Unique Supply Function Equilibrium with Capacity Constraints

Consider a market where producers submit supply functions to a procurement auction — e.g. an electric power auction — under uncertainty, before demand has been realized. In the Supply Function Equilibrium (SFE), every firm commits to the supply function maximizing his expected profit given the supply functions of the competitors. The presence of multiple equilibria is one basic weakness of SFE. This paper shows that with (i) symmetric producers, (ii) inelastic demand, (iii) a reservation price, and (iiii) capacity constraints that bind with a positive probability, there is a unique symmetric SFE.Supply function equilibrium; auction; oligopoly; capacity constraint; wholesale electricity market

Planning of outsourced operations in pharmaceutical supply chains

In this dissertation, we focus on the planning and control of supply chains where part of the supply chain is outsourced to a contract manufacturer(s). Supply Chain Management deals with the integration of business processes from end-customers through original suppliers that provide products, services and information that add value for customers (Cooper et al., 1997). In a narrow sense, a supply chain can be ‘owned’ by one large company with several sites, often located in different countries. Planning and coordinating the materials and information flows within such a worldwide operating company can be a challenging task. However, the decision making is easier than in case more companies are involved in a supply chain, since the sites are part of one organization with one board and it is likely that the decision makers have full access to information needed for the supply chain planning. Outsourcing is an ‘act of moving some of a firm’s internal activities and decision responsibilities to outside providers’ (Chase et al., 2004) and it has been studied extensively in the literature.Outsourcing is developing in many industries, but in this dissertation, we focus on outsourcing in the pharmaceutical industry, where outsourced supply chain structures are rapidly developing. Recent studies show that the global pharmaceutical outsourcing market has doubled from 2001 to 2007 and it is expected to further increase in the upcoming years. In the pharmaceutical industry, the outsourcing relationship is typically long-term and customers often require high service levels. Due to high setup costs, production is conducted in fixed large batch sizes and campaign sizes. The cumulative lead time within the supply chain is more than one year, whereas the customer lead time is about two months. In this industry, production activities are outsourced for three main reasons. First, intellectual property legislation requires outsourcing the production activities to a contract manufacturer that owns the patent for specific technologies that are needed to perform the production activities. Second, expensive technologies or tight (internal) capacity restrictions also result in outsourcing. Third, to limit the supply uncertainty, companies outsource to have an external source producing the same product next to an internal source. This dissertation deals with the planning and control of outsourced supply chains, which are supply chains where part of the supply chain is outsourced to a contract manufacturer. Most supply chain operations planning models from the literature assume that the supply chain is planned at some level of aggregation and that further coordination is conducted at a more detailed level by lower planning levels. These concepts implicitly assume that the lower planning level and the operations are conducted within the same company with full information availability and full control over the operations, which is not case when part of the supply chain is outsourced. Hence, the objective of this dissertation is to obtain insights into the implications of outsourcing on the supply chain planning models. First, we review the literature on outsourcing research and we find that little is known on the operational planning decisions in an outsourced supply chain and on the implications of outsourcing on the operations planning. The literature on outsourcing at the operational level uses outsourcing purely as a secondary source to control performances such as the delivery reliability. Consequently, we discuss two case studies that we conducted into outsourced supply chains to understand the implications of outsourcing on the supply chain operations planning function, where the contract manufacturer is the only source of supply. The main implications of the planning and control of outsourced supply chains can be summarized in three categories: limited information transparency, limited control over the detailed planning and priorities at the contract manufacturer, and contractual obligations. Below, we discuss these in more detail. In order to decide on the release of materials and resources in a supply chain, it is required that the decision maker is able to frequently monitor the status of the supply chain. In an outsourced supply chain, the outsourcer does not have access to all relevant information of the entire supply chain, especially not to the available capacity in each period, also because the contract manufacturer serves a number of different (and sometimes even competing) outsourcers on the same production line. Moreover, the contract manufacturer plans and controls its part of the supply chain based on rules and priorities that are unknown to the outsourcer. This results in facing an uncertain capacity allocation by the outsourcer. Another implication is that the contract manufacturer requires by contract to reserve capacity slots prior to ordering. These reservations are subject to an acceptation decision, which means that part of the reservation quantity can be rejected. The accepted reservation quantity bounds the order quantity that follows later on. Therefore, another main insight from the case study is that in an outsourcing relationship, the order process consists of different (hierarchically connected) decisions in time. In the ordering process, the uncertain capacity allocation of the contract manufacturer should be incorporated. Hence, the order release mechanism requires a richer and more developed communication and ordering pattern than commonly assumed in practice. In a subsequent study, we build on this insight and we design three different order release mechanisms to investigate to what extent a more complicated order release function improves (or deteriorates) the performance of the supply chain operations planning models. The order release mechanisms differ in the number of decision levels and they incorporate the probabilistic behaviour of the contract manufacturer. Based on a simulation study, we show that a more advanced order release strategy that captures the characteristics of outsourcing performs significantly better than a simple order release strategy that is commonly used in practice. We also discuss the conditions for a successful implementation of the more advanced order release strategy. In another study, we study the case where the contract manufacturer is a second source next to an internal manufacturing source for the same product and where the outsourcer faces inaccurate demand forecasts. The two sources are constraining the supply quantities in different ways. Its own manufacturing source is more rigid, cheaper and tightly capacitated, whereas the contract manufacturer is more flexible but more expensive. In that study, we compare the performance of two different allocation strategies by a simulation study in which we solve the model in a rolling horizon setting. The results show that the rigid allocation strategy (the cheaper source supplies each period a constant quantity) performs substantially better than the dynamic allocation strategy (each period the allocation quantities are dynamic) if the parameters are chosen properly. In another study, we study the outsourcer’s problem of deciding on the optimal reservation quantity under capacity uncertainty, i.e., without knowing what part of the reservation will be accepted. In that study, we develop a stochastic dynamic programming model for the problem and we characterize the optimal reservation and order policies. We conduct a numerical study where we also consider the case where the capacity allocation is dependent on the demand distribution. For that case, we show the structure of the optimal policies based on the numerical study. Further, the numerical results reveal several interesting managerial insights, such as that the optimal reservation policy is little sensitive to the uncertainty of the capacity allocation from the contract manufacturer. In that case, the optimal reservation quantities hardly increase, but the optimal policy suggests increasing the utilization of the allocated capacity. We also study the outsourced supply chain from the contract manufacturer’s perspective. In that study, we consider the case where the contract manufacturer serves a number of outsourcers with different levels of uncertainty. The contract manufacturer faces the question of how to allocate the contractual capacity flexibility in an optimal way. More precisely, we focus on the contract manufacturer’s decision to make the acceptation decision under uncertainty. The more the contract manufacturer accepts from an outsourcer, the more risk is taken by the contract manufacturer, as the outsourcer might not fully utilize the accepted reservation quantity. However, we assume that the outsourcer is willing to pay an additional amount to compensate the contract manufacturer for that risk. We develop a mixed-integer programming model, which optimizes the allocation of capacity flexibility by maximizing the expected profit. Offering more flexibility to the more risky outsourcer generates higher revenue, but also increases the penalty costs. The allocated capacity flexibilities are input (parameters) to the lower decision level, where the operational planning decisions are made and demands are observed. The simulation results reveal interesting managerial insights, such that the more uncertain outsourcer gets at least the same capacity flexibility allocated as the less uncertain outsourcer. Moreover, we have seen that when the acceptation decision is made, priority is given to the less uncertain outsourcer, because that information is the most valuable. However, we see the opposite effect when orders are placed, namely that priority is given to the more uncertain outsourcer, i.e., the most paying outsourcer, as no uncertainty is involved anymore. These insights are helpful for managers of contract manufacturers when having contract negotiations with the outsourcers. We believe that the results and insights that we obtained in the various research studies of this dissertation can contribute to solving the broader real-life problems related to the planning and control of outsourced supply chains. We also discuss potential managerial implications of our findings explicitly addressing the management decisions that may be affected by using the insights from our studies. Considering the operational implications of outsourcing when taking the strategic outsourcing decision will lead to a different and a better estimate of the transaction costs and probably to a different strategic outsourcing decision. Based on our research, we think that the transaction cost estimate will be higher if the outsourcer and the contract manufacturer do not agree on operational issues, such as the multi-level order release mechanism. From a tactical point of view, the outsourcer may include the options of postponement and cancellation in the contract, even if the contract manufacturer would charge little extra for these options. The results show that the benefits of including these options are substantial. Moreover, we showed that controlling a contract manufacturer operationally in the same way as an internal manufacturing source leads to a nervous ordering behaviour with a lot of changes and a lot of panicky communication between the outsourcer and the contract manufacturer. Combining the insights from different studies, one can also conclude that including little reservation cost is beneficial to both parties; it leads to a win-win situation. The outsourcer with a high level of demand uncertainty secures sufficient capacity allocation from the contract manufacturer and avoids more expensive penalty costs. For the outsourcer with less demand uncertainty, it is wise to set the contract such that the reservation costs are subtracted from the total paid amount. Moreover, this outsourcer may gain competitive advantage if his competitors operate in the same market by securing sufficient capacity allocation (by paying little reservation costs). For the contract manufacturer, including reservation cost is also beneficial, as it leads to a better match between the outsourcer’s reservation and ordering behaviour

Capacity Reservation under Spot Market Price Uncertainty

The traditional way of procurement, using long-term contract and capacity reservation, is competing with the escalating global spot market. Considering the variability of the spot prices, the flexibility of combined sourcing can be used to benefit from occasional low short-term spot price levels while the long-term contract is a means to hedge the risk of high spot market price incidents. This contribution focuses on the cost-effective management of the combined use of the above two procurement options. The structure of the optimal combined purchasing policy is complex. In this paper we consider the capacity reservation - base stock policy to provide a simple implementation and comparison to single sourcing options. Our analysis shows that in case of large spot market price variability the combined sourcing is superior over spot market sourcing even in case of low average spot market price and also superior over long-term sourcing even in case of high average spot market price.Capacity reservation; spot market; purchasing policy; supply chain contracts; stochastic inventory control

The structure of the optimal combined sourcing policy using capacity reservation and spot market with price uncertainty

This contribution focuses on the cost-effective management of the combined use of two procurement options: the short-term option is given by a spot-market with random price, whereas the long-term alternative is characterized by a multi period capacity reservation contract with fixed purchase price, reservation level and capacity reservation cost. Considering a multiperiod problem with stochastic demand, the structure of the optimal combined purchasing policy is derived using stochastic dynamic programming.Capacity reservation, spot market, purchasing policy, supply contracts, stochastic inventory control

Endogenous capacities and price competition: the role of demand uncertainty

This paper analyzes a model of capacity choice followed by price competition under demand uncertainty. Under various assumptions regarding the nature and timing of demand realizations, we obtain general predictions concerning the role of demand uncertainty on equilibrium outcomes. We show that it reduces the multiplicity of equilibria, it may rule out the existence of symmetric equilibria, and it leads to endogenous capacity asymmetries even though firms are ex-ante symmetric. Furthermore, as compared to the certainty equivalent game, demand uncertainty reduces prices and increases consumer surplus, but it also decreases total welfare because of the emergence of idle capacity. By relying on the analysis of firms' reaction functions as well as on the theory of submodular games, we are able to show that a subgame perfect equilibrium always exists and to fully characterize it

On-demand or Spot? Selling the cloud to risk-averse customers

In Amazon EC2, cloud resources are sold through a combination of an on-demand market, in which customers buy resources at a fixed price, and a spot market, in which customers bid for an uncertain supply of excess resources. Standard market environments suggest that an optimal design uses just one type of market. We show the prevalence of a dual market system can be explained by heterogeneous risk attitudes of customers. In our stylized model, we consider unit demand risk-averse bidders. We show the model admits a unique equilibrium, with higher revenue and higher welfare than using only spot markets. Furthermore, as risk aversion increases, the usage of the on-demand market increases. We conclude that risk attitudes are an important factor in cloud resource allocation and should be incorporated into models of cloud markets.Comment: Appeared at WINE 201

Capacity precommitment and price competition yield the Cournot outcome

We introduce a simple model of oligopolistic competition where firms first build capacity, and then, after observing the capacity decisions, choose a reservation price at which they are willing to supply their capacities. This model describes many markets more realistically than the model of Kreps and Scheinkman [Kreps, D., Scheinkman, J., 1983. Quantity precommitment and Bertrand competition yield Cournot outcomes. Bell J. Econ. 14, 326–337]. We show that in this new model every pure strategy equilibrium yields the Cournot outcome, and that the Cournot outcome can be sustained by a pure strategy subgame perfect equilibrium.Publicad

Capacity precommitment and price competition yield Cournot outcomes

We study an industry of a homogeneous good where n firms with identical technology compete by first building capacity, and then, after observing the capacity decisions, choosing a “reservation price” at which they are willing to sell their entire capacities. We show that every pure strategy equilibrium yields the Cournot outcome, and that the Cournot outcome can be sustained by a pure strategy subgame perfect equilibrium.