The "classical" dynamic lot-sizing problem was first
introduced by Wagner and Whitin (1958), and it has become one of the most
studied problems in the area of production planning and inventory control. In
their seminal work, Wagner and Whitin considered a facility/warehouse that was
facing a deterministic time-varying demand for a single item over a
discrete-time, finite planning horizon. In association with each inventory
replenishment decision at the facility/warehouse, a fixed set-up cost was
considered, and a linear production cost was
incurred
for each unit produced. Also, a linear holding cost was incurred for each unit
held in inventory per unit of time. Under these assumptions, Wagner and Whitin
developed a dynamic programming model that allows managers to develop an
inventory replenishment plan satisfying demand at minimum cost.
The classical model is widely applicable, especially in
the context of material requirements planning as well as supply contracts with
advance purchase commitments, i.e., deterministic time-varying demand. Hence, it
has been the subject of extensive research for more than four decades. A
significant number of researchers have generalized the classical model with
various considerations. These extensions include finite production capacity
models, multi-echelon models, and multi-item models. The general objective of
the extensions is to mimic real-life problems. However, with today's changing
logistics practices, real-life problems demand even more complex extensions
because some of the early studies may no longer be applicable. This is the major
motivation for this paper.
The classical dynamic lot-sizing model and its existing
extensions assume that goods can be purchased from one supplier and/or delivered
using one shipment mode. This is a valid assumption if one particular supplier
or shipment mode is always superior (cheaper and faster) to the others or only
one mode is feasible due to some restrictions, e.g., requirements imposing use
of a refrigerated truck or a company-owned truck. On the other hand, instead of
using a particular supplier or shipment mode at all times, it may be more cost
effective to consider the availability of various suppliers and shipment modes
in making inventory replenishment decisions. Recognizing a need for research in
this area, this paper studies a dynamic lot-sizing problem with two-mode
replenishments where each mode is characterized by a different cost structure
and lead time. In the remainder of the paper, the term "mode" is used in a
general way to refer to a replenishment/delivery option, i.e., a supply or
delivery mode.
