Linear Cost Structure Research Articles

Modeling of Critical Threshold of Preference for Collusion (C.T.P.C.) and Cost Structure in Tunisian Mobile Market

We present in this paper a modeling of the critical threshold of preference for collusion (C.T.P.C.) in different market structure using the interconnection fees and their marginal cost, in a Cournot competition. The objective is to compare the preference for collusion regarding this threshold in market structures and within two contexts: linear interconnection costs and quadratic ones. Collusion is more difficult in private duopoly that in a mixed one. This difficulty is increased with linear cost structure than quadratic costs. The findings we obtain from the application of our results to the Tunisian mobile market between (2002-2019) are consistent with our theoretical model.

Linear or mixed integer programming in long-term energy systems modeling – A comparative analysis for a local expanding heating system

Most computer models used in energy systems optimization modeling studies are formulated using linear equations. However, since linear formulations do not always well reflect real-world conditions, they may not always be adequate as policy and support tools. This is particularly the case for local system studies attempting to represent technologies at the individual scale, as in the case for local heating system modeling. Thus, the aim of this paper is to investigate differences in the resulting heating solutions and model solution times for a local expanding heating system. Three different investment cost structures for individual and district heating solutions for the heating of new housing are investigated using linear and mixed integer linear programming. The results show that the use of district heating is higher for the cost structures that use mixed integer linear programming than it is for the linear cost structures. This result is attributed mainly to the fact that individual air-to-water heat pumps benefit from the linear equation formulation due to its high coefficient of performance during summertime. This finding is important to consider when modeling local energy systems. The solution time is, however, significantly shorter for the linear formulations than for the mixed integer linear formulations.

Production-inventory strategies for a linear reverse logistics system

Abstract The paper investigates an one-product reverse logistics system. The aim is to analyze the functioning of such a system with continuous time and linear cost structure. The costs consist of linear holding costs for both warehouse, and the linear remanufacturing, manufacturing, and disposal costs. The demand and return rates are known deterministic parameters. The problem is solved with the Pontyagin’s maximum principle. Solving the control problem, it is corrected an earlier paper [1].

Analysis of an unreliable N – policy queue with set-up period under Bernoulli schedule and re-service approach

This research article investigates the stationary N-policy with a set-up time of a single server bulk arrival queueing model rendering two-heterogeneous optional repeated service (THORS) with the factor of unreliability. The server studied here is allowed to take a single vacation after each busy period following Bernoulli Schedule (BS). An extensive analysis of the proposed model is carried out using the Supplementary Variable Technique (SVT) under some suitable transformations. The joint distribution of the server’s state and queue length are obtained under both elapsed and remaining times along with their double transforms. Probability generating function (PGF) of the queue size distribution together with the mean system size of the model are determined for any arbitrary time point and service completion epoch, besides the busy period distribution and various pivotal system characteristics. A suitable linear cost structure of the underlying model is developed, and with the help of a difference operator, a locally optimal N-policy at a lower cost is obtained. Finally, some numerical experiments are carried out in support of the theory.

Analysis of a bulk arrival N-policy queue with two-service genre, breakdown, delayed repair under Bernoulli vacation and repeated service policy

This article deals with an unreliable bulk arrival single server queue rendering two-heterogeneous optional repeated service (THORS) with delayed repair, under Bernoulli Vacation Schedule (BVS) and N-policy. For this model, the joint distribution of the server’s state and queue length are derived under both elapsed and remaining times. Further, probability generating function (PGF) of the queue size distribution along with the mean system size of the model are determined for any arbitrary time point and service completion epoch, besides various pivotal system characteristics. A suitable linear cost structure of the underlying model is developed, and with the help of a difference operator, a locally optimal N-policy at a lower cost is obtained. Finally, numerical experiments have been carried out in support of the theory.

Effective Algorithms for the Economic Lot-Sizing Problem with Bounded Inventory and Linear Fixed-Charge Cost Structure

Efficient algorithms for the economic lot-sizing problem with storage capacity are proposed. On the one hand, for the cost structure consisting of general linear holding and ordering costs and fixed setup costs, an OT2 dynamic programming algorithm is introduced, where T is the number of time periods. The new approach induces an accurate partition of the planning horizon, discarding most of the infeasible solutions. Moreover, although there are several algorithms based on dynamic programming in the literature also running in quadratic time, even considering more general cost structures and assumptions, the new solution uses a geometric technique to speed up the algorithm for a class of subproblems generated by dynamic programming, which can now be solved in linearithmic time. To be precise, the computational results show that the average occurrence percentage of this class of subproblems ranges between 13% and 45%, depending on both the total number of periods and the percentage of storage capacity availability. Furthermore, this percentage significantly increases from 13% to 35% as the capacity availability decreases. This reveals that the usage of the geometric technique is predominant under restrictive storage capacities. Specifically, when the percentage of capacity availability is below 50%, the average running times are on average 100 times faster than those when this percentage is above 50%. On the other hand, an OT on-line array searching method in Monge arrays can be used when the costs are non-speculative costs.

On the optimality of small research tournaments

A central result in Fullerton and McAfee’s (1999) analysis of fixed-prize research tournaments shows that if firms’ heterogeneous marginal effort costs are publicly known and the procurer can charge non-discriminatory entry fees, restricting entry to the two most efficient firms is optimal under a (fairly restrictive) sufficient condition on the form of heterogeneity. This note provides a complementary result. I prove a sharp, worst-case bound (across all linear cost structures) for the ratio between the cost of procuring a given total effort from the optimal number of contestants and the corresponding cost for a tournament featuring only the two most efficient firms. The analysis confirms the attractiveness of the smallest possible tournament, with some notable exceptions.

Structural Results for Average‐Cost Inventory Models with Markov‐Modulated Demand and Partial Information

We consider a discrete‐time infinite‐horizon inventory system with non‐stationary demand, full backlogging, and deterministic replenishment lead time. Demand arrives according to a probability distribution conditional on the state of the world that undergoes Markovian transitions over time. But the actual state of the world can only be imperfectly estimated based on past demand data. We model the inventory replenishment problem for this system as a Markov decision process (MDP) with an uncountable state space consisting of both the inventory position and the most recent belief, a conditional probability mass function, about the actual state of the world. Assuming that the state of the world evolves as an ergodic Markov chain, using the vanishing discount method along with a coupling argument, we prove the existence of an optimal average cost that is independent of the initial system state. For our linear cost structure, we also establish the average‐cost optimality of a belief‐dependent base‐stock policy. We then discretize the uncountable belief space into a regular grid and observe that the average cost under our discretization converges to the optimal average cost as the number of grid points grows large. Finally, we conduct numerical experiments to evaluate the use of a myopic belief‐dependent base‐stock policy as a heuristic for our MDP with the uncountable state space. On a test bed of 108 instances, the average cost obtained from the myopic policy deviates by no more than a few percent from the best lower bound on the optimal average cost obtained from our discretization.

High Speed FIR Filter Design using Multiplier Sharing and Sub-Expression Elimination Method

FIR filter is the basic filter used in many DSP applications because of its linear phase , stability , low cost and simple structure . Designing a high- speed and hardware efficient FIR filter is a very difficult task as the complexity increases with the filter order .In most Application the higher order filters are required but the memory usage of filter increases exponentially with the order of the filter using multipliers occupy a large chip area and need more access time. So the design and implementation of highly efficient look up table (LUT) based circuit for the implementation using DA Algorithm increases the speed. Multiplier sharing and sub-expression elimination methods are proposed to optimize the Structural adders. These methods split the structural adders into smaller adder blocks to reduce the delay. In order to reduce the complexity of structural adders round-off can be performed at the cost of sacrificing precision of the filter.

A Note on Pricing With Market Power: Third-Degree Price Discrimination With Quality-Differentiated Demand

The article points up limitations in the standard undergraduate treatment of third-degree price discrimination by monopolists. While such treatments allude to qualitative distinctions between higher and lower priced alternatives, failure to capture those distinctions in underlying cost and demand structures results in only partial and possibly misleading conclusions about the nature and consequences of such discrimination. Deriving quality-differentiated linear demand and cost structures from the constructs underlying undergraduate microeconomics, the article compares the standard analysis of price discrimination with one that explicitly accounts for quality choices and monopoly power in manipulating those choices. The analysis illustrates the potential for substantially greater monopoly profits and greater efficiency losses by forcing some groups of consumers into suboptimal quality choices once quality variations are explicitly accounted for. JEL Classifications: A1, A22, D11, D21, D42

Optimal Sample Allocation in Group-Randomized Mediation Studies with a Group-Level Mediator

We derive sample-allocation formulas that maximize the power of several mediation tests in two-level–group-randomized studies under a linear cost structure and fixed budget. The results suggest that the optimal individual sample size is typically smaller than that associated with the detection of a main effect and is frequently less than 10 under parameter values commonly seen in the literature. However, the optimal sample allocation can be heavily influenced by the group-to-individual cost ratio, the ratio of the treatment-mediator to mediator-outcome path coefficients, and the outcome variance structure. We illustrate these findings with a hypothetical group-randomized trial examining a school-discipline reform policy. To encourage utilization of the sample allocation formulas we implement them in the R package PowerUpR and powerupr Shiny application.

Optimal lot-sizing and joint replenishment strategy under a piecewise linear warehousing cost structure

In the general lot-sizing replenishment problem, warehousing costs are considered as part of the inventory holding cost. When decision makers need warehouse space to store their products, they generally think about the warehousing cost as included in the inventory cost. In this study, we investigate an optimal lot-sizing and replenishment problem under a piecewise linear warehousing cost structure. Theoretical analysis of the optimality structure of a model of multiple stock-keeping units with joint inventory costs is conducted, and an effective search algorithm is proposed. Based on our random experiments, we demonstrate that our search algorithm outperforms the approach that the existing literature offers as solution.

Note on a Binomial Schedule for an MX/G/1 Queueing System with an Unreliable Server

We consider in this paper a batch arrival queueing system with an unreliable server. If the queue is empty at a service completion, then the server becomes inactive and begins an idle period. However, if the queue is not empty, then the server will take at most vacation before serving the next customer. A linear cost structure is developed for the system and the optimal value of is obtained.

Analysis and optimization of a repairable M (x) /G/1 queue with an additional optional vacation

This paper investigates an M[x]/G/1 queueing system with an unreliable server, where the server may take an additional vacation after the essential vacation. If the system becomes empty, the server leaves the system and takes the essential vacation. At the end of the essential vacation, the server may return to the system with probability p or take another vacation with probability 1-p. When the additional vacation is completed, the server returns from the vacation. If there are no customers waiting for service in the system, the server waits idly for the first arrival and starts working. It is assumed that the server is subject to break down according to a Poisson process and the repair time obeys a general distribution. For such a system, we derive the system size distribution at a random epoch, as well as various system characteristics. Finally, we develop an iterative procedure to find the optimal threshold values under a linear cost structure. Some numerical experiments are also presented. Key words: Cost, optimization, server breakdowns, vacation queue.

A facility location model with safety stock costs: analysis of the cost of single-sourcing requirements

We consider a supply chain setting where multiple uncapacitated facilities serve a set of customers with a single product. The majority of literature on such problems requires assigning all of any given customer's demand to a single facility. While this single-sourcing strategy is optimal under linear (or concave) cost structures, it will often be suboptimal under the nonlinear costs that arise in the presence of safety stock costs. Our primary goal is to characterize the incremental costs that result from a single-sourcing strategy. We propose a general model that uses a cardinality constraint on the number of supply facilities that may serve a customer. The result is a complex mixed-integer nonlinear programming problem. We provide a generalized Benders decomposition algorithm for the case in which a customer's demand may be split among an arbitrary number of supply facilities. The Benders subproblem takes the form of an uncapacitated, nonlinear transportation problem, a relevant and interesting problem in its own right. We provide analysis and insight on this subproblem, which allows us to devise a hybrid algorithm based on an outer approximation of this subproblem to accelerate the generalized Benders decomposition algorithm. We also provide computational results for the general model that permit characterizing the costs that arise from a single-sourcing strategy.

The optimal control of an [formula omitted] unreliable server queue with two phases of service and Bernoulli vacation schedule

This paper deals with an M X / G / 1 Bernoulli vacation queue with two phases of service and unreliable server under N -policy. While the server is working with any phase of service, it may break down at any instant and the service channel becomes unavailable. The breakdown period is followed by a delay period. If no customer arrives when the server is unavailable, the server becomes idle in the system until the queue size builds up to a threshold value N ( ≥ 1 ) . As soon as the queue size becomes at least N , the server immediately begins to serve the waiting customers in two successive phases of service. The first phase of service is followed by a second phase, after the completion of which, the server may take a vacation or may remain in the system to serve the next unit, if any. We derive the queue size distribution at a random epoch and at a departure epoch, as well as various system performance measures. Finally, we derive a simple procedure to obtain the optimal stationary policy under a linear cost structure.

A production-transportation problem with piecewise linear cost structures

A production-transportation problem with piecewise linear cost structures

Analysis of a two-phase queueing system with a fixed-size batch policy

We consider a single-server, two-phase queueing system with a fixed-size batch policy. Customers arrive at the system according to a Poisson process and receive batch service in the first-phase followed by individual services in the second-phase. The batch service in the first-phase is applied for a fixed number ( k) of customers. If the number of customers waiting for the first-phase service is less than k when the server completes individual services, the system stays idle until the queue length reaches k. We derive the steady state distribution for the system’s queue length. We also show that the stochastic decomposition property can be applied to our model. Finally, we illustrate the process of finding the optimal batch size that minimizes the long-run average cost under a linear cost structure.

A stochastic programming approach for planning horizons of infinite horizon capacity planning problems

Planning horizon is a key issue in production planning. Different from previous approaches based on Markov Decision Processes, we study the planning horizon of capacity planning problems within the framework of stochastic programming. We first consider an infinite horizon stochastic capacity planning model involving a single resource, linear cost structure, and discrete distributions for general stochastic cost and demand data (non-Markovian and non-stationary). We give sufficient conditions for the existence of an optimal solution. Furthermore, we study the monotonicity property of the finite horizon approximation of the original problem. We show that, the optimal objective value and solution of the finite horizon approximation problem will converge to the optimal objective value and solution of the infinite horizon problem, when the time horizon goes to infinity. These convergence results, together with the integrality of decision variables, imply the existence of a planning horizon. We also develop a useful formula to calculate an upper bound on the planning horizon. Then by decomposition, we show the existence of a planning horizon for a class of very general stochastic capacity planning problems, which have complicated decision structure.

Imperfect Monitoring May Be Perfectly Fine: Differential Game Theory and an Application to Climate Change

We study a class of finite-horizon differential games with control-state separable objective functionals and state equations. In this context, we introduce simple mechanisms that give a dynamic payoff to agents that only depends on the current value of the state variable. Thus, in many applications their implementation requires moderate monitoring capability. We are able to show that these mechanisms induce, in Markov-perfect equilibrium, any economically meaningful control path that is continuously differentiable and satisfies certain mild regularity assumptions. Moreover, if the target control-state path represents a Pareto improvement over an inefficient unregulated outcome, a suitably chosen ex-ante cost-sharing scheme ensures ex-post individual rationality, in addition to budget balance. At the same time, if the differential game has pre-existing linear cost structure no such agreement is necessary. Our results extend to an infinite time horizon and a multi-dimensional state space. We apply our analysis to a simple differential-game model of global climate change and exhibit a mechanism, which induces the globally optimal emissions path in Markov-perfect equilibrium.