On the flexibility of demand and production rate

In the manufacturing practice, cycle time is usually optimized in order to plan the batch size, and production time among other parameters. In certain situations, the production rate is decreased in order to have lower inventory levels or to deal with a shelf life constraint. This technical note examines the increase/decrease in the demand level along with a discussion concerning flexibility of the production rate. A generalized problem is also formulated in the context of the costs that are incurred in order to maintain certain demand level.     

Analysis of a two-sided production policy with inventory-level-dependent production rates

In this paper we analyse a stochastic production/inventory problem with compound Poisson demand and state (i.e. inventory level) dependent production rates. Customers arrive according to a Poisson process where the amount demanded by each customer is assumed to have a general distribution. When the inventory W(t) falls below a critical level m, production is started at a rate of r[W(t)], i.e. production rate dynamically changes as a function of the inventory level. Production continues until a level M (œ w m) is reached. Excess demand is assumed to be lost. We identify a dam content process X that is a dual for the inventory level W and develop the stationary distribution for the X process. To achieve this we use tools from renewal and level crossing theories. The two-sided (m, M) policy is optimized using the expected cost obtained from the stationary density of W and a conditional (on w) expected cost function for this process. For a special case, we obtain explicit results for all the relevant expressions. Numerical examples are provided for several test problems. © 1996 John Wiley & Sons, Ltd.     

A deterministic inventory/production model with general inventory cost rate function and piecewise linear concave production costs

We present a thorough analysis of the economic production quantity model with shortages under a general inventory cost rate function and piecewise linear concave production costs. Consequently, an effective solution procedure, particularly useful for an approximation scheme, is proposed. A computational study is appended to illustrate the performance of the proposed solution procedure.     

生产率、需求率、变质率及损失率均随时间变化的生产库存模型

建立了生产率、需求率、变质率及损失率均随时间变化的生产库存模型,在假定了(I)变质率线性依赖于时间及库存开始点;(II)损失率线性依赖于时间及短缺量拖后供货的结束点的前提下,给出了寻求最优策略的方法,指出了文[10]中不合理的假设,并以实际的例子与已有结果作比较,其结果为生产管理部门的决策提供了理论依据.     

Monotonicity of optimal flow control for failure-prone production systems

In this paper, we consider the problem of the optimal flow control for a production system with one machine which is subject to failures and produces one part type. In most previous work, it has been assumed that the machine has exponential up and down times, i.e., its state process is a Markov process. The system considered in our study has general machine up and down times. Our main result is establishing monotone properties for the optimal control policy.This work was partially supported by the National Science Foundation under Grants DDM-9215368 and EDI-9212122. The authors thank two anonymous reviewers for helpful comments and suggestions.     

Dam processes with state dependent batch sizes and intermittent production processes with state dependent rates

We consider a dam process with a general (state dependent) release rule and a pure jump input process, where the jump sizes are state dependent. We give sufficient conditions under which the process has a stationary version in the case where the jump times and sizes are governed by a marked point process which is point (Palm) stationary and ergodic. We give special attention to the Markov and Markov regenerative cases for which the main stability condition is weakened. We then study an intermittent production process with state dependent rates. We provide sufficient conditions for stability for this process and show that if these conditions are satisfied, then an interesting new relationship exists between the stationary distribution of this process and a dam process of the type we explore here.Supported in part by The Israel Science Foundation, grant no. 372/93-1.     

The exact blow-up rates of large solutions for semilinear elliptic equations

In this paper, combining the method of lower and upper solutions with the localization method, we establish the boundary blow-up rate of the large positive solutions to the singular boundary value problem

     

The exponential rates of convergence of posterior distributions

After the observations were observed, the posterior distribution under mild conditions becomes more concentrated in the neighbourhood of the mode of the posterior distribution as sample size n increase. In this paper, the exponential rate of convergence of posterior distribution around the mode is established by using the generalized Laplace method. An example is also given.This work was supported in part by the Natural Sciences and Engineering Research Council of Canada under Grant NSERC A-9216.     

The performance evaluation of a multi-stage JIT production system with stochastic demand and production capacities

This paper discusses a single-item, multi-stage, serial Just-in-Time (JIT) production system with stochastic demand and production capacities. The JIT production system is modeled as a discrete-time, M/G/1-type Markov chain. A necessary and sufficient condition, or a stability condition, under which the system has a steady-state distribution is derived. A performance evaluation algorithm is then developed using the matrix analytic methods. In numerical examples, the optimal numbers of kanbans are determined by the proposed algorithm. The optimal numbers of kanbans are robust for the variations in production capacity distribution and demand distribution.     

The impact of preventive activities on the economics of production systems: Modeling and application

In this paper, the impact of preventive activities on the economics of production systems has been discussed. A defective production system has been used to evaluate the financial return of a system with and without preventive activity. A mathematical model has been developed to simulate the situation. A practical case in the automotive industry has been used to verify the model. According to this research, it has been found that preventive activities will affect the return of the production system, and the effect depends on the cost of the action that has been taken.     

The blow-up rates for systems of heat equations with nonlinear boundary conditions

This paper deals with the blow-up rate estimates of positive solutions for systems of heat equations with nonlinear boundary conditions. The upper and lower bounds of blow-up rate are obtained.     

Speculative production and anticipative reservation of reactive capacity by a multi-product newsvendor

In this paper the optimal sourcing decisions of a multi-product newsvendor prior to the selling season of the products are studied. To satisfy the uncertain demands, the newsvendor can either utilize speculative production, or anticipatively reserve capacity. During the selling season when demand has become known, the newsvendor can utilize its reserved capacity and reactively satisfy demand uncovered by its speculative production. For the case where capacity for speculative production may be limited, but potential reservation of reactive capacity is unlimited two capacity reservation settings are analyzed and compared. In the first one capacity for each product has to be reserved separately, while in the second setting one joint capacity reservation for all products is permitted which can then be allocated to the different products optimally during the selling season. For the case of separate individual reservations the optimal strategies are analytically derived and structural insights concerning their existence are presented. As the model allowing for joint reservation can not be tackled analytically in general an approximation based on an LP formulation is used. Through a numerical example insights on the value of the increased flexibility induced by joint reservation, the cost-premium acceptable for joint reservation and the relative levels of capacity reservation in the two settings are given.     

The not-quite non-atomic game: Non-emptiness of the core in large production games

We show that, in cooperative production games, when the production functions are not concave, the core may well be empty. However, as the number of players increases (subject to some regularity conditions), the relative deficit obtained by using concavified functions decreases to zero. Furthermore, differentiability of the functions will cause the absolute deficit to go to zero.     

On computational complexity of membership test in flow games and linear production games

Let Γ≡(N,v) be a cooperative game with the player set N and characteristic function v: 2^N→R. An imputation of the game is in the core if no subset of players could gain advantage by splitting from the grand coalition of all players. It is well known that, for the flow game (and equivalently, for the linear production game), the core is always non-empty and a solution in the core can be found in polynomial time. In this paper, we show that, given an imputation x, it is NP-complete to decide x is not a member of the core, for the flow game. And because of the specific reduction we constructed, the result also holds for the linear production game. Received: October 2000/Final version: March 2002     

The structure of two-parabolic space: parabolic dust and iteration

A non-elementary Möbius group generated by two-parabolics is determined up to conjugation by one complex parameter and the parameter space, the parameter space for representations of groups generated by two parabolics into \({PSL(2, \mathbb{C})}\) modulo conjugacy, has been extensively studied. In this paper, we use the results of Gilman and Waterman to obtain an additional structure for the parameter space, which we term the two-parabolic space. This structure allows us to identify groups that contain additional conjugacy classes of primitive parabolics, which we call parabolic dust groups, non-free groups off the real axis, and groups that are both parabolic dust and non-free; some of these contain \({\mathbb{Z} \times \mathbb{Z}}\) subgroups. The structure theorem also attaches additional geometric structure to discrete and non-discrete groups lying in given regions of the parameter space and allows a new explicit geometric construction of some non-classical T-Schottky groups.     

Optimization of power production through coordinated use of hydroelectric and conventional power units

In the present work a methodology to tackle the problem of simultaneous utilization of hydroelectric and conventional power units with the goal of optimizing power production operations over the short term is presented. Most problem formulations found in the literature result in the development of nonlinear optimization programs, which are solved with stochastic methods. The methodology presented in this paper leads to the development of a convex mixed integer quadratic programming (MIQP) model, which is a special type of nonlinear model that enables reaching the global optimum solution in short computational time. The efficiency of the proposed approach is demonstrated by its application to a realistic power production system.     

Learning effects and the phenomenon of moving bottlenecks in a two-stage production system

This paper studies the effects of learning and forgetting on a two-stage production system and the position of a potential bottleneck in the system. We start with developing a model for a two-stage serial production system where semi-finished items are fed by the first stage to the second stage, which, in turn, processes the items to their final state. The finished items are transferred either to a subsequent stage or to customers. The paper assumes that both stages of the production system considered are subject to learning and forgetting effects. Learning quickens the production rate as more experience is gained (i.e., when the number of repetitions increases), while forgetting has the opposite effect when production is intermittent (i.e., experience is lost over production breaks). The paper studies how different values of the learning and forgetting parameters influence the ratio of the production rates of both stages and the flow of material in the system. The results of the paper indicate that learning may cause a bottleneck to shift its position in a production system. This happens when an initially slower stage overtakes a previously faster stage over time due to a higher learning rate. The paper thus contributes to the literature on moving bottlenecks and provides practitioners with a model that helps predicting where bottlenecks may arise in the production system, and which enables the system to flexibly react to moving bottlenecks.     

Two-sided bounds and leading term for rates of convergence in the multivariate central limit theorem

For a sequence of independent and identically distributed random vectors, upper and lower bounds are obtained for the discrepancy between the probability measure P_n, induced by their normalized sum, and the Normal measure Φ. The upper and lower bounds are of the same order of magnitude. These results may be derived by a “leading term” approach, in which a signed measure Q_n is introduced as a first order approximation to P_n − Φ. The purpose of this paper is to investigate properties of the leading term.