Taimaz Soltani

6.1

risk with options can lead to cost reduction for a firm that employs a dual-sourcing strategy. Furthermore, our numerical studies in chapter three yield several managerial insights.

First, our numerical studies demonstrate that dual-sourcing strategies limit price risk exposure and offer the firm flexibility by allowing the firm to take advantage of low domestic costs.

Second, our investigation shows that cost savings may be achieved by chartering larger tankers and container ships even though they may cost more to charter.

Third, our numerical studies further show that buying freight options may increase the proportion of demand procured on the offshore market.

Fourth, the results show that when the volatility of freight rate is relatively high the firm should procure more on the domestic market.

Finally, our study demonstrates that the firm should buy more on the offshore market when the volatility of commodity price is relatively high.

In Chapter 4 we move from OTC options to real options. In Chapter 4 we consider switching options as an approach which can protect the firm against adverse price changes. The chapter is a pure methodological research, although it can be applied in many real life problems such as tolling agreements. In the chapter we develop a computational method based on Moving-Boundary to solve the optimal switching problem in two regimes over a finite time horizon. The idea is to convert a free boundary problem into a sequence of fixed boundary problems as was first developed for singular control problems in Kumar & Muthuraman (2004). In this study we demonstrate that the idea of converting to a sequence of fixed boundary problems is still possible for free boundary problems arising from switching problems; the specific method, however, is different. We further establish the theoretical guarantees for the method by proving that the solution to associated Quasi Variational Inequalities is unique, and that the optimal condition can be violated by superset conditions. Consequently, by the Moving-Boundary iterations from a violated region, the value monotonically increases in the next iteration and converges to the true value function. Then the optimal switching policy can be easily obtained.

To show that our algorithm works properly we solved a numerical example. In the example we present the shape of optimal policy and show how the policy and the value function converges to the optimum. We also study the impact of volatility on the optimal policy. Our study shows that the inaction region becomes smaller as the volatility increases. This implies that the firm should switch more frequently when the underlying is more risky.

Chapter 5 concerns operationalizing the offshoring strategy by using switching options. Limited literature on the operational aspect of the offshoring-backshoring strategy motivated us to contribute to the literature by considering a dynamic model for making offshoring decisions. We show that by using switching options, we are able to derive optimal control policies which are easy to obtain, understand and implement. Our model considers a firm that could choose two locations for the site of production: domestic or offshore. The firm has a stochastic profit margin in the offshore facility, while its domestic profit margin is deterministic. Our aim is to find an optimal policy for the firm to maximize its profit over a finite time horizon. To do so, we propose a model based on switching options. Our model differs from Nembhard et al. (2003) in that we consider the switching costs. We implemented several numerical experiments and obtained interesting managerial insights.

First, our study shows that the relocation cost has an important role in the offshoring policy such that high relocation costs result in large inaction regions, and consequently the frequency of switching between the locations should significantly decrease.

Second, our numerical experiments demonstrate that the discount rate does not have a significant effect on the offshoring decision; however, as the discount rate increases substantially, the inaction region becomes slightly larger, and consequently the firm should switch less frequently.

Third, our study shows that the profit difference between the domestic and the offshore location does not affect the frequency of switching between them; however, it obviously shifts the policy towards the offshore facility as the profit margin decreases in the domestic location.

Finally, our experiments demonstrate that the time horizon is an important factor in the offshoring decisions such that the manager should switch between the domestic and offshoring plants more frequently when the time horizon is relatively long.

6.2 Impact of Flexibility on Decision Making

In today’s world managers are faced with an increasing number of alternatives in order to make an optimal decision. This obviously leads to an increase in flexibility for the manager and better management of risks faced by the firm; however, it also leads to an increase in complexity of the problem to solve. In this thesis we have taken into account the alternatives available to the manager making decisions in the setting of operational efficiency and financial risk management. In the current global environment, firms are able to source their supplies from multiple locations in the world and transport them even by different means back to their factory. Firms also have the ability to engage in OTC option contracts on commodities as well as freight rates. Further, firms can have multiple manufacturing locations.

In terms of the simple problem of purchasing raw materials the firm faces price fluctuations. This risk can be managed by purchasing option contracts. However, in the transportation of raw materials from the source to the factory managers face two kinds of price risks, in the commodity as well as the transportation. It is possible to engage in option contracts for both at the same time. Chapter 2 shows how such flexibility offered by these option contracts helps the manager to better hedge against the price risk. Another level of flexibility afforded to the managers is the choice between multiple sources for the procurement as well as multiple ways to transport them. Chapter 3 takes this into account and shows how to optimally procure goods from multiple sources and transport them to the factory.

Chapters 2 and 3 talk about optimizing procurement strategies, but upper management also faces different issues in order to maintain profit margins. The first of these issues is the decision whether or not to procure a particular item, i.e. buy or do not buy decision. This is the same problem as keeping the factory running or shutting it down. Also, analogous to this is the problem of offshoring in which the manager has to decide in which of the firm’s multiple factories production should take place. In Chapters 4 and 5 we tackle these issues by providing the managers with an optimal policy to make this decision.

6.3 Future Research Directions

In this section we briefly discuss some future research directions regarding the underlying concepts presented in this thesis.

In Chapters 2 and 3 we have presented an optimal policy to hedge against the freight rate risk. One interesting extension could be to include a shipping lead time in the model. We may consider a stochastic lead time, then the firm faces another important risk. Another challenging extension could be to add the inventory aspect to the model. To do so we need to extend the model to at least two periods. Subsequently, it might be interesting to extend the model to a multi-period one, something that would make the problem very complex to solve. One more extension could be considering multi products instead of one product and see how the firm can manage their transportation when they can be carried in one type of ships.

In chapter 4 we proposed a Moving-Boundary approach to solve the switching options. Our method works in the two regimes setting. Our next step would be to extend the method for more than two regimes. To do so we might use simulation based methods.

In chapter 5 we studied a switching based model for offshoring problem. Then we introduced a model based on impulse control; however, we did not propose a solution for that. Our future work will aim to solve the impulse control model, and subsequently investigate the effect of the proportional relocation cost on the offshoring policy. To do so, our plan is to apply the idea of Moving-Boundary method.

Besides future directions for each chapter, we can aim a future direction for this area of research at large. In this thesis our approach is modelling the real world problems by using mathematical techniques. Strictly speaking, we have a model-based study in this thesis. However, we believe there is still much space to examine the models with real data to see how these models fit to the real world. In other words, an interesting future direction could be empirical research to test models and policies developed in this thesis. We believe by doing so, we can find additional nice managerial insights. For example, in Chapters 2 and 3 we build mathematical models to obtain hedging policies against the freight risk. However, by using available public data for freight rates we might be able to examine our models in the real world and find out the real value created for the firms by using freight options.