Optimal Dynamic Procurement Policies for a Storable Commodity with L\'evy Prices and Convex Holding Costs

In this paper we study a continuous time stochastic inventory model for a commodity traded in the spot market and whose supply purchase is affected by price and demand uncertainty. A firm aims at meeting a random demand of the commodity at a random time by maximizing total expected profits. We model the firm's optimal procurement problem as a singular stochastic control problem in which controls are nondecreasing processes and represent the cumulative investment made by the firm in the spot market (a so-called stochastic "monotone follower problem"). We assume a general exponential L\'evy process for the commodity's spot price, rather than the commonly used geometric Brownian motion, and general convex holding costs. We obtain necessary and sufficient first order conditions for optimality and we provide the optimal procurement policy in terms of a "base inventory" process; that is, a minimal time-dependent desirable inventory level that the firm's manager must reach at any time. In particular, in the case of linear holding costs and exponentially distributed demand, we are also able to obtain the explicit analytic form of the optimal policy and a probabilistic representation of the optimal revenue. The paper is completed by some computer drawings of the optimal inventory when spot prices are given by a geometric Brownian motion and by an exponential jump-diffusion process. In the first case we also make a numerical comparison between the value function and the revenue associated to the classical static "newsvendor" strategy.Comment: 28 pages, 3 figures; improved presentation, added new results and section

Comparison between minimum purchase, quantity flexibility contracts and spot procurement in a supply chain

When, in a supply chain, a supplier and a buyer have the choice of transaction form to do business, the equilibrium transaction form which emerges is much more constrained than previously envisaged in literature. In this paper, two forms of long-term supply contracts and procurement in the spot market are compared. A capacity constrained service provider and a buyer of such service choose among three different transaction forms: spot procurement, minimum purchase commitment and quantity flexibility contracts. The ultimate demand the buyer has to satisfy and the spot market price of the input she has to purchase from the supplier are exogenous stochastic processes. Complete analytical results and a numerical example are presented. This paper builds upon recent supply chain contract literature by trying to join in one setting problems which up till now were considered in isolation.contracts, supply chain, statistical decision theory, optimization techniques, transactional relationships

Choosing a transport contract over multiple periods

We offer a shipper and a carrier the choice among three contracts in which to frame their relationship. Both can also take recourse in the transport spot market. Demand and price on the spot market are dependent exogenous stochastic processes. We model the outcome of this endogenous choice of contract. The results, given in closed form, are different from those presented in the literature. Using numeric instances, we show how a choice is made and which contract would be preferred. Comparison on the variance of the economic returns are offered. The conclusions are applicable when the carrier is not capacity constrained.

Interaction between intelligent agent strategies for real-time transportation planning

In this paper we study the real-time scheduling of time-sensitive full truckload pickup-and-delivery jobs. The problem involves the allocation of jobs to a fixed set of vehicles which might belong to dfferent collaborating transportation agencies. A recently proposed solution methodology for this problem is the use of a multi-agent system where shipper agents other jobs through sequential auctions and vehicle agents bid on these jobs. In this paper we consider such a multi-agent system where both the vehicle agents and the shipper agents are using profit maximizing look-ahead strategies. Our main contribution is that we study the interrelation of these strategies and their impact on the system-wide logistical costs. From our simulation results, we conclude that the system-wide logistical costs (i) are always reduced by using the look-ahead policies instead of a myopic policy (10-20%) and (ii) the joint effect of two look-ahead policies is larger than the effect of an individual policy. To provide an indication of the savings that might be realized with a central solution methodology, we benchmark our results against an integer programming approach

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

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 Impact of E-Procurement on the Number of Suppliers: Where to Move to?

This paper examines how electronic procurement influences the organization of economic transactions. It seeks evidence for ICT-induced changes in how companies organize their activities and whether ICT lead to more competitive and transparent markets. Testing the relationship between the effect of electronic procurement on procurement cost and sourcing strategy, I provide new evidence that electronic procurement leads to more market transactions. This leads to the conclusion that electronic procurement increases market transparency, lowers search and supplier switching costs and improves the management of supply chain and contradicts the predictions that ICT will lead to a dominance of network-like organizational form and an increasing reliance on hybrid forms of organizing economic transactions. Two implications emerge from these results. The first one is relevant for companies engaging in ICT projects. ICT combined with changes in business strategy leads to a reduction of market transaction costs and, as a result, opens up new possibilities in terms of how business activities can be organized and/or how to structure competition in upstream markets. This effect of new technologies is of clear benefit to companies successfully implementing and using new technologies. The second implication is of great importance for companies whose customers implement ICT to intensify competition among suppliers. Changing environment forces them to adapt to new market conditions and look for new ways of maintaining profitability.information technology and firm boundaries, markets vs. hierarchies, sourcing strategy, electronic procurement

Strategic procurement in spot and forward markets considering regulation and capacity constraints.

With the generalization of business-to-business electronic exchanges, online spot markets have become an important component of suppliers' procurement strategies in their aim to increase flexibility and reduce transaction costs. In this article we analyze, both analytically and computationally, how these online spot markets interact with forward contracts as strategic procurement tools. We consider non-storable commodity markets in which the suppliers have market power. We derive the equations describing the equilibrium of this game considering capacity constraints and regulation. We show that price caps increase forward trading and we analyze the conditions under which, in the capacitated model, some suppliers can buy forward to sell spot. Furthermore, we prove that inefficient producers continue to operate in the market as arbitrageurs, selling forward and buying spot. We model the game with asymmetric suppliers, identifying the situations in which it is well defined, and describing how these asymmetries are important for market equilibrium. Finally, we analyze a game with multiple sequential forward contracts: we prove that, when suppliers readjust their forward positions until the start of the spot market, the number of time periods (i.e., market liquidity) has neither effect on the suppliers' strategic procurement nor on market efficiency

Mixed contracts for the newsvendor problem with real options

In this paper we consider the newsvendor model with real options. We consider a mixed contract where the retailer can order a combination of q units subject to the conditions in a classical newsvendor contract and Q real options on the same items. We provide a closed form solution to this mixed contract when the demand is discrete and study some of its properties. We also offer an explicit solution for the continuous case. In particular we demonstrate that a mixed contract may be superior to a real option contract when a manufacturer has a bound on how much variance she is willing to accept.Newsvendor model; real options; discrete demand; mixed contract