Efficient Solution Procedure Research Articles

Efficient heuristics for cost optimisation in multi stage supply chain network with a fixed transportation charge

This paper addresses multi stage supply chain network (MSCN) problem associated with fixed cost. The MSCN problem involves the selection of suppliers, locating manufacturing plants and distribution centres and determining the optimum/best strategy for distributing the products from the plants to the distribution centres and from the distribution centres to the customers. The objective is to select the optimum numbers, locations and capacities of plants and distribution centres to open so that all customer demand is satisfied at minimum cost. The problem chosen goes beyond the traditional mathematical programming and it becomes a non-polynomial (NP) hard while considering the fixed costs. We develop a mixed integer programming model and provide an efficient heuristic solution procedure for this distribution system problem. Several numerical experimental results are presented and compared with the approximate and lower bound solutions to show the effectiveness of the proposed method. The comparison reveals that the proposed heuristics generates better solution than the approximation method and closer to lower bound solutions.

Determining the Optimal Configuration of Hospital Inpatient Rooms in the Presence of Isolation Patients

We study the optimal configuration of hospital inpatient rooms with private and semiprivate rooms when some of the patients have infectious diseases and need to be isolated. We assume that the demand is random and seasonal. We propose a computationally efficient solution procedure that is based on a stochastic program that uses asymptotic approximations for the system performance under different admission policies and show its accuracy for large systems. Using our model, we study the appropriateness of the recent trends in hospital design calling for 100% private rooms. We show that even with isolation patients such an extreme approach could result in a significant degradation in the access of patients to hospital beds.

Supplier–retailer inventory coordination with credit term for inventory‐dependent and linear‐trend demand

AbstractIn this paper, a nonintegrated and collaborative replenishment policy is considered, respectively, which incorporates varying demand depending on both inventory level and time during the finite planning horizon. For additional cost savings realized from coordination, the paper adopts trade credit as a cost‐saving shift means and introduces a brand new parameter, that is, credit period rate. Then, the equitable credit period rate is determined, and different values of the credit period rate reflect the allocation of additional cost savings between the supplier and retailer. Furthermore, the conditions for the existence and uniqueness of an optimal solution are proved for the nonintegrated and collaborative replenishment policy, and an efficient solution procedure is developed to determine the optimal results and coordination of the inventory model. Finally, several numerical examples are provided to illustrate the proposed strategy and algorithm, and the sensitivity analysis of the optimal solution with respect to each parameter is presented. The sensitivity analysis suggests that the size of the credit period rate has a strong relationship with the supplier's and retailer's inventory cost (including capital cost) and setup cost. In real‐life situations, this proposed strategy may be applied to some consumer products in the growth phase or best‐selling consumer goods, etc.

An optimal consignment stock production and replenishment policy with controllable lead time

This paper considers a single-vendor and single-buyer production system in which the lead-time is controllable with an extra investment under a long-term agreement between the two trading partners. The vendor produces at a finite rate, ships the outputs in lots of equal size within a production cycle, and delays those shipments for a certain period when the buyer’s inventory approaches the capacity limits. Therefore, the arrival of these shipments does not lead to an increase in the buyer’s inventory. Meanwhile, the buyer holds the payment until the complete consumption of the products. The holding cost consists of a storage component and a financial component. A joint EOQ/EPQ model is then established under cases where the buyer’s unit storage holding cost might be greater or less than that of the vendor to jointly determine the number of shipments, the size of each shipment, the number of delayed shipments, and the lead time that minimise the yearly joint total expected cost (JTEC) of the system. An efficient solution procedure is provided to solve the non-linear integer optimisation model that defined the system under consideration. A method to determine the integer global optima from the real global optima is also presented. Two numerical experiments are conducted to illustrate the procedure and the results show that considering the combined effect of adopting a consignment stock policy and lead time crashing opportunities may lead to a better result than any of these two policies considered separately.

Fitting concentric circles to measurements

Measurements for fitting a given number of concentric circles are recorded. For each concentric circle several measurements are taken. The problem is to fit the given number of circles to the data such that all circles have a common center. This is a generalization of the problem of fitting a set of points to one circle. Three objectives, to be minimized, are considered: the least squares of distances from the circles, the maximum distance from the circles, and the sum of the distances from the circles. Very efficient optimal solution procedures are constructed. Problems based on a total of 10,000 measurements are solved in about 10 s with the least squares objective, $$<$$ 2 s with the maximum distance objective, and a little more than 1 min for the minisum objective.

An unsteady aerodynamic formulation for efficient rotor tonal noise prediction

An aerodynamic/aeroacoustic solution methodology for predction of tonal noise emitted by helicopter rotors and propellers is presented. It is particularly suited for configurations dominated by localized, high-frequency inflow velocity fields as those generated by blade–vortex interactions. The unsteady pressure distributions are determined by the sectional, frequency-domain Küssner–Schwarz formulation, with downwash including the wake inflow velocity predicted by a three-dimensional, unsteady, panel-method formulation suited for the analysis of rotors operating in complex aerodynamic environments. The radiated noise is predicted through solution of the Ffowcs Williams–Hawkings equation. The proposed approach yields a computationally efficient solution procedure that may be particularly useful in preliminary design/multidisciplinary optimization applications. It is validated through comparisons with solutions that apply the airloads directly evaluated by the time-marching, panel-method formulation. The results are provided in terms of blade loads, noise signatures and sound pressure level contours. An estimation of the computational efficiency of the proposed solution process is also presented.

Reliability evaluation of a multistate network subject to time constraint under routing policy

A multistate network is a stochastic network composed of multistate arcs in which each arc has several possible capacities and may fail due to failure, maintenance, etc. The quality of a multistate network depends on how to meet the customer's requirements and how to provide the service in time. The system reliability, the probability that a given amount of data can be transmitted through a pair of minimal paths (MPs) simultaneously under the time constraint, is a proper index to evaluate the quality of a multistate network. An efficient solution procedure is first proposed to calculate it. In order to further enhance the system reliability, the network administrator decides the routing policy in advance to indicate the first and the second priority pairs of MPs. The second priority pair of MPs takes charge of the transmission duty if the first fails. The system reliability under the routing policy can be subsequently evaluated.

A parametric programming solution to the F-policy queue with fuzzy parameters

This paper investigates the F-policy queue using fuzzy parameters, in which the arrival rate, service rate, and start-up rate are all fuzzy numbers. The F-policy deals with the control of arrivals in a queueing system, in which the server requires a start-up time before allowing customers to enter. A crisp F-policy queueing system generalised to a fuzzy environment would be widely applicable; therefore, we apply the α-cuts approach and Zadeh's extension principle to transform fuzzy F-policy queues into a family of crisp F-policy queues. This study presents a mathematical programming approach applicable to the construction of membership functions for the expected number of customers in the system. Furthermore, we propose an efficient solution procedure to compute the membership function of the expected number of customers in the system under different levels of α. Finally, we give an example of the proposed system as applied to a case in the automotive industry to demonstrate its practicality.

The burn-in test scheduling problem with batch dependent processing time and sequence dependent setup time

The burn-in test scheduling problem (BTSP) is a variation of the complex batch processing machine scheduling problem, which is also a generalisation of the liquid crystal injection scheduling problem with incompatible product families and classical identical parallel machine problem. In the case we investigated on the BTSP, the jobs are clustered by their product families. The product families can be clustered by different product groups. In the same product group, jobs with different product families can be processed as a batch. The batch processing time is dependent on the longest processing time of those jobs in that batch. Setup times between two consecutive batches of different product groups on the same batch machine are sequentially dependent. In addition, the unequal ready times are considered in the BTSP which involves the decisions of batch formation and batch scheduling in order to minimise the total machine workload without violating due dates and the limited machine capacity restrictions. Since the BTSP involves constraints on unequal ready time, batch dependent processing time, and sequence dependent setup times, it is more difficult to solve than the classical parallel batch processing machine scheduling problem with compatible product families or incompatible product families. These restrictions mean that the existing methods cannot be applied into real-world factories directly. Consequently, this paper proposes a mixed integer programming model to solve the BTSP exactly. In addition, two efficient solution procedures which solve the BTSP are also presented.

Application of a genetic algorithm to n-K power system security assessment

This paper addresses the security assessment of power systems when the simultaneous loss of K components is considered. The problem is formulated as a bilevel program. The upper-level optimization identifies a set of simultaneous out-of-service components in the power system, whereas the lower-level optimization models the reaction of the system operator against the outages selected in the upper level. The system operator reacts by determining the optimal power system operation under contingency. Due to the inherent nonconvexity and nonlinearity of the resulting bilevel problem, efficient solution procedures are yet to be explored. A genetic algorithm is proposed in this paper to attain high-quality near-optimal solutions with moderate computational effort. The modeling flexibility provided by this evolution-inspired methodology makes it suitable for this kind of bilevel programming problems. Numerical results demonstrate the effectiveness of the proposed approach in the identification of critical power system components.

Tradeoff Analysis for Optimal Multiobjective Inventory Model

Deterministic inventory model, the economic order quantity (EOQ), reveals that carrying inventory or ordering frequency follows a relation of tradeoff. For probabilistic demand, the tradeoff surface among annual order, expected inventory and shortage are useful because they quantify what the firm must pay in terms of ordering workload and inventory investment to meet the customer service desired. Based on a triobjective inventory model, this paper employs the successive approximation to obtain efficient control policies outlining tradeoffs among conflicting objectives. The nondominated solutions obtained by successive approximation are further used to plot a 3D scatterplot for exploring the relationships between objectives. Visualization of the tradeoffs displayed by the scatterplots justifies the computation effort done in the experiment, although several iterations needed to reach a nondominated solution make the solution procedure lengthy and tedious. Information elicited from the inverse relationships may help managers make deliberate inventory decisions. For the future work, developing an efficient and effective solution procedure for tradeoff analysis in multiobjective inventory management seems imperative.

Earthquake time-frequency analysis using a new compatible wavelet function family

Earthquake records are often analyzed in various earthquake engineering problems, making time-frequency analysis for such records of primary concern. The best tool for such analysis appears to be based on wavelet functions; selection of which is not an easy task and is commonly carried through trial and error process. Furthermore, often a particular wavelet is adopted for analysis of various earthquakes irrespective of record's prime characteristics, e.g. wave's magnitude. A wavelet constructed based on records' characteristics may yield a more accurate solution and more efficient solution procedure in time-frequency analysis. In this study, a low-pass reconstruction filter is obtained for each earthquake record based on multi-resolution decomposition technique; the filter is then assigned to be the normalized version of the last approximation component with respect to its magnitude. The scaling and wavelet functions are computed using two-scale relations. The calculated wavelets are highly efficient in decomposing the original records as compared to other commonly used wavelets such as Daubechies2 wavelet. The method is further advantageous since it enables one to decompose the original record in such a way that a clear time-frequency resolution is obtained.

Optimal pricing and ordering policies for deteriorating items with multivariate demand under trade credit and inflation

In this paper we develop an extended economic order quantity model for deteriorating items under inflation and permissible delay in payments where demand rate is a linear function of price and decreases negative exponentially with time. The mathematical models are derived to determine the optimal replenishment and pricing policies over a finite planning horizon under two different trade credit period circumstances. An efficient solution procedure is presented to determine the optimal number of replenishment, the cycle time and selling price. Thus the optimal order quantity and the total present value of profits are obtained. Finally, a numerical example is given to illustrate the theoretical results and sensitivity analysis with respect to major parameters is also performed.

A SIMPLE based discontinuous Galerkin solver for steady incompressible flows

In this paper we present how the well-known SIMPLE algorithm can be extended to solve the steady incompressible Navier–Stokes equations discretized by the discontinuous Galerkin method. The convective part is discretized by the local Lax-Friedrichs fluxes and the viscous part by the symmetric interior penalty method. Within the SIMPLE algorithm, the equations are solved in an iterative process. The discretized equations are linearized and an equation for the pressure is derived on the discrete level. The equations obtained for each velocity component and the pressure are decoupled and therefore can be solved sequentially, leading to an efficient solution procedure. The extension of the proposed scheme to the unsteady case is straightforward, where fully implicit time schemes can be used.Various test cases are carried out: the Poiseuille flow, the channel flow with constant transpiration, the Kovasznay flow, the flow into a corner and the backward-facing step flow. Using a mixed-order formulation, i.e. order k for the velocity and order k-1 for the pressure, the scheme is numerically stable for all test cases. Convergence rates of k+1 and k in the L2-norm are observed for velocity and pressure, respectively. A study of the convergence behavior of the SIMPLE algorithm shows that no under-relaxation for the pressure is needed, which is in strong contrast to the application of the SIMPLE algorithm in the context of the finite volume method or the continuous finite element method. We conclude that the proposed scheme is efficient to solve the steady incompressible Navier–Stokes equations in the context of the discontinuous Galerkin method comprising hp-accuracy.

A possibilistic multiple objective pricing and lot-sizing model with multiple demand classes

We address an inventory-marketing system to determine the production lot size, marketing expenditure and selling prices where a firm faces demand from two or more market segments in which the firm can set different prices. Considering pricing, marketing and lot-sizing decisions simultaneously, the model maximizes the profit and return on inventory investment under multiple time varying demand classes. The model is formulated as a fuzzy non-linear multi-objective one where some parameters are ill-known and modeled by fuzzy numbers. A hybrid possibilistic-flexible programming approach is proposed to handle imprecise data and soft constraints concurrently. After transforming the original model into an equivalent multi-objective crisp model, it is then converted to a classical mono-objective one by a fuzzy goal programming method. An efficient solution procedure using particle swarm optimization (PSO) is also provided to solve the resulting non-linear problem.

Application of a fuzzy multilevel multiobjective production planning model in a network product manufacturing supply chain

This article formulates a novel fuzzy multilevel multiobjective production planning model for a supply chain under a fuzzy environment. An efficient two-phase interactive solution procedure is developed to obtain a good solution that maximizes the total supply chain profit and the satisfactory degree. The proposed solution procedure, modified from Sakawa et al.’s interactive fuzzy programming approach, can be easily adopted by practitioners. Through a negotiation case study, a well-known network product manufacturing supply chain in Taiwan is presented to demonstrate the effectiveness and aptness of the proposed model and the solution procedure, as compared with Sakawa et al.’s method with only one objective at the manufacturer level. Finally, several important findings and managerial implications are drawn from the results of this study.

Production scheduling with outsourcing scenarios: a mixed integer programming and efficient solution procedure

When market demand exceeds the company's capacity to manufacture, outsourcing is commonly considered as an effective alternative option. In traditional scheduling problems, processing of received orders is just possible via in-house resources, while in practice, outsourcing is frequently found in various manufacturing industries, especially in electronics, motor and printing companies. This paper deals with the scheduling problem, minimising the cost of outsourcing and a scheduling measure represented by weighted mean flow time, in which outsourcing of manufacturing operations is allowed through subcontracts. Each order can be either scheduled for in-house production or outsourced to an outside supplier in order to meet customer due dates. In this problem, not only should the sequence of orders be determined, but also decision on picking the jobs for outsourcing, selecting the appropriate subcontractor, and scheduling of the outsourced orders are considered as new variables. To formulate the given problem, four different outsourcing scenarios are derived and mixed integer programming models are developed for each one separately. Furthermore, to solve the suggested problem, a computationally effective team process algorithm is devised and then a constraint handling technique is embedded into the main algorithm in order to ensure satisfaction of customer due dates. Numerical results show that the suggested approach possesses high global solution rates as well as fast convergence.

Adaptive task-space metal strip-flatness control in cold multi-roll mill stands

The automatic flatness control system applied to cold multi-roll mills for the production of metal strips has been subject of research efforts in many directions since the last 30 years. An innovative multivariable control approach for this application context is presented by means of which potential stability problems of controllers based on least mean squares are addressed. The proposed methodology decomposes the array of strip-elongation measurements produced by a conventional shape-meter into orthogonal components corresponding to the main actuator directions in order to reduce the dimensionality of the problem. Then, the control actions are computed by solving a prioritized constrained quadratic optimization problem. In this regard, the control problem is reformulated within a task-space control formalism – originally conceived in the robotics context – for which very efficient solution procedures do exist. Furthermore, in order to account for the model uncertainties that typically affects this kind of systems, the model of the process is adapted on-line by a numerically robust technique. The adaptive task-space flatness control scheme dealt with in the paper has been already commissioned in several installations having different actuator configurations and the experimental results shows its effectiveness and its easy configurability.

Model and algorithm for fuzzy joint replenishment and delivery scheduling without explicit membership function

We study a joint replenishment and delivery scheduling (JRD) problem in which a central warehouse serves n-retailers in the presence of vague operational conditions such as ordering cost and inventory holding cost. In the proposed fuzzy set-based approach, an exact membership function is not assumed and instead can be approximated using piecewise linear functions based on alpha level sets because of their easy handling and efficiency. Subsequently, the fuzzy total cost is defuzzified by the widely used signed distance method to ranking fuzzy numbers. However, due to the JRD's difficult mathematical properties, efficient and effective solution procedures for the problem have eluded researchers. To find an optimal solution, an effective and efficient differential evolution (DE) algorithm is designed. After determining the appropriate parameters of the DE by parameter tuning test, the effectiveness of the DE is verified by numerical examples. We compare the DE with the available best approach and results show that DE can solve this non-deterministic polynomial hard problem in a robust way with a high convergence rate and low average error.

Convergence analysis of an iterative algorithm for a class of constrained dynamic problems

In this paper, we consider numerical simulation to a class of constrained dynamic problems where the overall dynamics are determined by the interactions between two sub-systems. We present an iterative algorithm that naturally decouples the computation of the two sub-systems and that ensures an accurate and efficient solution procedure. We conduct rigorous error analysis for the convergence of the iterative algorithm, and verify the analytical results through careful numerical tests.