Linear Production Costs Research Articles

Capacitated lot sizing problem with periodic carbon emission constraints and multiple resources

We study the single item capacitated lot sizing problem with multiple resources and periodic carbon emission constraints that impose an upper bound for the average emission per product produced in any period. Although the uncapacitated version of this problem can be solved in polynomial time, generalisation of the problem including the resource capacities is NP-Hard, in general. We present important structural properties for the optimal solutions of the problem. We consider the special cases with two resources and under non-speculative costs, construct the piecewise linear total production cost function when the resource capacities, and the emission and cost parameters are time-invariant, and develop a polynomial time dynamic programming algorithm (DP) to solve them. Then, we generalise the procedure to construct the total production cost function and the DP for the general setting with fixed number of capacitated resources. We test our algorithm for different problem instances, and compare it with a commercial solver and a DP available in the literature for solving the lot sizing problem with piecewise concave production cost functions. The results reveal that our DP outperforms the other one, and it performs better than the commercial solver when the number of breakpoints of the total production cost function is small.

Market equilibrium in interregional trade models under monopolistic competition

We study a homogeneous model of interregional trade under monopolistic competition of producers with additively separable utility and linear production costs. The mass of firms (“the length of the product line”) is determined endogenously, from conditions of free entry. We obtain the local comparative statics of the market equilibrium with respect to transport costs of “iceberg types”. Particular attention is paid to situations of free trade and autarky. We establish the following counter-intuitive result: under high transport costs, trade liberalization can decrease public welfare.

Effect of Irrigation System on Production and Profit in Red Chili Farming on Rice Land, Kretek District, Bantul Regency

The purposes of this research are to determine the factors that affect the costs, income, income, and profits of red chili farming on rice land in Bantul Regency. Determination of respondents using a random sampling method with 45 samples of farmers and the census method with 15 samples of farmers. Data were obtained through interviews using the help of a questionnaire. Then the data were analyzed using multiple linear regression analysis, production costs, revenues, revenues, and profits. The results showed that the production factors that significantly influenced the production of red chili were land area, labor, manure and type of irrigation technology. The production costs incurred on an area of 3,500 m2 are IDR. 13,674,700 for manual irrigation and IDR. 10,214,518 in the shower irrigation area. The income obtained by red chili farmers is IDR. 21,345,619 for manual irrigation and IDR. 20,252,666 for shower irrigation. The income received by farmers is IDR. 12,643,8182 for manual irrigation and IDR. 12,770,400 in shower irrigation. The profit obtained by the farmer is IDR. 7,670,919 for manual irrigation and IDR. 10,038,148 shower irrigation.

Stability of cartels in Multimarket Cournot oligopolies

AbstractWe investigate the stability of cooperation agreements, such as those agreed by cartels, among firms in a Cournot model of oligopolistic competition embedded in a multimarket contact setting. Our analysis considers a broad array of 64 potential market structural configurations under linear demand and quadratic production costs. We establish that for an appropriate range of parameter values there exists a unique core stable market configuration in which an identical two‐firm cartel is sustained in both markets. Our result highlights the significance of multimarket presence for cartel formation in light of the well‐known result from the single‐market setting where cartels are non‐profitable.

On Mixed-Integer Programming Formulations for the Unit Commitment Problem

We provide a comprehensive overview of mixed-integer programming formulations for the unit commitment (UC) problem. UC formulations have been an especially active area of research over the past 12 years due to their practical importance in power grid operations, and this paper serves as a capstone for this line of work. We additionally provide publicly available reference implementations of all formulations examined. We computationally test existing and novel UC formulations on a suite of instances drawn from both academic and real-world data sources. Driven by our computational experience from this and previous work, we contribute some additional formulations for both generator production upper bounds and piecewise linear production costs. By composing new UC formulations using existing components found in the literature and new components introduced in this paper, we demonstrate that performance can be significantly improved—and in the process, we identify a new state-of-the-art UC formulation.

Exact equilibrium quantities in spatially separated markets under production constraints

We deal with the Cournot game with production constraints, where the competing firms deliver an homogeneous product to spatially separated markets, linear demand functions may be different at each market, and linear production costs are non-identical. Despite the simplicity of this setting and although the existence and uniqueness of a Nash equilibrium have been proved, the problem of finding the exact equilibrium quantities has not been solved in the literature yet. In this paper, we analytically determine the unique equilibrium quantities for the constrained game when some conditions are verified. The equilibrium quantities and profits are compared with those obtained for the traditional Cournot game.

Delivered pricing and endogenous delegation of contract type

AbstractThis article demonstrates for the first time that owners will delegate the location decision under delivered pricing using a relative performance contract rather than a market share contract. It goes on to evaluate the welfare consequences of this demonstration. With linear production costs and simultaneous location, both incentive contracts reduce welfare, but the chosen relative performance contract reduces it by less. Yet, with linear costs and sequential location, the chosen relative performance contract reduces welfare by more. Finally, with enough convexity in production costs, welfare can be improved by the chosen relative performance contracts.

Vendor managed inventory contracts – coordinating the supply chain while looking from the vendor’s perspective

The paper studies coordination of a supply chain when the inventory is managed by the vendor (VMI). We also provide a general mathematical framework that can be used to analyze contracts under both retailer managed inventory (RMI) and VMI. Using a simple newsvendor scenario with a single vendor and single retailer, we study five popular coordinating supply chain contracts: buyback, quantity flexibility, quantity discount, sales rebate, and revenue sharing contracts. We analyze the ability of these contracts to coordinate the supply chain under VMI when the vendor freely decides the quantity. We find that even though all of them coordinate under RMI, quantity flexibility and sales rebate contracts do not generally coordinate under VMI. Furthermore, buyback and revenue sharing contracts are equivalent. Hence, we propose two new contracts which coordinate under VMI (one of which coordinates under RMI too, provided a well-known assumption holds). Finally, we extend our analysis to consider multiple independent retailers with the vendor incurring linear or convex production cost, and show that our results are qualitatively unchanged.

Approximation Approaches for Inventory Systems with General Production/Ordering Cost Structures

The production/ordering cost structure is fundamental to determining an optimal inventory control policy. For example, it is well known that a base‐stock policy is optimal for inventory systems with linear production costs, whereas an ( s, S) policy is optimal if both linear and fixed costs exist. However, many of the cost structures that have arisen from the practice are quite complex and make the optimal policies too complicated for managers to implement. In this study, we propose several easy‐to‐implement and efficient heuristic policies for inventory systems with general production costs, which include multiple linear pieces and fixed costs, suggesting a wide application to many practical problems that were previously difficult to solve. We establish the worst‐case performance bounds on the proposed heuristic policies by using the concept of K‐approximate convexity. Our extensive numerical studies, which are designed to reflect practical inventory control applications, evaluate the performance of the heuristic policies and show that the best heuristic policy we propose performs extremely well. We also try to provide explanations for the performance of different heuristic policies.

A SPATIAL MODEL OF CARTEL STABILITY: THE INFLUENCE OF PRODUCTION COST CONVEXITY

ABSTRACTWe uniquely introduce convex production costs into a cartel model involving spatial price discrimination. We demonstrate that greater convexity improves cartel stability and that for sufficient convexity first best locations will be adopted. We show that allowing locations to vary over the game reduces cartel stability but that greater convexity continues to improve that stability. Moreover, when the degree of convexity does not support the first best collusive locations, other collusive locations exist that require less stability and these may either increase or decrease social welfare relative to competition. Critically, these locations that require less stability are more dispersed in sharp contrast to the known result assuming linear production costs.

Extended Dynamic Oligopolies with Flexible Workforce and Isoelastic Price Function

Single-product oligopolies without product differentiation are examined with linear production, production adjustment, flexible workforce and investment costs. The price function is assumed to be hyperbolic which makes the nonlinearity of the model much stronger than in the case of linear price function examined earlier in the literature. The best responses of the firms are determined which are not monotonic in contrast to the linear case. The set of all steady states is then characterized and in the case of a duopoly it is illustrated. The asymptotical behavior of the steady states is examined by using simulation. We analyze the effects of such costs on the industry dynamics and compare them to the prediction by the well known model with hyperbolic price function and no product adjustment and investments costs.

Improved exact algorithms to economic lot-sizing with piecewise linear production costs

In this article we study a classical single-item economic lot-sizing problem, where production cost functions are assumed to be piecewise linear. The lot-sizing problem is fundamental in lot-sizing research, and it is applicable to a wide range of production planning models. The intractability of the problem is related to the value of m, the number of different breakpoints of the production cost functions. When m is arbitrary, the problem is known to be NP-hard (Florian, Lenstra & Rinnooy Kan, 1980). However, if m is fixed, then it can be solved in polynomial time (Koca, Yaman & Akturk, 2014). So far, the most efficient algorithm to solve the problem has a complexity of O(T2m+3), where T is the number of periods in the planning horizon (Koca et al., 2014). In this article we present an improved exact algorithm for solving the problem, where the complexity is reduced to O(Tm+2·logT). As such it also improves upon the computational efficiency of solving some existing lot-sizing problems which are important special cases of our model. In order to achieve a more efficient implementation, our algorithm makes use of a specific data structure, named range minimum query (RMQ).

Manufacturing High-Tech Products Subject to Rapid Obsolescence

We formulate a production problem in high-tech industry as a free-final-time optimal control problem. The instance with linear production cost is equivalent to a problem proposed by Pangburn and Sundaresan. The instance with quadratic production cost allows us to find a solution which is closer to what is seen in the real world. In the latter instance, the optimal production rate is strictly decreasing in a neighborhood of the final time.

Consistent location conjectures under spatial price discrimination

This paper is the first to model consistent location conjectures under spatial price discrimination. With linear production cost, the well-known association of spatial price discrimination with efficiency vanishes as duopolists with consistent conjectures collocate at the center. With convex production cost, the duopolists do not collocate but continue to locate closer to the center than under Nash conjectures. Yet, with sufficient cost convexity, this movement to the center can actually increase welfare relative to Nash. We extend the results with linear costs to multiple private firms.

Spatial price discrimination, monopoly upstream and convex costs downstream

Under spatial price discrimination a critical cost of an upstream monopoly is the resulting distortion in downstream locations. While this is well-established for linear production costs it is examined here for the first time for convex production costs. Convex production costs create their own location distortions yet it is shown that the presence of the upstream monopoly has a smaller influence on efficiency with such costs.

A periodic review lot sizing problem with random yields, disruptions and inventory capacity

This paper examines a periodic-reviewed lot sizing problem with random yields, disruptions and limited inventory capacity. To characterise the continuous production, an additive random yield model is considered rather than a multiplicative one. Disruptions cause breakdowns to production. Inventory capacity is included since the production has to be shut down when the inventory buffer is full. Both disruptions and shutdowns lead to a start-up cost and a stochastic lead time to recover the production. These compound factors of uncertainty are encountered in practical planning decisions in process industries. We review the existing random yield models, which are then compared with the additive model. With a linear production cost, the additive model has an order-up-to policy to be optimal. Disruptions deteriorate the expected actual production quantity and the fill-rate dramatically, even though the optimal order-up-to level increases compared with the cases of no disruption. Considering inventory capacity makes the problem to be a non-convex dynamic programming problem. Numerical analysis shows that the performance is dramatically deteriorated when the inventory capacity is rather tight, which indicates the importance of selecting a proper inventory capacity to reduce the negative impacts and avoid redundant investment on capacity. Moreover, the start-up cost plays an important role in determining the level of inventory capacity.

Structural Versus Behavioral Remedies in the Deregulation of Electricity Markets: An Experimental Investigation Guided by Theory and Policy Concerns

Abstract We experimentally study the effects of introducing a forward market and of increasing the number of competitors in a quantity-setting market under strictly convex production costs. Our key interest is to better understand which of these two remedies is more effective at enhancing competition. Allaz and Vila (1993) theorized that forward markets can have a pro-competitive effect under linear production costs. Le Coq and Orzen (2006) and Brandts et al. (2008) investigated this and related issues experimentally. All three experiments (including ours) support the prediction by Allaz and Vila (1993) that introducing a forward market does indeed intensify competition. The results of the present study, however, differ from previous experimental results in that we find the forward market to be the more effective remedy. Brandts et al. (2008) increase the number of competitors by entry, which thus increases the aggregate stock of production assets and makes output cheaper. In contrast, we increase the number of competitors by divestiture, which leaves the aggregate stock of production assets constant. Our results address an important policy issue and provide tentative evidence on the competition-enhancing effect of forward markets, which can be considered a behavioral remedy.

Structural versus behavioral remedies in the deregulation of electricity markets: An experimental investigation motivated by policy concerns

We experimentally study the effects of introducing a forward market and of increasing the number of competitors in a quantity-setting market under strictly convex production costs. Our key interest is to better understand which of these two remedies is more effective at enhancing competition. Allaz and Vila (1993) theorized that forward markets can have a pro-competitive effect under linear production costs. Le Coq and Orzen (2006) and Brandts et al. (2008) investigated this and related issues experimentally. All three experiments (including ours) support the prediction by Allaz and Vila (1993) that introducing a forward market does indeed intensify competition. The results of the present study, however, differ from previous experimental results in that we find the forward market to be the more effective remedy. Brandts et al. (2008) increase the number of competitors by entry, which thus increases the aggregate stock of production assets and makes output cheaper. In contrast, we increase the number of competitors by divestiture, which leaves the aggregate stock of production assets constant. Our results address an important policy issue and provide tentative evidence on the competition-enhancing effect of forward markets, which can be considered a behavioral remedy.

Entry, Profit and Welfare under Asymmetric R&D Costs

We show the effects of entry of a new firm on the profits and welfare when the firms share the same initial cost of production but differ in terms of the costs of undertaking R&D. Considering a Cournot oligopoly model with innovation and linear demand and production costs, we show that entry reduces the profits of the incumbent firms and it can be welfare reducing.

Spatial price discrimination and mergers with convex production costs

We examine duopolists that have convex production costs and locate under spatial price discrimination in anticipation of a merger. We show that the merger frequently results in locations that reduce social cost. This contrasts with the well-known result that with linear production costs the merger distorts locations to increase social cost. While mergers in our model can generate location asymmetry and so higher production costs, the locations frequently reduce transport cost sufficiently that the sum of transport and production costs is reduced.