Essays in Retail Operations and Humanitarian Logistics

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This dissertation introduces and analyzes research problems related to Retail Operations and Humanitarian Logistics. In Retail Operations, the inventory that ends up as unsaleable at primary markets can be significant (up to 20% of the retail product). Thus retailers look for strategies like selling in secondary markets at a discounted price. In such a setting, the decisions of how much to order for a product of limited shelf life and when (if at all) to start selling the product in the secondary market become critical because these decisions not only affect the retailer's cost of procurement and sales revenues obtained from the product but also affect utilization of shelf space, product rollover and assortment decisions of the retailer. Apart from using secondary markets, retailers that sell seasonal products or products with sales horizons shorter than the typical production/procurement lead time also enter into contractual agreements with suppliers. These contracts are in place to share risks associated with unknown or uncertain demand for the product. Presence of such contracts does affect a retailer's order quantity as well as the time to start selling in the secondary market. In our two essays on retail operations, we analyze a retailer's optimal order quantity and when he/she starts selling in the secondary market. We refer to the former as the 'ordering decision' and the latter as the 'timing decision.' These two decisions are studied first without risk sharing contracts in Essay 1, and then in the presence of contracts in Essay 2.

In Essay 1, we build a two-stage model with demand uncertainty. The ordering decision is made in the first stage considering cost of procurement and expected sales revenue. The timing decision is made in the second stage and is conditional on the order quantity determined in the first stage. We introduce a new class of aggregate demand model for this model. We study the structural properties of the retailer's timing and ordering problem and identify optimality conditions for the timing decision. Finally, we complement our analytical results with computational experiments and show how retailer's optimal decisions change when problem parameters are varied.

In Essay 2, we extend the work in first essay to include the contracts between the retailer and a supplier. In this essay, we introduce a time-based Poisson demand model. We define three di®erent types of contracts and investigate the effect of each of these contracts on the retailer's ordering and timing decisions. We investigate how the analytical structure of the retailer's decision changes in the presence of these contracts. For a given order quantity, we show that the timing decision depends on the type of contract. Our analytical results on the timing decision are complemented with computational experiments where we investigate the impact of contract type on the optimal order quantity of the retailer.

In Humanitarian Logistics, non-profit organizations receive several-billion-dollars-worth of donations every year but lack a sophisticated system to handle their complex logistics operations; the absence of expertly-designed systems is one of the significant reasons why there has been a weak link in the distribution of relief aid. The distribution of relief aid is a complex problem as the goal is humanitarian yet at the same time, due to limited resources, the operations have to be efficient. In the two essays on humanitarian logistics, we study the distribution of aid using homogeneous fleet, with and without capacity restrictions.

In Essay 3, we discuss routing for relief operations using one vehicle without capacity restrictions. Contrary to the existing vehicle routing models, the key property of our routing models is that the nodes have priorities along with humanitarian needs. We formulate this model with d-Relaxed Priority rule that captures distance and response time. We formulate routing models with strict and relaxed forms of priority restrictions as Mixed Integer Programs (MIP). We derive bounds for this problem and show that this bound is attained in limiting condition for a worst-case example. Finally, we evaluate the optimal solutions on test problems for response time and distance and show that our vehicle routing model with priorities captures the trade-off between distance and response time unlike existing Vehicle Routing Problem (VRP) models without priorities.

In Essay 4, we extend the problem dealt in third essay to consider fleet consisting of multiple vehicles (homogeneous) with capacity and route length restrictions. First, we show that the humanitarian aspect imposes additional challenges and develop routing models that capture performance metrics like fill rate, distance traversed, response time and number of victims satisfied. Proposed routing models are formulated as Mixed Integer Programs and are solved to optimality for small test problems. We conduct computational experiment and show that our models perform well on these performance metrics.