The implication of time-based payment contract in the decentralized assembly system

This paper investigates the impact of two time-based payment contracts in an assembly system that consists of one assembler and two suppliers, in which both suppliers’ production times are stochastic. The assembler initially chooses the contract type (delay payment contract vs on-time payment contract) and the buffer time, and two suppliers have to simultaneously determine their production lead times. We find that in equilibrium, both suppliers cut down their production lead times under the delay payment contract, and this makes them worse off than that under the on-time payment contract. Differently, the delay payment contract is the assembler’s dominant option. This is because by setting the buffer time, the assembler can significantly mitigate the possible delay risk caused by the suppliers’ decentralization under the delay payment contract. It also shows that the entire supply chain achieves the same service level under either the centralized condition or the decentralized condition, regardless of the applied payment contract type. Note that these results are robustness when we extend the model into the system containing N (N\(>\) 2) independent suppliers.     

A novel ant colony optimization approach for on-line scheduling and due date determination

This paper aims to develop an on-line Ant Colony Optimization (ACO) framework, where jobs arrive over time, and at any time we lack knowledge concerning future jobs. A due date is determined upon job arrival, and jobs are sequenced on the machine to optimize the sum of weighted lead times with all due dates met. We propose that each ant is associated with a sequence of waiting jobs with quoted due dates. This waiting sequence is constantly updated over time (whenever a job is selected to be processed or a new job arrives). The on-line schedule is constructed by selecting the first job in the waiting list of the “best” ant to process (along with its due date) as the machine becomes available. However, for the ant where this job is not the first one in the list, processing it pushes back the waiting jobs positioned before it. If such push back results in a due date violation, this ant will be eliminated. Further, our ACO framework does not include the iterative procedure due to the characteristics of the on-line problem; this is one difference from the traditional ACO framework besides ant elimination. The computational testing on generated instances shows that our ACO algorithm outperforms an existing effective on-line algorithm in the literature. Also, with local search incorporated using the EDD (Earliest Due Date) rule, improvements can be obtained in both computational outcome and time.     

A time-based formulation and upper bounding scheme for the selective travelling salesperson problem

The selective travelling salesperson problem (STSP) involves determining a tour of maximal value over a set of cities subject to a tour length constraint. The problem has the characteristic that not all cities have to be visited. An integer formulation which combines permutation variables with flow variables is presented. An upper bounding scheme for the number of nodes visited in the final solution is used to reduce the size of the integer programme. The problem is solved using an off-the-shelf mixed-integer solver called CPLEX. Results demonstrating the usefulness of the bound are presented. The methodology is also applied to solve a 15-zone fisheries surveillance problem.     

Efficient computation of time-based customer service levels in a multi-item, multi-echelon supply chain: A practical approach for inventory optimization

Time-based item fill rates, or “channel” fill rates, are the building blocks needed to evaluate steady-state compliance with time-based customer service agreements. Exact computation of channel fill rates is both difficult and time-consuming, yet their accurate assessment is essential for system-wide inventory optimization. We describe and validate a practical method for computing channel fill rates in a multi-item, multi-echelon service parts distribution system. A simulation study is presented which shows that, in a three-echelon setting, our estimation errors are very small over a wide range of base stock level vectors. A more accurate, though less efficient, approximation method is also evaluated for comparison.     

Decentralized communication, trail connectivity and emergent benefits of ant pheromone trail networks

Communication improves decision-making for group-living animals, especially during foraging, facilitating exploitation of resources. Here we model the trail-based foraging strategy of Pharaoh’s ants to understand the limits and constraints of a specific group foraging strategy. To minimise assumptions we used model parameters acquired through behavioural study. Pharaoh’s ants (Monomorium pharaonis) exploit the geometry of trail networks bifurcations to make U-turns, if they are walking the wrong way. However, 7% of foragers perform apparently incorrect U-turns. These seemingly maladaptive U-turns are performed by a consistent minority of specialist U-turners that make frequent U-turns on trails and lay trail pheromones much more frequently compared to the rest of the colony. Our study shows a key role for U-turning ants in maintaining the connectivity of pheromone trails. We produced an agent-based model of a heterogeneous ant community where 7% of agents were specialised frequent U-turners whilst the remaining 93% rarely U-turned. Simulations showed that heterogeneous colonies enjoyed significantly greater success at foraging for distant food resources compared to behaviourally homogeneous colonies. The presence of a cohort of specialised trail-layers maintains a well-connected network of trails which ensures that food discoveries are rapidly linked back to the nest. This decentralised information transfer might ensure that foragers can respond to dynamic changes in food distribution, thereby allowing more individuals in a group to benefit by successfully locating food finds.     

An ant colony system for enhanced loop-based aisle-network design

The purpose of this paper is to develop a global optimization model, simplification schemes, and a heuristic procedure for the design of a shortcut-enhanced unidirectional loop aisle-network with pick-up and drop-off stations. The objective is to minimize the total loaded and empty trip distances. This objective is the main determinant for the fleet size of the vehicles, which in turn is the driver of the total life-cycle cost of vehicle-based unit-load transport systems. The shortcut considerably reduces the length of the trips while maintaining the simplicity of the system. The global model solves simultaneously for the loop design, stations’ locations and shortcut design. We then develop two simplifications each containing two serial phases. Phase-1 of the first simplification step focuses on both loaded and empty trips, while that of the second simplification focuses only on loaded trips. In phase-2, both designs are enhanced with a shortcut to minimize both loaded and empty trip distances. The quality and efficiency of the three alternative designs are tested for a set of problems with different layout size and product mix. While the solution time of the second simplification procedure is a small percentage of the global formulation, it generates satisfactory solutions. On this foundation, we then develop a heuristic procedure to replace phase-1 of the second simplification. The heuristic procedure is using ant colony system to generate feasible solutions and then we implement a local search algorithm to improve the results. The heuristic algorithm quickly generates close to optimal solutions for phase-1 of the second simplification. By applying phase-2 of the this second simplification on a set of loops generated by the heuristic, close to optimal solutions are also quickly obtained for the global model.     

A multi-objective multi-population ant colony optimization for economic emission dispatch considering power system security

With increasing concern about global warming and haze, environmental issue has drawn more attention in daily optimization operation of electric power systems. Economic emission dispatch (EED), which aims at reducing the pollution by power generation, has been proposed as a multi-objective, non-convex and non-linear optimization problem. In a practical power system, the problem of EED becomes more complex due to conflict between the objectives of economy and emission, valve-point effect, prohibited operation zones of generating units, and security constraints of transmission networks. To solve this complex problem, an algorithm of a multi-objective multi-population ant colony optimization for continuous domain (MMACO_R) is proposed. MMACO_R reconstructs the pheromone structure of ant colony to extend the original single objective method to multi-objective area. Furthermore, to enhance the searching ability and overcome premature convergence, multi-population ant colony is also proposed, which contains ant populations with different searching scope and speed. In addition, a Gaussian function based niche search method is proposed to enhance distribution and accuracy of solutions on the Pareto optimal front. To verify the performance of MMACO_R in different multi-objective problems, benchmark tests have been conducted. Finally, the proposed algorithm is applied to solve EED based on a six-unit system, a ten-unit system and a standard IEEE 30-bus system. Simulation results demonstrate that MMACO_R is effective in solving economic emission dispatch in practical power systems.     

A polyhedral approach to the alldifferent system

This paper examines the facial structure of the convex hull of integer vectors satisfying a system of alldifferent predicates, also called an alldifferent system. The underlying analysis is based on a property, called inclusion, pertinent to such a system. For the alldifferent systems for which this property holds, we present two families of facet-defining inequalities, establish that they completely describe the convex hull and show that they can be separated in polynomial time. Consequently, the inclusion property characterises a group of alldifferent systems for which the linear optimization problem (i.e. the problem of optimizing a linear function over that system) can be solved in polynomial time. Furthermore, we establish that, for systems with three predicates, the inclusion property is also a necessary condition for the convex hull to be described by those two families of inequalities. For the alldifferent systems that do not possess that property, we establish another family of facet-defining inequalities and an accompanied polynomial-time separation algorithm. All the separation algorithms are incorporated within a cutting-plane scheme and computational experience on a set of randomly generated instances is reported. In concluding, we show that the pertinence of the inclusion property can be decided in polynomial time.     

Mathematical programming time-based decomposition algorithm for discrete event simulation

Mathematical programming has been proposed in the literature as an alternative technique to simulating a special class of Discrete Event Systems. There are several benefits to using mathematical programs for simulation, such as the possibility of performing sensitivity analysis and the ease of better integrating the simulation and optimisation. However, applications are limited by the usually long computational times. This paper proposes a time-based decomposition algorithm that splits the mathematical programming model into a number of submodels that can be solved sequentially to make the mathematical programming approach viable for long running simulations. The number of required submodels is the solution of an optimisation problem that minimises the expected time for solving all of the submodels. In this way, the solution time becomes a linear function of the number of simulated entities.     

A system approach to the optimal health-care districting

The paper presents a methodology for partitioning a given region in geographical areas in such a way as to insure an optimal allocation of the available health services. Two steps compose the proposed approach. In the first step, via mathematical programming one determines optimal hospital districts by taking into account demand and capacity, measured in number of hospital-beds. In the second step, one determines health-districts by aggregating together hospital districts, by taking into account lower and upper bounds for the population in each district and the existence of districts with a different nature (political, educational, etc.). A case study is presented for the Italian province of Cosenza. Although developed within the context of health-care services, the approach is general enough to be applicable also to the partition in a given region of other social services, i.e. school districts.     

A quantile-based approach to system selection

We propose a quantile-based ranking and selection (R&S) procedure for comparing a finite set of stochastic systems via simulation. Our R&S procedure uses a quantile set of the simulated probability distribution of a performance characteristic of interest that best represents the most appropriate selection criterion as the basis for comparison. Since this quantile set may represent either the downside risk, upside risk, or central tendency of the performance characteristic, the proposed approach is more flexible than the traditional mean-based approach to R&S. We first present a procedure that selects the best system from among K systems, and then we modified that procedure for the case where K − 1 systems are compared against a standard system. We present a set of experiments to highlight the flexibility of the proposed procedures.     

A new approach for asymptotic stability system of the nonlinear ordinary differential equations

In this paper, we use measure theory for considering asymptotically stable of an autonomous system [1] of first order nonlinear ordinary differential equations(ODE’s). First, we define a nonlinear infinite-horizon optimal control problem related to the ODE. Then, by a suitable change of variable, we transform the problem to a finite-horizon nonlinear optimal control problem. Then, the problem is modified into one consisting of the minimization of a linear functional over a set of positive Radon measures. The optimal measure is approximated by a finite combination of atomic measures and the problem converted to a finite-dimensional linear programming problem. The solution to this linear programming problem is used to find a piecewise-constant control, and by using the approximated control signals, we obtain the approximate trajectories and the error functional related to it. Finally the approximated trajectories and error functional is used to for considering asymptotically stable of the original problem.     

A geometric approach to the separability of the Neumann-Rosochatius system

We study the separability of the Neumann-Rosochatius system on the n-dimensional sphere using the geometry of bi-Hamiltonian manifolds. Its well-known separation variables are recovered by means of a separability condition relating the Hamiltonian with a suitable (1,1) tensor field on the sphere. This also allows us to iteratively construct the integrals of motion of the system.     

An improved approach to attribute reduction with ant colony optimization

Attribute reduction problem (ARP) in rough set theory (RST) is an NPhard one, which is difficult to be solved via traditionally analytical methods. In this paper, we propose an improved approach to ARP based on ant colony optimization (ACO) algorithm, named the improved ant colony optimization (IACO). In IACO, a new state transition probability formula and a new pheromone traps updating formula are developed in view of the differences between a traveling salesman problem and ARP. The experimental results demonstrate that IACO outperforms classical ACO as well as particle swarm optimization used for attribute reduction.     

A comprehensive analytical approach for policy analysis of system dynamics models

Formal tools to link system dynamics model’s structure to the system modes of behavior have recently become available. In this paper, we aim to expand the use of these tools to perform the model’s policy analysis in a more structured and formal way than the exhaustive exploratory approaches used to date. We consider how a policy intervention (a parameter change) affects a particular behavior mode by affecting the gains of particular feedback loops as well as how it affects the presence of that mode in the variable of interest. The paper demonstrates the utility of considering both of these aspects since the analysis provides an assessment of the overall impact of a policy on a variable and explains why the impact occurs in terms of structural changes in the model. Particularly in the context of larger models, this method enables a much more efficient search for leverage policies, by ranking the influence of each model parameter without the need for multiple simulation experiments.     

A system reliability approach to linear programming

Summary A system reliability approach to linear programming is developed here for the case when the restrictions are chance-constrained. Methods of characterizing a system reliability measure for a linear programming system, its implications under alternative probability distribution assumptions and its uses for specifying policies with an improved system reliability routine are analytically discussed.

---

Zusammenfassung In der vorliegenden Arbeit wird ein Verfahren zur Untersuchung der Zuverlässigkeit eines Systems für den Fall entwickelt, daß die Beschränkungen eines L. P.-Problems zufallsabhängig sind. Es werden Methoden zur Charakterisierung eines Maßes für die Zuverlässigkeit eines L. P.-Systems, die sich daraus ergebenden Implikationen bei verschiedenen Annahmen über die Wahrscheinlichkeitsverteilung und die Möglichkeit zur Bestimmung von Politik-Arten mittels eines verbesserten Verfahrens zur Untersuchung der System-Zuverlässigkeit diskutiert.

---

---

Work done under the National Science Foundation Project GS 1810/420-41-17 at the Department of Economics, Iowa State University. This work develops the theoretical ideas originally fromulated in a paper by this author: Safety first rules under chance-constrained linear programming.Operations Research: The Journal of Operations Research Society of America, Vol.17, No. 1, 1969, pp. 112–132.

---

Vorgel. v.:W. Wittmann     

Control methods for dynamic time-based manufacturing under customized product lead times

For manufacturers, the integration of high performance manufacturing with customer-oriented practices plays an important role in improving the performance of their business system. The benefits from such integration can only be maximized when the two parts are designed to work cooperatively. Though previous research has contributed much to manufacturing control algorithms and customer service practices, there has been little consideration of the two parts as a whole; consequently, the methods proposed may not be well supported by the other practices adopted in the system. This study develops production control methods that support a customer-oriented lead time policy, and aims to increase the performance of both manufacturing and customer service. The control methods are proposed for hybrid flow shops handling orders arriving dynamically. Computer simulations are conducted on a large number of problem instances, and the results show that the designed distributed feedback and decision-making functions enable the proposed methods to significantly outperform existing methods in achieving just-in-time (JIT) job completion under customized product lead times. Even taking into account the possible tradeoff between JIT job completion and flow time length, the proposed methods still deliver competitive performance.     

Three time-based scale formulations for the two-stage lot sizing and scheduling in process industries

In this paper, we propose three novel mathematical models for the two-stage lot-sizing and scheduling problems present in many process industries. The problem shares a continuous or quasi-continuous production feature upstream and a discrete manufacturing feature downstream, which must be synchronized. Different time-based scale representations are discussed. The first formulation encompasses a discrete-time representation. The second one is a hybrid continuous-discrete model. The last formulation is based on a continuous-time model representation. Computational tests with state-of-the-art MIP solver show that the discrete-time representation provides better feasible solutions in short running time. On the other hand, the hybrid model achieves better solutions for longer computational times and was able to prove optimality more often. The continuous-type model is the most flexible of the three for incorporating additional operational requirements, at a cost of having the worst computational performance.