Nonlinear Production Costs Research Articles

Strategic information sharing in the dual-channel closed loop supply chain with nonlinear production cost

This paper explores the strategy of information sharing within a closed loop supply chain comprising three echelons and dual channels. By considering the supplier’s collecting activities and the two formats of nonlinear production costs (i.e., production diseconomy and production economy) faced by the manufacturer, we construct and utilize game-theoretic models to determine the optimal strategy (i.e., no sharing, sharing information solely with the manufacturer, sharing with the supplier, and sharing with both the manufacturer and supplier) for information sharing by the retailer. The findings indicate that the retailer's inclination to voluntarily share information and the most effective approach are significantly influenced by the interplay between the supplier's recycling efficiency and the manufacturer's nonlinear production cost. Specifically, in the context of production diseconomy, it is commonly observed that the retailer can derive advantages by engaging in information sharing with a supplier who possesses a high recycling efficiency. In contract, the retailer would share the information when the recycling efficiency is high or the production economy coefficient is large. Otherwise, no sharing strategy can be considered as the optimal choice. Ultimately, the study aims to assess the effects of various approaches to sharing information on the remaining participants within the supply chain.

Solving a hold-up problem may harm all firms: Downstream R&D and transport-price contracts

This study considers transport-price contracts in a two-country duopoly model with firm-specific carriers. It is well-known that when an upstream firm fails to commit to keeping its transaction (or transport) price after a downstream firm's R&D investment, it causes the hold-up problem and diminishes the incentive for R&D investment. While previous literature emphasizes that the commitment to keep the transaction price is needed to overcome the hold-up problem, we show that this commitment may harm all firms. We also discuss the robustness of our results in cases with R&D spillovers, product differentiation, and non-linear production costs.

Supply chain coordination with multiple retailers and nonlinear production costs

We consider coordination with multiple retailers when supplier's production costs are nonlinear. Microeconomics typically assumes increasing marginal production costs (i.e., convex production costs). The nonlinearity of the production costs introduces indirect dependence among the retailers, as the order quantity of one influences the cost of producing the others' lots. We consider a fixed retail price scenario, as well as price-dependent linear additive and iso-elastic demands. We explore these scenarios under wholesale-price-only contract, as well as revenue sharing contract.

Supply chain coordination with multiple retailers and nonlinear production costs

Supply chain coordination with multiple retailers and nonlinear production costs

Manufacturing newsvendors and inventory pooling with nonlinear production costs

We discuss a manufacturing newsvendor problem with nonlinear production costs. We perform comparative statics with respect to the unit revenue, the production cost function and the demand distribution. We provide several specific examples. Then we analyse inventory pooling between manufacturing newsvendors with nonlinear production costs, which involves comparing joint production to individual production. We illustrate the findings by using examples with demands following i.i.d. uniform and normal distributions.

Inclusive Innovation: Broader Market Coverage for Innovative Products with Deliberate Supply Chain Leadership

New technological and product innovations, including some life-saving ones, conventionally traverse a sequentially downward path of gradually lowering costs and prices, which limits their initial availability and affordability to the lower-end of the market. In this paper, we focus on the central question of how to achieve broader market coverage for innovative products, which we refer to as inclusive innovation. We unearth a new innovation investment degree of freedom in a multi-tiered supply chain that offers product development firms the ability to expand market coverage. Through an analytical model grounded in industrial practice, we show that deliberately choosing which firm in a multi-tiered supply chain invests in product quality improvement and acts as a leader by initiating contract offers can have a significant impact on the market coverage of the product. Our model deals with products that have non-linear development and production costs and a product lifecycle that is characterized initially by product innovation being the most dominant effect followed by a period of process innovation. We demonstrate that aligning product innovation investment decision making with price-quantity decision-making leads to greater total supply chain profits and market coverage. In addition, we are able to identify a sequence of deliberate leadership transfers by which contract leadership is shifted upstream during the product innovation phase and shifted back to downstream entities during the process innovation phase so as to maintain highest market coverage during the lifecycle of a product. We go beyond a normative prescription by identifying conditions under which tierwise rational leadership transfers occur and discuss how to align individually rational schedule of leadership transfers with an optimal schedule that results in the highest market coverage. These findings have subtle, but important, implications for firms launching innovative products and aspiring to expand market coverage. Specifically, to obtain broader market coverage for its innovations, innovating firms in a supply chain should finely tune the level of innovation investment, identity of the investor, and contract leadership. These results help to explain the evolution of industries such as automotives and personal computers and also offer opportunities for new industries and firms to expand both market coverage and profits.

Simple Auctions for Supply Contracts

This paper studies an optimal procurement mechanism for a newsvendor-like problem where the buyer's (newsvendor's) purchase price of the supplies is not fixed, but determined through interaction with candidate suppliers. The buyer has priors on the suppliers' costs but does not know their costs exactly. Recent literature has shown how the buyer can implement the optimal procurement mechanism by announcing a revenue function (specifying a payment for each quantity the buyer may purchase), then auctioning off the supply contract with the specified revenue function. In this paper, we show that a simple modified version of the standard open-descending auction for a fixed quantity is also an optimal mechanism for obtaining supplies. What distinguishes this mechanism is its simplicity and familiarity for the suppliers—open-descending auctions are very easy to run and ubiquitous in practice, whereas auctioning supply contracts with a specified revenue function is much less observed and more difficult to explain to suppliers. Furthermore, we show that this simple mechanism can be easily generalized to ex ante asymmetric suppliers and a class of nonlinear production costs. This paper was accepted by Yossi Aviv, operations management.

Strategic Inventories in Vertical Contracts

Classical reasons for carrying inventory include fixed (nonlinear) production or procurement costs, lead times, nonstationary or uncertain supply/demand, and capacity constraints. The last decade has seen active research in supply chain coordination focusing on the role of incentive contracts to achieve first-best levels of inventory. An extensive literature in industrial organization that studies incentives for vertical controls largely ignores the effect of inventories. Does the ability to carry inventory influence the problem of vertical control? Conversely, can inventories arise purely due to incentive effects? This paper explicitly considers both incentives and inventories, and their interplay, in a dynamic model of an upstream firm (supplier) and a downstream firm (buyer) who can carry inventories. In our model, none of the classical reasons for carrying inventory exists. However, as we prove, the buyer's optimal strategy in equilibrium is to carry inventories, and the supplier is unable to prevent this. These inventories arise out of purely strategic considerations not yet identified in the literature, and have a significant impact on the equilibrium solution as well as supplier, buyer, and channel profits. We prove that strategic inventories play a pivotal role under arbitrary contractual structures, general (arbitrary) demand functions and general (finite or infinite) horizon lengths. As one example, two-part tariff contracts do not lead to optimal channel performance, nor can the supplier extract away all of the channel profits, in our dynamic model. Our results imply that firms can and must carry inventories strategically, and that optimal vertical contracts must take the possibility of inventories into account.

Untruthful probabilistic demand forecasts in vendor‐managed revenue‐sharing contracts: Coordinating the chain

AbstractVendor‐managed revenue‐sharing arrangements are common in the newspaper and other industries. Under such arrangements, the supplier decides on the level of inventory while the retailer effectively operates under consignment, sharing the sales revenue with his supplier. We consider the case where the supplier is unable to predict demand, and must base her decisions on the retailer‐supplied probabilistic forecast for demand. We show that the retailer's best choice of a distribution to report to his supplier will not be the true demand distribution, but instead will be a degenerate distribution that surprisingly induces the supplier to provide the system‐optimal inventory quantity. (To maintain credibility, the retailer's reports of daily sales must then be consistent with his supplied forecast.) This result is robust under nonlinear production costs and nonlinear revenue‐sharing. However, if the retailer does not know the supplier's production cost, the forecast “improves” and could even be truthful. That, however, causes the supplier's order quantity to be suboptimal for the overall system. © 2007 Wiley Periodicals, Inc. Naval Research Logistics, 2007

Supply chain coordination with downstream operating costs: Coordination and investment to improve downstream operating efficiency

We endow the downstream firm in a supply chain with operating costs in addition to the traditional overage and underage costs. We reanalyze Lariviere and Porteus's “Selling to a Newsvendor” model (2001), allowing for non-linear production costs, and provide comparative statics. We then explore investment in reducing downstream operating costs. To overcome the fact that investment is lower in a decentralized chain than in an integrated one, we propose several coordination mechanisms––buybacks, revenue sharing and operating subsidy with a license fee.

A fuzzy approach to modelling production & inventory planning

Considering that the demand requirements are fuzzy demand in each period, especially in the future period, this paper focuses on a fuzzy approach in modeling production and inventory planning (PIP) problems. The objective of the problem considered is to minimize the total costs of nonlinear production costs and linear inventory holding costs. By taking a fuzzy approach, the production-inventory balance equation is formulated as a soft equation in terms of a degree of truth, which depends on the membership function of fuzzy demand. The fuzzy demand and cumulative demand from the start of the horizon to a period are represented in fuzzy numbers of triangular type. By means of addition of soft equations and some reductions, the production and inventory planning (PIP) problem with fuzzy demand can be modelled into a fuzzy nonlinear programming problem with fuzzy objective and fuzzy constraints.

A Newton-like approach to solvingan equilibrium problem

The paper deals with the problem of finding out an equilibrium in an oligopolistic market model where several subjects supply a single homogeneous product in a non-cooperative manner. The problem is reduced to a nonlinear equation some terms of which are determined by solving nonlinear complementarity problems. An algorithm is presented that combines the Newton method steps with the dichotomy techniques. Under certain assumptions, the algorithm is shown to be convergent at the quadratic rate. Finally, the algorithm is extended to the case of nonlinear production costs, and its linear convergence is demonstrated.

Futures Markets: A Consequence of Risk Aversion or Transactions Costs?

A two-period model of an industry of risk-neutral processors who have nonlinear production costs and who face transact ions costs in the spot and futures markets is put forth as a countere xample to the models of commodity markets in which processors' risk a version plays the major role. The model's equilibrium exhibits the sa lient endogenous features of actual commodity markets, namely, that t he futures price is below the current spot price, that processors hol d inventories despite this opportunity cost, that those holding inven tories are short in futures, and that processors as a group hold an u nbalanced, usually net short, position in the futures market. Copyright 1987 by University of Chicago Press.

The Location‐Production‐Allocation Problem With Nonlinear Production Costs

This paper develops a location‐production‐allocation model for the multiplant producer selling under the conditions of nonlinear production costs and a uniform pricing system. The primary goals of this paper are to incorporate the following criteria into a model: (1) production factors and location factors should be synthesized into a location‐production‐allocation problem; (2) the production function is nonlinear, implying economies and diseconomies of scale; (3) a systems approach should be utilized to solve for a global optimum. Within the context of these criteria, equilibrium conditions are derived for a location‐production‐allocation model. Finally, a heuristic technique to solve this problem is derived from the equilibrium conditions.

A Decomposition Algorithm for Solving the Multifacility Production-Transportation Problem with Nonlinear Production Costs

A Decomposition Algorithm for Solving the Multifacility Production-Transportation Problem with Nonlinear Production Costs