Scheduling with a common due-window: Polynomially solvable cases

The single machine scheduling problem to minimize maximum weighted absolute deviations of job completion times from a common due-date, is known to be NP-hard. However, two special cases have been shown to have polynomial time solutions: the case of unit processing time jobs, and the case of due-date assignment for a given job sequence. We extend both cases to a setting of a common due-window. We show that the unit-job problem includes 12 different sub-cases, depending on the size and location of the (given) due-window. Scheduling and due-window assignment for a given job sequence is solved for a single machine, for parallel identical machines and for flow-shops. For each of the above cases, an appropriate special-structured linear program is presented.     

Optimal single-replacement for repairable products with different failure rate under a finite planning horizon

This paper provides a replacement policy for repairable products with free-repair warranty (FRW) under a finite planning horizon from the consumer's viewpoint. Assume that the product is replaced once within a finite planning horizon, and the failure rate of the second product is lower than the failure rate of the first product. Within FRW, the failed product is corrected by minimal repair without any cost to the consumers. After FRW, the failed product is repaired with a fixed repair cost to the consumers. However, each failure incurs a fixed downtime cost to the consumers over a finite planning horizon. In this paper, we derive the three models of the expected total disbursement cost within a finite planning horizon and some properties of the optimal replacement policy under some reasonable conditions are obtained. Finally, numerical examples are given to illustrate the features of the optimal replacement policy under various maintenance costs.     

Optimal decisions for continuous time Markov decision processes over finite planning horizons

The computation of ϵ-optimal policies for continuous time Markov decision processes (CTMDPs) over finite time intervals is a sophisticated problem because the optimal policy may change at arbitrary times. Numerical algorithms based on time discretization or uniformization have been proposed for the computation of optimal policies. The uniformization based algorithm has shown to be more reliable and often also more efficient but is currently only available for processes where the gain or reward does not depend on the decision taken in a state. In this paper, we present two new uniformization based algorithms for computing ϵ-optimal policies for CTMDPs with decision dependent rewards over a finite time horizon. Due to a new and tighter upper bound the newly proposed algorithms cannot only be applied for decision dependent rewards, they also outperform the available approach for rewards that do not depend on the decision. In particular for models where the policy only rarely changes, optimal policies can be computed much faster.     

An inventory model for ameliorating and deteriorating items taking account of time value of money and finite planning horizon

The objective of this study is to develop an optimal replenishment inventory strategy to consider both ameliorating and deteriorating effects taking account of time value of money and finite planning horizon. The amelioration rate and the deterioration rate are assumed to follow a Weibull distribution. The inventory system is particularly useful for young livestock whose utility increase over time. The discounted cash flow and optimisation technique are used to derive an optimal solution. A numerical example and sensitivity analysis are given to illustrate the theory of the inventory system.     

Motion planning for cooperative unicycle-type mobile robots with limited sensing ranges: A distributed receding horizon approach

This paper presents a decentralized motion planner for a team of nonholonomic mobile robots subject to constraints imposed by sensors and the communication network. The motion planning scheme consists of decentralized receding horizon planners that reside on each vehicle to achieve coordination among flocking agents. The advantage of the proposed algorithm is that each vehicle only requires local knowledge of its neighboring vehicles. The main requirement for designing an optimal conflict-free trajectory in a decentralized way is that each robot does not deviate too far from its presumed trajectory designed without taking the coupling constraints into account. A comparative study between the proposed algorithm and other existing algorithms is provided in order to show the advantages, especially in terms of computing time. Finally, experiments are performed on a team of three mobile robots to demonstrate the validity of the proposed approach.     

产品随机缺陷生产系统有限时域最优生产控制

针对合格产品产量呈随机分布的单设备单产品类型不可靠生产系统,假设所生产合格产品的产量占所生产产品总量比例的概率分布已知,且产品质量检测消耗时间与生产控制时域相比较小.本文通过对目标函数的离散化,在离散空间上对生产控制策略进行寻优,得到基于当前状态下的最优生产控制策略,该策略可解析表示为合格产品产量分布、成本惩罚系数c~ (c~-)、当前状态及产品质量检测时间的函数.与同类文献所得结果相比较,该控制策略克服了文献[8]结论有可能导致系统状态发散的缺点,并且最优控制策略表达式更简洁,所得结论对实际工程应用而言有显著意义.     

The regulator problem with indefinite quadratic cost for boundary control systems: the finite horizon case

In this paper we study the finite horizon non-standard LQ-problem for an abstract dynamics, which models a large class of hyperbolic-like partial differential equations. We provide necessary/sufficient conditions for finiteness of the value function corresponding to the control problem. Sharpness of sufficient conditions is shown by means of counterexamples. The specific features of the finite, in contrast to infinite, horizon case are illustrated.     

Scheduling production for a sawmill: A comparison of a mathematical model versus a heuristic

Sawmill production scheduling is complex. It involves determining which logs to process taking into account the diameter, length, and grade of each log, on one hand, and the finished products that are needed to fulfill the orders, on the other. The cutting pattern determines which products are generated and also the yield, which is how much of the volume of the log ends as finished products. We used two approaches to solve the problem: a mathematical model, which calculates the volume and the schedule of various types of logs, and a heuristic that solves the problem by systematically applying the criteria used by a sawmill programmer in southern Chile. We compare the results of using both approaches under various scenarios in a 6 week planning horizon, with the mathematical model showing a superior performance in almost all instances except two, were both found the optimal solution. The proposed mathematical model can be solved in a relatively short time, which makes it a suitable basis of a practical optimization-based decision support system.     

Scheduling a dynamic job shop production system with sequence-dependent setups: An experimental study

This paper presents the salient aspects of a simulation-based experimental study of scheduling rules for scheduling a dynamic job shop in which the setup times are sequence dependent. A discrete event simulation model of the job shop system is developed for the purpose of experimentation. Seven scheduling rules from the literature are incorporated in the simulation model. Five new setup-oriented scheduling rules are proposed and implemented. Simulation experiments have been conducted under various experimental conditions characterized by factors such as shop load, setup time ratios and due date tightness. The results indicate that setup-oriented rules provide better performance than ordinary rules. The difference in performance between these two groups of rules increases with increase in shop load and setup time ratio. One of the proposed rules performs better for mean flow time and mean tardiness measures.     

A partial backlogging production-inventory lot-size model for deteriorating items with time-varying production and demand rate over a finite time horizon

In this article, I extend Balkhi ((2001), ‘On a Finite Horizon Production Lot Size Inventory Model for Deteriorating Items: An Optimal Solution’, European Journal of Operational Research, 132, 210–223), by considering a generalised mathematical production-inventory model for deteriorating items with partial backlogging. The demand, production and backlogging rates are assumed to be continuous and varying with time. The objective is to find the optimal production restarting and stopping time to keep the total relevant cost as low as possible. To ascertain the optimal solution exists, the conditions for the total relevant cost in the system which attains its global minimum are provided. In addition, based on the minimum total relevant cost, an alternative among the proposed four cases is also suggested. Finally, a numerical example and sensitivity analysis is illustrated and some management insights are presented.     

Multi-choice multi-objective mathematical programming model for integrated production planning: a case study

This article develops a multi-choice multi-objective linear programming model in order to solve an integrated production planning problem of a steel plant. The aim of the integrated production planning problem is to integrate the planning sub-functions into a single planning operation. The sub-functions are formulated by considering the capacity of different units of the plant, cost of raw materials from various territories, demands of customers in different geographical locations, time constraint for delivery the products, production cost and production rate at different stages of production process. Departure cost is also considered in the formulation of mathematical programming model. Some of the parameters are decided from a set of possible choices, therefore such parameters are considered as multi-choice type. Multi-choice mathematical programming problem cannot be solved directly. Therefore an equivalent multi-objective mathematical programming model is established in order to find the optimal solution of the problem. Computation of the mathematical programming model is performed with the practical production data of a plant to study the methodology.     

Combined planning and scheduling in a divergent production system with co-production: A case study in the lumber industry

Many research initiatives carried out in production management consider process planning and operations scheduling as two separate and sequential functions. However, in certain contexts, the two functions must be better integrated. This is the case in divergent production systems with co-production (i.e. production of different products at the same time from a single product input) when alternative production processes are available. This paper studies such a context and focuses on the case of drying and finishing operations in a softwood lumber facility. The situation is addressed using a single model that simultaneously performs process planning and scheduling. We evaluate two alternative formulations. The first one is based on mixed integer programming (MIP) and the second on constraint programming (CP). We also propose a search procedure to improve the performance of the CP approach. Both approaches are compared with respect to their capacity to generate good solutions in short computation time.