Capacity Reservation Contract Research Articles

Capacity management in supply chains under risk of supply disruptions: a mathematical model for establishing capacity reservation contracts

ABSTRACT Capacity management and supply chain disruptions are the most challenging problems faced in high tech industries. This paper focuses on establishing a capacity reservation contract between a single supplier and two heterogeneous retailers in a two-stage supply chain, wherein the retailers purchase a product from the supplier and sell it to the customers. In this study, a mathematical model is built for all parties involved, incorporating numerous essential elements of a real contract. The proposed model aims to assist in determining the best solutions for the retailers’ reserved capacities to the supplier and the supplier’s constructed capacity. Analytical results and sensitivity analyses are presented to demonstrate how various cost elements, price, and uncertainty affect the optimal capacity decisions.

A two-stage capacity reservation contract model with backup sourcing considering supply side disruptions

ABSTRACT To deal with disruption at the supply side, the use of backup suppliers is among the commonly employed strategies. In this research, we derived a dual sourcing model using capacity reservation contracts for a supply chain consisting of a retailer, a primary supplier who may experience disruption, and a reliable backup supplier. This dual sourcing model is a reactive strategy that balances flexibility and redundancy to improve supply chain resilience. The aim of the proposed model is to help find optimal solutions for the reserved capacities of the retailer to the suppliers and the constructed capacities of the suppliers. It has been derived in this research that the above-mentioned reserved/constructed capacities exist uniquely. Sensitivity analyses were also conducted to examine the impact of contract parameters on decision variables. This research contributes to existing knowledge by providing deeper insights into the application of the capacity reservation contract to handle supply disruption.

A mathematical model for a capacity reservation contract with backup sourcing

A mathematical model for a capacity reservation contract with backup sourcing

On capacity reservation contract in semiconductor supply chain

This paper investigates capacity reservation and capacity preparation issue in the semiconductor industry under stochastic demand. By comparing the manufacturer's optimal production capacity preparation in vertical integrated and decentralised supply chains, it shows that the manufacturer's production capacity preparation and the market satisfaction rate of the decentralised supply chain are lower. We propose a deductible reservation (DR) contract where the retailer reserves production capacity with a fee that can be deductible from the wholesale price. In the DR contract model, channel coordination and profit split are achieved respectively by setting expanded production capacity and unit reservation fee. The DR contract provides a risk-pooling mechanism not only motivates the manufacturer to expand production capacity but also preserves the retailer's flexibility.

On capacity reservation contract in semiconductor supply chain

This paper investigates capacity reservation and capacity preparation issue in the semiconductor industry under stochastic demand. By comparing the manufacturer's optimal production capacity preparation in vertical integrated and decentralised supply chains, it shows that the manufacturer's production capacity preparation and the market satisfaction rate of the decentralised supply chain are lower. We propose a deductible reservation (DR) contract where the retailer reserves production capacity with a fee that can be deductible from the wholesale price. In the DR contract model, channel coordination and profit split are achieved respectively by setting expanded production capacity and unit reservation fee. The DR contract provides a risk-pooling mechanism not only motivates the manufacturer to expand production capacity but also preserves the retailer's flexibility.

Single-item lot-based supplying and batch production under a bilateral capacity reservation: A partnership structure

This paper studies a single-item lot-based supplying and batch production under a bilateral capacity reservation contract based on a partnership structure in which some suppliers, a manufacturer, and a third-party logistics provider are connected through long-term cooperation agreements. This configures a partnership supply chain and promotes the manufacturer’s performance in a continuous improvement cycle. Since in this paper, it is assumed that the products are perishable, there is not any inventory storage. Moreover, due to a settled contract, the final products are delivered by third-party logistics corporate providing vehicles according to the products’ features, their expiration time lengths, customers’ demands and other considerations in each period. Thus, the delivery batch size, which is equal to the vehicle capacity in a full truckload mode, is targeted for the manufacturer operations resulting in a dynamic improvement environment. In this problem, respect to the performance level of the manufacturer, in each period, a certain capacity is reserved at each selected supplier level according to the appointed batch deliveries. Here, in addition to the ordinary costs incurred due to ordering and delivery processes, some penalties are imposed for orders/delivers exceeding or falling behind the reserved capacity. After investigating the computational complexity of the problem, we propose three dynamic programming algorithm as well. Finally, numerical results and some potential future researches are presented.

Inventory routing under stochastic supply and demand

It is well known that the integrated optimization of multiple and inter-related decisions in a supply chain can bring important benefits to companies. In this spirit, the inventory routing problem focuses on jointly optimizing inventory replenishment and vehicle routing decisions in a distribution context. In practice, the presence of uncertainty often further complicates the problem. We address a stochastic inventory routing problem under the consideration that both the product supply and the customer demands are uncertain. We propose a two-stage stochastic programming formulation, where routing decisions are made in the first stage, while delivery quantities, inventory levels and specific recourse actions are determined in the second stage. In this context, we analyze different recourse mechanisms such as lost sales, backlogging and an additional source for the product in a capacity reservation contract setting. We provide managerial insights from the results of computational experiments using instances based on a benchmark test set. In particular, we study the response mechanisms of the optimal solutions for different levels of uncertainty and cost configurations. Furthermore, we observe that supply and demand uncertainty have different effects on the value of taking the uncertainty into account. We also study the effect of incorporating a service level. Finally, we propose a heuristic solution method which is based on the progressive hedging algorithm and provides high-quality solutions within reasonable running times for problems with a large number of scenarios.

Supply chain coordination through capacity reservation contract and quantity flexibility contract

This study considers a supply chain consisting of two independent agents, a manufacturer and a retailer. The demand and the price of the product are both uncertain, whereas capacity cost is high and capacity lead time is long. As a result, the manufacturer may not have the incentive to expand capacity if the retailer does not share the risk with her. This result induces a lower performance of the supply chain. We propose two types of contracts, i.e., capacity reservation contract and quantity flexibility contract, as risk-sharing mechanisms to encourage the manufacturer to expand the capacity and improve the overall performance of the supply chain. We find that when supply chain coordination is not achieved, our contracts can bring more system profit than other contracts with less flexibility. We further show that by setting elaborate parameters, the two contracts can coordinate the supply chain so that the total profit in the decentralized supply chain is the same as that in the centralized system. Furthermore, we compare the two contracts in terms of capacity and profits. We also show that the retailer prefers the quantity flexibility contract under coordination. Our conclusions are robust when the demand and retail price are correlated.

Moral hazard problem and collaborative coordination in supply chain with capacity reservation contract

This paper has considered collaborative coordination in supply chains with capacity reservation contracts using the game theory. In some traditional papers, the capacity reservation contracts have contained a capacity quantity, a reservation quantity and a reservation fee as a decision variable. Each decision variable is determined separately based on individual profit functions of a supplier and a manufacturer under the noncooperative game theory. Those papers have assumed that the supplier is always forced to build sufficient capacity to cover the reservation amount of the manufacturer. However, the supplier might not always comply with the reservation amount of the manufacturer since the capacity quantity is a private decision in the supplier and not released to external companies in practice. For instance, the supplier may choose to under-build knowingly to ensure high utilisation of his capacity. This is a kind of moral hazard problems. This paper has investigated such a strategy that the supplier and manufacturer voluntarily comply with the contract for the purpose of solving the moral hazard problem in the capacity reservation contract. Consequently, we have proposed a method of determining the decision variables collaboratively in the contract such that a consensus of the supplier and manufacturer is built.

Batch replenishment planning under capacity reservation contract

We study the single-item Lot Sizing Problem (LSP) in a supply chain composed of a retailer and a supplier by integrating the buyback contract and the batch ordering. The purpose is to determine a replenishment planning for the retailer to satisfy his deterministic demands over a finite horizon, while minimizing the procurement and inventory costs. Regarding the procurement cost, we assume two different structures: FTL (Full Truck Load) and OFB (Only Full Batch). We consider three types of buyback contract: with fixed return periods, with a time limit on returns, and with returns permitted only in procurement periods. Each contract is characterized by the maximum return percentage being either equal to 100% (full return) or less than 100% (partial return). For the LSP under the buyback contract with fixed return periods, we assume the concept of lost sales. Another concept considered in the LSP's under the three types of buyback contract is the disposal of the unsold and unreturned quantities. We model these different LSP extensions as a Mixed Integer Linear Program (MILP). Thereafter, we develop exact polynomial time dynamic programming algorithms for some extensions and show the NP-hardness of others. For each problem solved in polynomial time, we compare the efficiency and the limits of the proposed algorithm with those of four MILP formulations by performing different tests. Finally, we propose mathematical models for the LSP's under other types of the capacity reservation contract in the deterministic and multi-period case.

Sustainable sourcing including capacity reservation for recycled materials: A newsvendor framework with price and demand correlations

Critical raw materials like rare-earth elements are essential inputs for the production process of many electronic products, but also for environmentally-friendly green-energy technology products. The market for these materials faces high uncertainty associated with their supply. The use of recovered raw materials can help to mitigate the risk and simultaneously pave the way towards a circular economy. We investigate a sourcing strategy faced by a manufacturer considering the possibility to source critical raw materials from a supplier offering recycled material. As the recycling efficiency of these materials is still an ongoing research, and return flows from end-of-life products are highly volatile, we also rely on virgin material. We develop a single-period inventory model with procurement from a supplier offering recycled material according to a capacity reservation contract and a reactive supplier (spot market) offering virgin material. We consider uncertainties of demand, prices and recycling quantities as well as potential dependencies, in particular dependencies between prices for virgin and recycled materials and prices and demand. We provide results on the optimal policy structure and obtain a closed-form solution as a bound of the optimal procurement quantity. Our analysis gives us first insights on the effect of different economic parameters on the ordering decision. In an extensive numerical analysis we then study the impact of correlation on our results in order to derive managerial implications. We show that considering correlation when using such a sourcing strategy is especially important in environments with high demand uncertainty, high virgin material prices and yield uncertainty.

Win-Win Capacity Allocation Contracts in Coproduction and Codistribution Alliances

In some strategic alliances, a firm shares its manufacturing capacity with another, and the latter shares its distribution capacity with the former. Even though such bidirectional alliances have become more common, they remain challenging to manage because of the frequent disputes over capacity allocation, especially when demand is uncertain. In this paper, we investigate whether there exists a contractual mechanism that can mitigate the extent of these disputes while improving the profits of all participating firms. We consider two types of bidirectional contracts, namely, the ex post transfer payment contract and the ex ante capacity reservation contract. By modeling the capacity allocation and the bidirectional contract design as a noncooperative game between two firms with noncompeting product lines, we show that, relative to a situation with no contract, either contract can improve the alliance’s total profit in equilibrium. In terms of distribution of the total surplus, we find that capacity reservation contracts always make both firms better off, whereas ex post transfer payment contracts may make one firm worse off. Hence, capacity reservation contracts are more likely to be implemented in practice in such bidirectional alliances. This paper was accepted by Gad Allon, operations management.

Backup sourcing with capacity reservation under uncertain disruption risk and minimum order quantity

Ample evidence has confirmed the importance of backup sourcing when disruption of the major supply source is inevitable. The decisions associated with how to work with the backup supplier to ensure backup or emergency supply when the primary source experiences shortfall have received a great deal of attention. We study a capacity reservation contract between a buyer and a backup supplier when there is uncertainty about the major supplier’s disruption risks. Additionally, we consider the constraint that requires the buyer to order either none or at least a minimum order quantity in the case of contingent sourcing. By committing to such backup contracts, the buyer seeks to lower its contingent purchasing cost and to ensure the availability of merchandise in the presence of risks. The involving players’ optimal decisions are investigated theoretically and the impacts of the key parameters and special scenarios are assessed numerically. The study contributes to the literature by providing a better understanding of how to use a capacity reservation contract as a vehicle to build long-term relationship in backup sourcing and of the impacts of disruption uncertainty and contingent supply availability.

NP-hard and polynomial cases for the single-item lot sizing problem with batch ordering under capacity reservation contract

In this paper, we study the single-item lot sizing problem under a capacity reservation contract. A manufacturer is replenished by an external supplier with batch deliveries and a certain capacity is reserved at the supplier level with an advantageous cost. In addition to the classical ordering and inventory holding costs, for each batch ordered under the reserved capacity a fixed cost per batch is incurred; and for batches exceeding this capacity a higher fixed cost per batch is paid, typically through the purchase from the spot market. We identify various NP-hard cases, propose a pseudo-polynomial time dynamic programming algorithm under arbitrary parameters, show that the problem admits an FPTAS and give polynomial time algorithms for special cases. We finally state a list of open problems for further research.

The implication of capacity reservation contracts in assembly system with asymmetric demand information

This paper investigates an assembly system that consists of one assembler and two suppliers who produce complementary components. The assembler possesses some private demand information that is unobservable to the upstream suppliers, and the two suppliers have to choose their capacity reservations ahead of the selling season. To induce credible vertical information sharing, we design three capacity reservation contracts: the price-quantity contract, the price-only contract and the hybrid price-quantity and price-only contract, so as to identify how the firms’ equilibrium reservation strategies and pay-offs react under different contract schemes. The results show that the assembler obtains the highest pay-off under either the price-only contract or the hybrid contract, which is determined by whether the private demand information or the demand fluctuation is sufficiently high. The suppliers’ optimal contract types are further influenced by their decision sequence. In particular, the supplier who makes decision earlier prefers the hybrid contract, while the supplier who makes decision later prefers any of the three contracts. The supply chain generates the highest pay-off from either the price-quantity contract or the hybrid contract.

Comparative Studies of Three Backup Contracts Under Supply Disruptions

We focus our research on a supply chain involving one buyer and two independent suppliers of the same product. The main supplier is prone to supply disruption and recurrent supply uncertainty, and the backup supplier is perfectly reliable but supply goods at higher prices. Three kinds of backup contracts between the buyer and the backup supplier are investigated to mitigate supply risks: A capacity reservation contract, a make-to-order contract, and a buy-back contract. Models are developed to study how the buyer's expected profit and optimal decisions related to each contract change with the supply risks. We also examine the sensitivity of various cost parameters on the optimal decisions, and compare the values of three backup contracts for the buyer. Furthermore, we present how these results differ from those obtained in the analysis with demand uncertainty considered. Our study provides managerial insights into the positive effects of different backup contracts on the buyer's expected profit in the events of unexpected disruption.

Win-Win Capacity Allocation Contracts In Co-Production and Co-Distribution Alliances

In some strategic alliances, a firm shares its manufacturing capacity with another, and the latter shares its distribution capacity with the former. Even though such bidirectional alliances have become common, they remain challenging to manage due to the frequent disputes over capacity allocation especially when demand is uncertain. In this paper, we investigate whether there exists a contractual mechanism that can mitigate the extent of these disputes while improving the profits of all participating firms. We consider two types of bidirectional contracts, namely, the ex-post transfer payment contract and the ex-ante capacity reservation contract. By modeling the capacity allocation and the bidirectional contract design as a multi-stage game between two firms with non-competing product lines, we show that, relative to a situation where capacity allocation is freely negotiated, either contract can improve the alliance’s total profit in equilibrium. In terms of distribution of the total surplus, we find that capacity reservation contracts always make both firms better off, whereas ex-post transfer payment contracts may make one firm worse off. Hence, capacity reservation contracts are more likely to be implemented in practice in such co-production and co-distribution alliances.

Horizontal coordinating contracts in the semiconductor industry

Integrated device manufacturers (IDMs) and foundries are two types of manufacturers in the semiconductor industry. IDMs integrate both design and manufacturing functions whereas foundries solely focus on manufacturing. Since foundries often have cost advantage over IDMs due to their specialization and economies of scale, IDMs have incentives to source from foundries for the purpose of avoiding excessive capacity investment risk. As the IDM is also a potential capacity source, the IDM and foundry are in a horizontal setting rather than a purely vertical setting. In the absence of sophisticated contracts, the benchmark contract for the IDM and foundry is a wholesale price contract. We define “coordinating” contracts as those that improve both the IDM’s and foundry’s expected profits over the benchmark wholesale price contract and also lead to the maximum system profit. This paper examines if there exist coordinating capacity reservation contracts. It is found that wholesale price contracts in the horizontal setting cannot achieve the maximum system profit due to either double marginalization effect, or “misalignment of capacity-usage-priority”. In contrast, if the IDM’s capacity investment risk is not too low, there always exist coordinating capacity reservation contracts. Furthermore, under coordinating contracts, the IDM’s sourcing structure, either sole sourcing from the foundry or dual sourcing, is contingent on the firms’ cost structures.

Outsourcing decision and order policy with forecast updating under capacity reservation contract

This paper investigates an optimal decision problem in a single-period, two-stage supply chain with capacity reservation contract. At the beginning of the planning horizon, the retailer, who faces stochastic demand, reserves future capacity according to his forecasting of the demand. The supplier then constructs capacity. At the beginning of the selling season, the retailer updates the demand forecasting and places an order. When the retailer’s demand is greater than the supplier’s capacity, the supplier can meet the retailer’s demand by outsourcing. We analyze the optimal decision of each player in both centralized and decentralized systems. Furthermore, under the case in which demand follows a uniform distribution, we obtain the closed-form optimal strategies of each player for both centralized and decentralized systems and conduct numerical studies to reveal additional conclusions. The numerical studies show that the optimal reservation capacity for the retailer and the optimal constructing capacity for the supplier in the decentralized system are both less than the optimal constructing capacity in the centralized system. Furthermore, we also find that the profit loss due to decentralization always exists and increases in indeterminacy.

Scenario-Based Modeling of Interdependent Demand and Supply Uncertainties

This paper develops a scenario generation framework for modeling demand and supply uncertainties. This framework is applied to a decision problem at an illustrative manufacturing company facing risks caused by uncertainties in end product demand and component availability. In particular, we focus on the impact of interdependent demand and supply uncertainty. To evaluate analytically the impact of interdependence between these two uncertainties, we analyze a simple newsvendor model with a bivariate normal distribution for demand and supply yield. Then, in more complex settings, we use scenarios based on copula functions, which can account for both linear and nonlinear dependences. These scenarios are used in conjunction with stochastic programming models to evaluate sourcing costs and risks under various conditions. In particular, we study a decision problem faced by a manufacturer which uses capacity reservation contracts in the presence of an unreliable supplier and uncertain product demand. Our results indicate that worst-case risks grow significantly when the dependences in uncertainties about demand and supply yield are stronger. We also highlight differences caused by linear and tail-dependent dependence structures. Based on the results, we argue that using the proposed framework to model uncertainties and their interdependences allows managers to better manage risks.