of a real system and conducting experiments with this model
for the purpose of either understanding system behaviour or of evaluating various strategies
within the limits imposed by a criterion or set of criteria for the operation of the system.”
Static simulation replicates the product flows and related expenses of existing or potential logistics
channel networks. The network includes plants, distribution centres, and markets. The major
expense components include raw material sourcing, manufacturing, inbound freight, fixed and
variable distribution centre cost, outbound customer freight, and inventory carrying cost.
Static simulation evaluates product flow as if it all occurred at a single point during the year. In
this sense, the primary difference between static and dynamic simulation is the manner in which
time-related events are treated. Whereas dynamic simulation evaluates system performance
across time, static simulation makes no attempt to consider the dynamics between time periods.
Static simulation treats each operating period within the overall planning horizon as a finite
interval. Final results represent an assumption of operating performance for each period in the
planning horizon.

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