Uncertain Production Cost Research Articles

Coordinating supply chains with uncertain production cost by incomplete contracts

ABSTRACT Production cost affects heavily supply chain coordination, but it is uncertain in many cases. We consider a supply chain consisting of a manufacturer and a retailer, where the unit production cost is uncertain when the firms sign a procurement contract. We derive the optimal decisions and profits for the centralised and decentralised cases. We show that production cost uncertainty exaggerates the supply chain’s incentive conflict, but may increase the expected profit in the centralised decision case. Then we design an incomplete contract, which sets a wholesale price and an order quantity in the first stage, which the firms can re-negotiate after the production cost is realised in the second stage. We prove that such an incomplete contract can lead to the first best outcome. We further consider the case with asymmetric cost information and show that the incomplete contract can also coordinate the supply chain. Furthermore, we discuss how the degree of contract incompleteness, re-negotiation freedom, and residual control rights affect the supply chain performance. The results reveal that the hold-up problem is prone to occur with improper contract incompleteness, re-negotiation freedom, and residual control rights, while the incomplete contract we propose can effectively avoid the problem.

Optimization of CCUS Supply Chains for Some European Countries under the Uncertainty

This paper develops a two-stage stochastic mixed integer linear programming model to optimize Carbon Capture, Utilization and Storage (CCUS) supply chains in Italy, Germany and the UK. Few works are present in the literature about this topic, thus this paper overcomes this limitation considering carbon supply chains producing different products. The objective of the numerical models is to minimize expected total costs, under the uncertainties of the production costs of carbon-dioxide-based compounds. Once carbon dioxide emissions that should be avoided are fixed, according to environmental protection requirements for each country, the optimal design of these supply chains is obtained finding the distribution of carbon dioxide captured between utilization and storage sections, the amount of different carbon-based products and the best connection between each element inside the system. The expected total costs for the CCUS supply chain of Italy, Germany and the UK are, respectively, 77.3, 98.0 and 1.05 billion€/year (1004, 613 and 164 €/ton CO2 captured). A comparison with the respective deterministic model, analyzed elsewhere, is considered through the evaluation of the Expected Value of Perfect Information (EVPI) and the Value of Stochastic Solution (VSS). The former is 1.29 billion€/year, 0.18 million€/year and 8.31 billion€/year, respectively, for the CCUS of Italy, the UK and Germany. VSS on the other hand is equal to 1.56 billion€/year, 0 €/year and 0.1 billion€/year, respectively, for the frameworks of Italy, the UK and Germany. The results show that the uncertain production cost in the stochastic model does not have a significant effect on the results; thus, in this case, there are few advantages in solving a stochastic model instead of the deterministic one.

Contracts Adjustment under Bilateral Information Updating in a Supply Chain

This paper investigates contracts adjustment between one manufacturer and one retailer under bilateral information updating. The manufacturer incurs uncertain production cost and the retailer faces uncertain demand, but they can acquire independent signals to update production cost and demand, respectively. They commit an initial agreement on an initial wholesale price, minimum order quantity, and information sharing as well as the transfer payment and decisions adjustment when information is updated. We find that due to the joint impact of production cost variation and market variation, the manufacturer may not decrease (increase) her wholesale price when the updated production cost is lower (higher) than expected. The retailer places an additional order even if the wholesale price rises when the market outlook is good, but places an order with the minimum order quantity even if the wholesale price falls when the market outlook is bad. Secondly, for a certain level of information accuracy of the production cost and market demand, the retailer is always better off with information updating, but the manufacturer may be worse off with information updating when facing a bad market outlook. Thirdly, when information accuracy of the production cost and market demand varies, the manufacturer only benefits from a high accuracy of production cost. Profits of the retailer and the supply chain are increasing (decreasing) with accuracy of production cost if the updated production cost is larger (smaller) than expected.

Rules of origin and uncertain compliance cost

This study considers the role of the cost uncertainty associated with meeting the rules of origin (ROO) in a free trade area/agreement (FTA). While the literature tends to overlook the cost uncertainties of ROO compliers, we show that the uncertain production costs resulting from meeting the ROO yield the coexistence of compliers and non-compliers in symmetric oligopoly firms. We also show that the regime in which compliers and non-compliers coexist is not the best one for an FTA importer, while it may be the best one for world welfare. We also discuss the case that uncertain production costs are firm-specific.

Vertical Cost-Information Sharing in a Food Supply Chain with Multiple Unreliable Suppliers and Two Manufacturers

This paper considers a food supply chain where multiple suppliers provide completely substitutable food products to two manufacturers. Meanwhile, the suppliers face yield uncertainty and the manufacturers face uncertain production costs that are private information. While the suppliers compete on price, the manufacturers compete on quantity. We build a stylized multistage game theoretic model to analyze the issue of vertical cost-information sharing (VCIS) within the supply chain by considering key parameters, including the level of yield uncertainty, two manufacturers’ cost correlation, the correlated coefficient of suppliers’ yield processes, and the number of suppliers. We study the suppliers’ optimal wholesale price and the manufacturers’ optimal order quantities under different VCIS strategies. Finally, through numerical analyses, we examine how key parameters affect the value of VCIS to each supplier and each manufacturer, respectively. We found that the manufacturers are willing to share cost information with suppliers only when the two manufacturers’ cost correlation is less than a threshold. While a high correlated coefficient of suppliers’ yield processes and a large number of suppliers promote complete information sharing, a high level of yield uncertainty hinders complete information sharing. All these findings have important implications to industry practices.

Dynamic pricing with uncertain production cost: An alternating-move approach

This article studies a two-firm dynamic pricing model with random production costs. The firms produce the same perishable products over an infinite time horizon when production (or operation) costs are random. In each period, each firm determines its price and production levels based on its current production cost and its opponent’s previous price level. We use an alternating-move game to model this problem and show that there exists a unique subgame perfect Nash equilibrium in production and pricing decisions. We provide a closed-form solution for the firm’s pricing policy. Finally, we study the game in the case of incomplete information, when both or one of the firms do not have access to the current prices charged by their opponents.

A robust optimization model for dynamic market with uncertain production cost

This article presents a robust optimization formulation for dealing with production cost uncertainty in an oligopolistic market scenario. It is not uncommon that players in the market face an equilibrium selling price but uncertain production costs. We show that, based on a nominal problem, the robust optimization formulation can be derived as a variational inequality with control and state variables. This convenient approach may be applied for computing optimal solutions efficiently, which help manufacturers dramatically and rapidly reform production and distribution schedules such that they can compete in the market successfully.

The trade-offs from pattern bargaining with uncertain production costs

Pattern bargaining is a negotiating strategy that is often employed by industry-wide unions in oligopolistic industries to set wages. The conventional wisdom is that pattern bargaining “takes labor out of competition” and therefore softens bargaining between the union and firms, resulting in higher industry wide wages. However, this does not explain why firms agree to pattern bargaining. We introduce a model in which the agents face uncertainty about the relative product-market positions of the firms and compare the trade-offs involved in adopting different bargaining mechanisms. We show that with sufficient heterogeneity in non-labor costs, there are situations in which both the union and the firms prefer pattern bargaining. We also show that in such situations, the adoption of pattern bargaining harms consumers. This provides an explanation as to how pattern bargaining can arise in equilibrium and why there is often strong political opposition to it.

Long-Term Contracts Under the Threat of Supplier Default

Contracting with suppliers prone to default is an increasingly common problem in some industries, particularly automotive manufacturing. We model this phenomenon as a two-period contracting game with two identical suppliers, a single buyer, deterministic demand, and uncertain production costs. The suppliers are distressed at the start of the game and do not have access to external sources of capital; hence, revenues from the buyer are crucial in determining whether default occurs. The production cost of each supplier is the sum of two stochastic components: a common term that is identical for both suppliers (representing raw materials costs, design specifications, etc.) and an idiosyncratic term that is unique to a given supplier (representing inherent firm capability). The buyer chooses a supplier and then decides on a single- or two-period contract. Comparing models with and without the possibility of default, we find that, without the possibility of supplier failure, the buyer always prefers short-term contracts over long-term contracts, whereas this preference is typically reversed in the presence of failure. Neither of these contracts coordinates the supply chain. We also consider dynamic contracts, in which the contract price is partially tied to some index representing the common component of production costs (e.g., commodity prices of raw materials such as steel or oil), allowing the buyer to shoulder some of the risk from cost uncertainty. We find that dynamic long-term contracts allow the buyer to coordinate the supply chain in the presence of default risk. We also demonstrate that our results continue to hold under a variety of alternative assumptions, including stochastic demand, allowing the buyer the option of subsidizing a bankrupt supplier via a contingent transfer payment or loan and allowing the buyer to unilaterally renegotiate contracts. We conclude that the possibility of supplier default offers a new reason to prefer long-term contracts over short-term contracts.

Fixed Price versus Spot Price Contracts: A Study in Risk Allocation

Thi spaper is concerned with the risk-allocation effects of alternative types of contracts used to set the price of a good tobe delivered in the future. Under a fixed price contract, the price is specified in advance. Under a spot price contract, the price is the price prevailing in the spot market at the time of delivery.These contract forms are examined in the context of a market in which sellers have uncertain production costs and buyers have uncertain valuations. The paper derives and interprets a general condition determining which contract form would be preferred when the seller and/or the buyer is risk averse. In addition, an example is provided in which a spot price contract with a floor price is superior both to a pure spot price contract and a fixed price contract.

A Note on Optimal Fixed-Price Bidding with Uncertain Production Cost

Firms often contract to deliver commodities at prices established before production costs are known. If the amount sold is a function of the quoted price, then the expected benefit profit per unit sold is not, in general, the difference between the unit cost estimate and the price quotation, but rather some smaller amount. Even though they may not understand why they are doing so, firms may learn by experience to add an amount to price quotations necessary to compensate for this effect. An understanding of this effect can lead to more optimal pricing procedures.