Extended Abstract for ‘Optimal Allocation of Reserved Inventories in a Supply
Network with Demand Surge’
(1) Problem definition: What is your research problem?
In this paper, we investigate how the firms strategically allocate reserved inventories
among different locations so as to mitigate the impact of demand surges. In particular, we
study how uncertainties involved in both the pre-positioning and deployment process
(such as the geographical locations of the warehouses, delivery lead times, and partial or
complete inventory losses) and the demand surge (such as the geographical distribution,
magnitude, demand variability and arrival patterns) affect the firm's reserved inventory
pre-positioning decisions.
(2) Academic / Practical Relevance: How is your research problem relevant to the OM research
/ practice community?
Demand surges -- the significant demand increments in addition to the regular demand in
a supply network -- arise from various sources in a supply network. In order to mitigate
the disruptive impact of sudden demand surges on firms' inventory flow and production
processes, firms usually either build up reactive capacities or keep a certain amount of
reserved inventories as a reactive buyer at warehouses in different geographical locations.
In the latter case, the reserved inventories are often managed separately from the regular
inventories that are used to satisfy the daily demand. When demand surge occurs at some
specific location(s), due to the geographical difference between the inventory reserve and
demand, the pre-positioned inventories at other non-surge-stricken locations need to be
deployed to the surge-occurring location(s). Such deployment process creates a time lag
between the demand and the arrival of the reserved inventories, which results in an
immediate mismatch between supply and demand and leads to a significant loss of
demand. Consequently, firms, governments and non-for-profit organizations often target
at minimizing the expected unmet demand, i.e., the immediate mismatch between the
supply of the reserved inventories and the demand surge. This is especially relevant for a
supply network where reserved inventories are kept at multiple geographically different
locations.
Our paper contributes to the emerging studies of inventory planning for random demand
surges. Past literature on mitigating random demand surges study pre-positioning
emergency inventories with the objective to minimize operational cost and joint
inventory stocking and capacity reserving problems for sudden demand surges. Our paper
complements previous works by considering uncertain demand locations and delivery
lead times. We also consider a different objective that aims to minimize supply-demand
mismatch while they consider cost minimization. In order words, we focus on finding the
optimal reserved inventory pre-positioning by taking into account the demand dynamics
and uncertainties involved in the deployment process.
(3) Methodology: What is the underlying research method?
We formulate the firm's reserved inventory pre-positioning problem as an allocation
problem with uncertainties coming from both the supply and demand sides. Because the
arrival sequence of reserved inventories depends on the demand surge location as well as
the realized delivery lead times, we define a novel ranking function that characterizes the
arrival sequence of reserved inventories and express the aggregated supply-demand
mismatch in closed form. We use stochastic comparison to illustrate conditions under
which the total expected unmet demand is larger.
(4) Results: What are your key findings?
When the demand surge occurs at a single location, we show that the total expected
unmet demand is larger when one of the following is true: the probability distribution of
the demand surge location is more dispersed, the post-surge delivery takes a longer time,
more demand arrives at the early times, or it has a higher volatility. When the probability
distribution of the demand surge locations is more dispersed, the surge may occur at a
wider range of locations. Thus, the inventory reserves need to be stocked so that the
delivery time to each possible demand location can be balanced, yet the time it takes to
deliver the inventories to each location may be on average longer. As a result, the
expected total unmet demand becomes larger. On the other hand, when the demand surge
occurs only at certain locations, the inventory reserves can be placed at or near these
locations to increase the responsiveness of the supply network and hence reduce the total
unmet demand. When more demand arrives at early times, the amount of inventory
reserve that can be used to satisfy the demand is less due to the positive delivery lead
time and thus, results in a larger unmet demand. Moreover, when the arrival demand is
more volatile, the probability of larger arrivals within shorter time periods is larger,
which leads to a larger unmet demand
(5) Managerial Implications: How can academics/managers/decision makers benefit from your
study?
When demand surge may occur at multiple locations, as the total amount of reserved
inventories increases, it may be optimal to reduce the reserves at certain locations and
pre-position the reserved inventories at fewer locations. It can also be optimal to preposition more reserved inventories at locations with a low probability of demand surge or
inventory survival rate. These results imply that the optimal prepositioning of reserved
inventories can be complex in a supply network with multiple demand surge locations.