In my dissertation I focus on three major areas of research. The goal of these studies is to
optimize inventory replenishment decisions for perishable products.
First, we presented a 2-SIP model for inventory replenishment and the administration of
childhood vaccines in targeted outreach immunization sessions. To our knowledge, this is the first
stochastic optimization model which captures the relationships that exist among these decisions.
The proposed model minimizes replenishment and OVW costs. Different from the current practice
which relies on the use of a single multi-dose vial, this study models the performance of an inventory
replenishment policy that allows the use of mix of multi-dose vials for vaccination. Motivated by
the solutions obtained from the proposed model we developed simple-to-implement vaccine adminis-
tration policies. Statistical analysis indicated that the performance of some policies is not different
than the optimal policy and others outperform the optimal policy. In order to solve the proposed
Via an extensive numerical study we showed that the proposed algorithm is scalable; it outperforms
the LS method by providing high quality solutions in a much shorter CPU time.
Second, we proposed a two-stage stochastic optimization model that identifies a replenish-
ment schedule for a periodic-review inventory system for perishable products with non-stationary
demand and dual sourcing. The model captures the relationship between price and stochastic de-
mands via a linear function. The model considers a price markdown as the means to stimulate
demand and minimize waste of this perishable product. In the proposed model, the first-stage prob-
lem is bilinear. Thus, we developed a solution approach which extends the LS method by employing
a piecewise linear approximation of the bilinear term in order to solve the first-stage problem. We
developed a case study in order to validate the model and evaluate its performance. We conducted
a thorough sensitivity analysis to observe the impact that timing and size of a price markdown has
on inventory replenishment decisions and retailer’s profits. We analyzed the impact of deterioration
rate, inventory holding cost, and service level on inventory replenishment decisions and retailer’s
profits. Via this model we also evaluated the impact of dual sourcing in replenishment decisions.
While the relationships identified via this analysis are intuitive, quantifying these relationships can-
not easily be accomplished without the aid of models similar to the one proposed in this research.
Finally, we proposed a data-driven stochastic optimization model that identifies distribution
strategies for vaccine vials. To the best of our knowledge, this is the first stochastic optimization
model that integrates transportation, inventory and replenishment decisions of vaccine supply chain.
The model captures uncertainties of demand for vaccination via chance constraints. The objective is
to maximize the number of fully immunized children in developing countries. Public health author-
ities can use this model to evaluate the impact of different supply chain designs on immunization
coverage; evaluate the impact of introducing a new vaccine on vaccine inventory at a clinic; and
develop vaccine administration policies which reduce OVW. We developed a case study using real-
life data from Niger. We conducted an extensive statistical analysis of the data in order to identify
the factors which impact immunization in different regions of Niger. Population size, poverty and
education levels do impact expected demand for vaccination. Analyzing the national level data sug-
gested that the country-wide population size does not significantly impact the expected demand for
vaccination. This highlights the importance of developing a single, region-based regression model
as presented in this study. The results of region-based regression models were incorporated on the
supply chain to a three-tier one by removing the regional stores , and changing Measles’s vial size
from multi-dose to single-dose on F IC and SR.
Overall, the main contributions of this dissertation can be summarized as follows:
1. Development of a two-stage SP model for integrating vial replenishment and vaccine admin-
istration which captures (a) the order frequency for respective quantities of different-sized
vials, (b) the opening schedule for these vials, and (c) the administration of available doses to
patients.
2. Development of simple to use and economic vaccine administration policies for outreach ses-
sions. The performance of these policies is evaluated and benchmarked with existing practice
via an extensive simulation analysis.
3. Development of a new solution approach for two-stage stochastic integer programs (2-SIP)
with continuous recourse by using GMI and MIR cuts to address the non-convexity of the
first-stage problem.
4. Development of a two-stage stochastic optimization model that integrates inventory replenish-
ment and pricing decisions for age-dependent perishable products in a periodic-review inven-
tory system.
5. Development of a solution approach for a two-stage stochastic, bilinear model with linear
recourse by using extensions of McCormick relaxation to approximate the non-linear first
stage problem.
6. Development of a regression-based estimate of the future demand for CIV for each vaccine
type and region in Niger.
7. Development of a data-driven chance constrained programming model for the vaccine supply
chain in developing countries.
8. Application of the data-driven chance constrained programming model to manage transporta-