ABC β–a heuristic for dynamic capacitated lot sizing with random demand under a fill rate constraint

This paper deals with the dynamic multi-item capacitated lot-sizing problem (CLSP) with random demand over a finite discrete time horizon. Unfilled demands are backordered. It is assumed that a fill rate constraint is in effect. We propose a heuristic solution procedure called ABC _β that extends the A/B/C heuristic introduced by Maes and Van Wassenhove for the deterministic CLSP to the case of random demands.     

A Framework For Probabilistic Vehicle Routing

The stochastic vehicle routing problem is a problem of considerable current importance in operations research and industrial engineering. The basic problem is to determine a fixed set of vehicle routes of minimal expected total distance. All vehicles must leave from and eventually return to a central depot, and capacity constraints and probabilistic customer demands must be satisfied. In previous work, we assumed that the demand at each node i could be modeled by a Poisson distribution with mean Λi and that demands at nodes are mutually independent. We then developed an efficient heuristic solution procedure which was quite effective in generating an excellent set of fixed vehicle routes, as evidenced by extensive computational results. With this previous work as a starting point, in this paper we investigate solution procedures for the case where other appropriate probability distributions are assumed. In addition, we present analytical results describing the various relationships between design parameters and provide a framework for performing perturbation analysis. Finally, we focus on a more flexible model in which demands are correlated.     

A DISCRETE LOCATION ASSIGNMENT PROBLEM WITH CONGESTION

Given a set of sites, this paper deals with the selection of sites for installing facilities and the assignment of customers to them. The customers have random demands for service and form finite source queues at the installed facilities. The objective is to minimize the expected total cost per unit of time consisting of travel cost, waiting cost for service, and fixed cost for installing and maintaining the facilities. A heuristic algorithm is developed. Computational results supporting the efficiency and accuracy of the heuristic are included. Under specific conditions, the problem is reduced to a linear integer programming problem and is solved by a branch and bound algorithm.     

Inventory control of raw materials under stochastic and seasonal lead times

Most inventory modelling has assumed stochastic demands and constant lead times. However, here we consider a problem for which the opposite situation holds; namely, there is a known constant demand rate, but lead times are random variables. Moreover, the probability distributions of the lead times change in a seasonal fashion. Also, shortages of raw materials result in lost sales. The goal of this paper is to propose heuristic methods for minimizing the expected costs in such a situation. This study was motivated by a problem of management of raw material at a sawmill.     

Replenishment planning in discrete-time, capacitated, non-stationary, stochastic inventory systems

In this paper, we examine a single-product, discrete-time, non-stationary, inventory replenishment problem with both supply and demand uncertainty, capacity limits on replenishment quantities, and service level requirements. A scenario-based stochastic program for the static, finite-horizon problem is presented to determine replenishment orders over the horizon. We propose a heuristic that is based on the first two moments of the random variables and a normal approximation, whose solution is compared with the optimal from a simulation-based optimization method. Computational experiments show that the heuristic performs very well (within 0.25% of optimal, on average) even when the uncertainty is non-normal or when there are periods without any supply. We also present insights obtained from sensitivity analyses on the effects of supply parameters, shortage penalty costs, capacity limits, and demand variance. A rolling-horizon implementation is illustrated.     

Integration of vendor selection into production and remanufacturing planning subject to emission constraints

This paper presents a new model formulation that incorporates vendor selection into production and remanufacturing planning subject to emission constraints. The objective is to determine a feasible production and remanufacturing plan at minimal cost. In each period, the given external demand must be satisfied for both new and remanufactured products. Remanufactured products can be substituted by new products, but not vice versa. When a product is (re)manufactured, the appropriate machine must be set up, which entails set-up costs and/or set-up time. The procurement of raw material that is offered by several vendors at different prices is integrated into this planning problem. To solve this integrated production and remanufacturing planning problem, we apply two solution approaches based on mathematical programming: first, a combination of column generation and a period-oriented fix-and-relax heuristic and second, an adapted fix-and-optimise heuristic. The results of our numerical investigation demonstrate the high solution quality of both solution approaches.     

Analysis and solution to the single-level batch production smoothing problem

Many companies use mixed-model production systems running under the Just-in-Time philosophy in order to efficiently meet customer demands for a variety of products. Such systems require demand be stable and production sequence be leveled. The production smoothing problem aims at finding level schedules in which the appearances of products are dispersed over the horizon as uniformly as possible. In this paper, the production smoothing problem is extended to a more general manufacturing environment where a single machine can be identified as either the final or the bottleneck stage of the system and products may have arbitrary non-zero setup and processing time requirements on this single machine. An optimization model is built for the problem and a two phase solution methodology is developed. The first phase problem is shown to be NP-hard and a parametric heuristic procedure is proposed for its solution. In contrast, the second phase problem is shown to be efficiently solvable and currently available solution methods are adopted from the literature. A computational study is designed to test the proposed two phase solution methodology and also the parametric heuristic procedure. Computational results show that the proposed two phase solution methodology enables effective and efficient control of the studied manufacturing system, and the heuristic procedure developed for the first phase problem is time efficient and promises near optimal solutions for a variety of test instances.     

The effect of the stabilization period on the economic lot scheduling problem

The Economic Lot Scheduling Problem (ELSP) is the problem of scheduling production of several items in a single facility, so that demands are met without stockouts or backorders, and the long run average inventory carrying and setup costs are minimized. One of the general assumptions in the ELSP is that the yield rates of a given manufacturing process are constant, or 100%, after setup. However, this assumption may not be true for certain manufacturing processes, in which the yield rates are quite low just after setup, and then increase over time. This period is called a stabilization period and yield rates gradually increase during this period until they reach the target rates, which are set empirically or strategically. The purpose of this paper is to clarify the effect of the stabilization period by applying the stabilization period concept to the ELSP, which has been widely applied to many production systems. In this paper, the problem is tackled in three stages: Firstly, we formulate a model and develop an algorithm, which provides a lower bound for a minimum cost. Secondly, we develop a heuristic procedure using the time-varying lot size approach. Finally, we solve a special case of the ELSP to find an upper bound using the common cycle approach.     

Initial allocation compensation algorithm for redundancy allocation: The scanning heuristic

The tiny feature size in current semiconductor integrated circuits naturally requires redundancy strategies to improve manufacturing yield and operating reliability. To find an optimal redundancy architecture that provides maximum yield and reliability is a trade-off problem. In the reliability optimization field, this type of problem is generally called a redundancy allocation problem. In this paper, we propose a new iterative algorithm, the scanning heuristic, to solve the redundancy allocation problem. The solution quality of conventional iterative heuristics is highly dependent on the initial starting point of the algorithm employed. To overcome this weakness, the scanning heuristic systematically divides the original solution space into several small bounded solution spaces. The local optimum in each divided solution space then becomes a candidate for the final solution. The experimental results demonstrate that the proposed heuristic, and subsequently some combinations of heuristics, are superior to existing heuristics in terms of solution quality.     

Scheduling doctors' appointments: optimal and empirically-based heuristic policies

Consider the problem facing a doctor (or other service provider) who is setting patient appointment times in the presence of random service times. He or she must balance the patients' waiting times (if the appointments are scheduled too closely together) against the doctor's idle time (if the appointments are spaced too far apart). Although this problem is fairly intractable, this paper uses the structure of the optimal solution as the basis for a simple closed-form heuristic for setting appointment times. Over a wide test bed of problems, this heuristic is shown to perform on average within 2% (and generally within 0.5%) of the optimal policy.     

The Buyer-Vendor Coordination Problem: Modeling Inbound and Outbound Cargo Capacity and Costs

In this paper, we generalize the deterministic demand buyer-vendor coordination problem to simultaneously consider cargo capacity constraints and general inbound/outbound transportation costs. To this end, we first consider a replenishment cost structure that includes a fixed cost as well as a stepwise inbound freight cost for the vendor. We then extend our results to consider the case where both the vendor and the buyer are subject to this freight cost structure. Hence, in the second model, both the inbound and the outbound transportation costs/constraints of the buyer-vendor pair are modeled explicitly. For each case, we provide heuristic algorithms with promising error bounds. The error bounds for these heuristic methods are 6 and 25%, respectively. Using the costs of these heuristics as upper bounds, we also develop finite time exact solution procedures.     

Application of simulated annealing to a linear model forthe formulation of machine cells ingroup technology

The central issue in group technology is the cell formation problem, which involves the grouping of parts into families and machines into cells, so that parts with similar manufacturing (and design) attributes are identified and processed by dedicated cells of machines. In the present work, the cell formation problem is modelled as a linear integer programming problem with the objective of minimizing the number of intercellular moves subject to cell-size constraints and taking into account the machine operation sequence of each part. An interesting feature of the proposed formulation is that there is no need of specifying a priori the number of cells to be used, which is automatically adjusted within the solution procedure. A very efficient random search heuristic algorithm, based on the simulated annealing method, is adopted for its solution. The heuristic is tested on a number of problems and its performance is evaluated. Subsequently, a straight forward model is presented to identify the families of parts which are to be processed by the corresponding machine cells.     

Locating capacitated facilities to maximize captured demand

We consider the problem of locating a set of facilities on a network to maximize the expected number of captured demand when customer demands are stochastic and congestion exists at facilities. Customers travel to their closest facility to obtain service. If the facility is full (no more space in the waiting room), they attempt to obtain service from the next-closest facility not yet visited from its current position on the network. A customer is lost either when the closest facility is located too far away or all facilities have been visited. After formulating the model, we propose two heuristic procedures. We combine the heuristics with an iterative calibration scheme to estimate the expected demand rate faced by the facilities: this is required for evaluating objective function values. Extensive computational results are presented.     

Lot streaming and scheduling multiple products in two-machine no-wait flowshops

We consider the problem of minimizing makespan in two-machine no-wait flowshops with multiple products requiring lot streaming. A “product” (or lot) consists of many identical items. Lot streaming (lot sizing) is the process of creating sublots (or transfer batches to move the completed portion of a production )sublot to downstream machines so that operations can be overlapped. The number of sublots for each product is fixed. When the flowshop produces only a single product, we obtain optimal continuous-sized sublots. It is shown that these sublot sizes are also optimal for the problem of simultaneous lot streaming and scheduling of multiple products. The optimal scheduling of products can be accomplished by application of the algorithm due to Gilmore and Gomory [1]. Then, we devise an efficient heuristic for the problem of simultaneous lot streaming (finding optimal integer-sized sublots) and scheduling of multiple products. Computational results indicate that this heuristic can consistently deliver close-to-optimal solutions for the problem. A comparison of this heuristic is also made with a heuristic that first divides items belonging to each product into nearly equal-sized sublots and then constructs a schedule for such sublots. Finally, we extend our solution procedures to a traditional and more general lot streaming model, where the number of sublots for each product is a decision variable.     

A simple and effective heuristic for the resource constrained project scheduling problem

This paper investigates the development and application of a simple heuristic to the resource constrained project scheduling problem (RCPSP). This computer heuristic, which is based on the COMSOAL heuristic, constructs a feasible solution at each iteration and chooses the best solution of several iterations. Although COMSOAL was originally a solution approach for the assembly-line balancing problem, it can be extended to provide solutions to the resource allocation problem. The Modified COMSOAL technique presented in this paper uses priority schemes intermittently with a random selection technique. This hybrid of randomness and priority scheme allows a good solution to be found quickly while not being forced into the same solution at each iteration. Several different priority schemes are examined within this research. The COMSOAL heuristic modified with the priority schemes heuristic was tested on several established test sets and the solution values are compared with both known optimal values and the results of several other resource allocation heuristics. In the vast majority of cases, the Modified COMSOAL heuristic outperformed the other heuristics in terms of both average and maximum percentage difference from optimal. The Modified COMSOAL heuristic seems to have several advantages over other RCPSP heuristics in that it is easy to understand, easy to implement, and achieves good results.     

A fiber-bundle model for the continuum deformation of brittle material

The deformation of brittle material is primarily accompanied by micro-cracking and faulting. However, it has often been found that continuum fluid models, usually based on a non-Newtonian viscosity, are applicable. To explain this rheology, we use a fiber-bundle model, which is a model of damage mechanics. In our analyses, yield stress was introduced. Above this stress, we hypothesize that the fibers begin to fail and a failed fiber is replaced by a new fiber. This replacement is analogous to a micro-crack or an earthquake and its iteration is analogous to stick–slip motion. Below the yield stress, we assume that no fiber failure occurs, and the material behaves elastically. We show that deformation above yield stress under a constant strain rate for a sufficient amount of time can be modeled as an equation similar to that used for non-Newtonian viscous flow. We expand our rheological model to treat viscoelasticity and consider a stress relaxation problem. The solution can be used to understand aftershock temporal decay following an earthquake. Our results provide justification for the use of a non-Newtonian viscous flow to model the continuum deformation of brittle materials.     

An efficient heuristic approach for parallel machine scheduling with job splitting and sequence-dependent setup times

In this paper, we consider a simplified real-life identical parallel machine scheduling problem with sequence-dependent setup times and job splitting to minimize makespan. We propose a heuristic to solve this problem. Our method is composed of two parts. The problem is first reduced into a single machine scheduling problem with sequence-dependent setup times. This reduced problem can be transformed into a Traveling Salesman Problem (TSP), which can be efficiently solved using Little's method. In the second part, a feasible initial solution to the original problem is obtained by exploiting the results of the first part. This initial solution is then improved in a step by step manner, taking into account the setup times and job splitting. We develop a lower bound and evaluate the performances of our heuristic on a large number of randomly generated instances. The solution given by our heuristic is less than 4.88% from the lower bound.     

Estimation of service life on the basis of a model of damage accumulation

We analyze interval estimates for the bounds of service life in the problem of damage accumulation with the help of a model based on the analysis of nonlinear phenomenological differential equations. The solution of this problem is obtained within the framework of the method of stochastic differential equations deduced as a generalization of the Kachanov-Rabotnov model of damage accumulation. By using the methods of the theory of stochastic differential equations, we find the variance of the estimate for the bounds of the periods of damage accumulation as a function of the parameters of the stochastic process. We also estimated the mean time to fracture for a statistically homogeneous rod subjected to constant loading taking into account the random component of the load. Petrozavodsk State University, Petrozavodsk, Russia. Translated from Problemy Prochnosti, No. 1, pp. 151–156, January–February, 2000.     

A Dual-based Heuristic for the Simple Facility Location Problem With Stochastic Demand

This paper deals with a stochastic version of the simple facility location problem where the demands of customers are random variables. Under the assumption of step function type distribution of demands, the problem is shown to be approximated by a mixed 0-1 linear programming problem. A heuristic procedure is developed to solve the problem, which successfully extends the well known dual-based approach by Bilde & Krarup, and Erlenkotter. Computational results with 20 test problems are presented to demonstrate the effectiveness of the proposed heuristic.     

Capacitated lot-sizing with sequence dependent setup costs

In this paper we consider a single-stage system where a number of different items have to be manufactured on one machine. Expenditures for the setups depend on the sequence in which items are scheduled on the machine. Holding costs are incurred for holding items in inventory. The demand of the items has to be satisfied without delay, i.e. shortages are not allowed. The objective is to compute a schedule such that the sum of holding and setup costs is minimized with respect to capacity constraints. For this problem which we call capacitated lot-sizing problem with sequence dependent setup costs (CLSD) we formulate a new model. The main differences between the new model and the discrete lot-sizing problem with sequence dependent setup costs (DLSDSD), introduced by Fleischmann, is that continuous lot-sizes are allowed and the setup state can be preserved over idle time. For the solution of the new model we present a heuristic which applies a priority rule. Since the priority values are affected by two significant parameters, we perform a local search in the parameter space to obtain low cost solutions. The solution quality is analyzed by a computational study. The comparison with optimal solutions of small instances shows that the solution quality of our heuristic is acceptable. The Fleischmann approach for the DLSPSD computes upper bounds for our new problem. On the basis of larger instances we show that our heuristic is more efficient to solve the CLSD.