Hierarchical cross-training in work-in-process-constrained systems

We study Work-In-Process (WIP)-constrained flowlines staffed by partially cross-trained workers with hierarchical skill sets. We characterize the optimal worker-to-task assignment policy for CONWIP systems with two workers and general stochastic processing times. This leads us to the “fixed-before-shared” principle, which states that a flexible worker should process a task he/she is uniquely qualified for before helping other workers with shared tasks. To provide insights on the performance opportunity of hierarchical cross-training in systems with limited WIP, we provide a complete characterization of the optimal policy and closed-form expressions of the resulting throughput for the case of exponential processing times. We extend our results to the more general case of floater workers, and illustrate their applicability to various real-world systems. Our analysis shows that hierarchical cross-training can provide significant benefits, but should be implemented with care in WIP-constrained environments such as those making use of pull systems.     

Approximation algorithms for optimal purchase/inventory policy when purchase price and demand are stochastic

We consider a purchase/inventory control problem in which the purchase price and demand are stochastic, a common situation encountered by firms that replenish in a foreign currency or from commodity markets. More specifically, we assume that the demand follows a Poisson arrival process and that the log-price evolves according to a general Wiener process. Under these circumstances, the optimal policy is a state dependent base-stock policy that can be described as a series of threshold prices. An iterative procedure for determining the optimal thresholds has been derived earlier but, even for the simplest price process, the solution quickly becomes numerically intractable. To deal with this, we propose an approximation that allows us to derive simple heuristics for finding thresholds that are close to optimal. For certain price processes the heuristics are just a series of closed-form expressions. The computational complexity is reduced significantly, and the numerical study shows that the new heuristics perform considerably better than earlier suggested heuristics.     

Periodic-review inventory systems with random yield and demand: Bounds and heuristics

We revisit the infinite-horizon decision problem of a single-stage single-item periodic-review inventory system under uncertain yield and demand. It is known that under some mild conditions the optimal replenishment policy is of the threshold type: an order is placed if and only if the starting inventory is below a threshold value. Although the structure of the optimal policy is well known, there has been little discussion about the optimal order quantities and the order threshold. In this paper, we construct upper and lower bounds for the optimal threshold value and the optimal order quantities through solving one-period problems with different cost parameters. These bounds provide interesting insights into the impact of yield uncertainty on the optimal policy. Heuristics are developed based on these bounds. Detailed computational studies show that, under some conditions, the performance of the heuristics is very close to that of the optimal solution and better than that of existing heuristics in the literature.     

Production planning with stochastic seasonal demandand capacitated production

We consider a production/inventory problem with stochastic seasonal demand. A scarce resource limits production in each time period, and setup time is negligible. Linear and stationary costs are assessed for production, holding inventory, and stock-outs. The calculation of optimal solutions is difficult so heuristics are used. The heuristics used in business practice are shown to cost an average of 30% above optimal policy costs. A superior heuristic is constructed utilizing an analytic approximation for optimal policies that costs an average of 2% over optimal policy costs.     

Dynamic admission control for two customer classes with stochastic demands and strict due dates

We study a dynamic capacity allocation problem with admission control decisions of a company that caters for two demand classes with random arrivals, capacity requirements and strict due dates. We formulate the problem as a Markov decision process (MDP) in order to find the optimal admission control policy that maximises the expected profit of the company. Such a formulation suffers a state-space explosion. Moreover, it involves an additional dimension arising from the multiple possible order sizes that customers can request which further increases the complexity of the problem. To reduce the cardinality of possible policies, and, thus, the computational requirements, we propose a threshold-based policy. We formulate an MDP to generate such a policy. To deal with the curse of dimensionality, we develop threshold-based approximate algorithms based on the state-reduction heuristics with aggregation proposed previously. Our results reveal that for the majority of instances considered the optimal policy has a threshold structure. We then demonstrate the superiority of the proposed threshold-based approximate algorithms over two benchmark policies in terms of the generated profits and the robustness of the solutions to changes in operational conditions. Finally, we show that our proposed policies are also robust to changes in actual demand from its estimation.     

Task assignment in loosely‐coupled multiprocessor systems

Abstract

In loosely‐coupled multiprocessor systems, a parallel program has its modules distributedly assigned among the processors. The assignment policy is to minimize interprocessor communication cost and to balance the workload of processors. However, there exists conflict between these two criteria and a compromise must be made to obtain an optimal solution. In this paper, we propose a new task assignment model for distributed computing systems, and for solving the assignment problem based on partitioning graphs. The problem of finding an optimal solution had been shown to be in the class of NP‐complete. For the sake of computation efficiency, we propose some heuristics for obtaining suboptimal solutions.     

Building a cascade detector and its applications in automatic target detection

A hierarchical classifier (cascade) is proposed for target detection. In building an optimal cascade we considered three heuristics: (1) use of a frontier-following approximation, (2) controlling error rates, and (3) weighting. Simulations of synthetic data with various underlying distributions were carried out. We found that a weighting heuristic is optimal in terms of both computational complexity and error rates. We initiate a systematic comparison of several potential heuristics that can be utilized in building a hierarchical model. A range of discussions regarding the implications and the promises of cascade architecture as well as of techniques that can be integrated into this framework is provided. The optimum heuristic--weighting algorithms--was applied to an IR data set. It was found that these algorithms outperform some state-of-the-art approaches that utilize the same type of simple classifier.     

Dynamic allocation of communicating tasks in computational grids

This paper studies task allocation in computational grids operating in a dynamic and uncertain environment. Computational grids consist of loosely coupled heterogeneous resources or agents with finite buffer capacities. These grids are primarily used to process large-scale applications consisting of several interdependent tasks. The task allocation problem is modeled as an infinite horizon Markov decision process, with the resource service times and the task arrivals following general probability distributions. We explicitly consider the communication cost between agents incurred in coordinating the execution of interdependent tasks. We show that a stationary optimal policy exists for this task allocation problem. Furthermore, we develop an action elimination procedure for reducing the complexity of computational methods in finding the optimal policy. We also present a real-time heuristic policy based on certain structural properties of the problem. Finally, computational results are presented that compare the performance of the heuristic policy with respect to other approaches for allocating tasks in the grid. Results from this paper are also applicable to the task allocation problem in manufacturing and service areas such as distributed design, project management and supplier coalitions.     

A stochastic multi-item inventory model with unequal replenishment intervals and limited warehouse capacity

Managing inventory levels for multiple products that share warehouse capacity often presents significant coordination challenges. These coordination challenges are further compounded when multiple suppliers use different replenishment schedules for supplying the warehouse. To address these challenges, this paper studies stochastic inventory models for multiple items with both equal and unequal replenishment intervals under limited warehouse capacity. We propose three efficient and intuitively attractive heuristics. We show that these heuristics provide the optimal replenishment quantities in the case of equal replenishment intervals. For the general model, a numerical comparison of the heuristic solutions to the optimal solutions shows that the heuristics yield high quality solutions in very limited time.     

Heuristics for allocation of reconfigurable resources in a serial line with reliability considerations

We consider the allocation of reconfigurable resources in a serial line with machine failures. Each station is equipped with non-idling dedicated servers while the whole system is equipped with a finite number of reconfigurable servers. The reconfigurable servers are available to be assigned to any station and all servers are allowed to collaborate on a single job. We provide conditions for a policy to achieve throughput optimality. We also show in the two-station case that transition monotone optimal policies exist. We discuss heuristics based on the two-server model that reduce average holding costs significantly. These heuristics are compared to several heuristics from the literature via a detailed numerical study.     

A general quantity discount and supplier selection mixed integer programming model

Recently, new models and heuristics for exploiting quantity discounts have been proposed that are applicable in classical purchasing as well as in an e-business environment and can be implemented as part of an advanced planning system. These models can now handle both the single- and multi-item case with fixed cost to be shared among several products ordered at the same point in time from a single supplier. Furthermore, the supplier selection problem is addressed, i.e., how to best exploit quantity discounts over time offered by several suppliers. Last but not least, additional constraints on the buyer’s or on the supplier’s side may be included. While so far only purpose-built heuristics have been proposed for this generalized problem, we present a linear mixed integer programming (MIP) model, which not only represents the all-units discount but also the incremental discount case. Furthermore, the objective function chosen resolves (former) conflicts among proponents of a purely cost oriented and a cash flow oriented modeling approach. Computational tests show that our model yields near optimal solutions within a given CPU time limit by making use of a standard MIP solver.     

Effective heuristics for the single machine sequencing problem with ready times

In this paper we consider the single machine sequencing problem with different ready times in which the objective is to minimize the mean completion time (or mean flow time, or the sum of completion times, or the sum of flow times). We propose some heuristics for the problem and give conditions under which the heuristics give optimal sequences. A MILP formulation and a branch and bound procedure are used to generate optimal solutions for comparison with those which the heuristics generate. Computational testing shows that the heuristics yield excellent sequences in a very short time. Full computational details and results are given in this paper.     

Analysis of scheduling algorithms for master–slave systems

The master-slave paradigm finds important applications in many industrial settings. In the master-slave model considered in this paper a set of jobs is to be processed by a system of processors. Each job consists of a preprocessing task, a slave task and a postprocessing task that must be executed in this order. The pre- and postprocessing tasks are to be processed by a master processor, whereas the slave task is processed by a slave processor. We consider three different specifications for the relative order of pre- and postprocessing tasks; namely order preserving sequences, reverse order sequences, and sequences where no order constraint is imposed. For the problem of minimizing makespan in master-slave systems with multiple masters, we develop heuristic algorithms with good bounded performance, for all three order specifications. Our computational results indicate that the average performance of our heuristics is near optimal. Furthermore, we identify the production environment and workload characteristics that favor each order specification.     

A two-stage three-machine assembly scheduling problem with a position-based learning effect

The two-stage assembly scheduling problem has attracted increasing research attention. In many such problems, job processing times are commonly assumed to be fixed. However, this assumption does not hold in many real production situations. In fact, processing times usually decrease steadily when the same task is performed repeatedly. Therefore, in this study, we investigated a two-stage assembly position-based learning scheduling problem with two machines in the first stage and an assembly machine in the second stage. The objective was to complete all jobs as soon as possible (or to minimise the makespan, implying that the system can perform better and efficient task planning with limited resources). Because this problem is NP-hard, we derived some dominance relations and a lower bound for the branch-and-bound method for finding the optimal solution. We also propose three heuristics, three versions of the simulated annealing (SA) algorithm, and three versions of cloud theory-based simulated annealing algorithm for determining near-optimal solutions. Finally, we report the performance levels of the proposed algorithms.     

A simple heuristic for perishable item inventory control under non-stationary stochastic demand

In this paper, we study the single-item single-stocking location non-stationary stochastic lot sizing problem for a perishable product. We consider fixed and proportional ordering cost, holding cost and penalty cost. The item features a limited shelf life, therefore we also take into account a variable cost of disposal. We derive exact analytical expressions to determine the expected value of the inventory of different ages. We also discuss a good approximation for the case in which the shelf-life is limited. To tackle this problem, we introduce two new heuristics that extend Silver’s heuristic and compare them to an optimal Stochastic Dynamic Programming policy in the context of a numerical study. Our results demonstrate the effectiveness of our approach.     

Capacity-constrained reorder intervals for materials requirements planning systems

This paper develops a model for the reorder interval problem for general production systems with constant demand, multiple capacity constraints, commonality, non-instantaneous production, and non-nested reorder intervals. We present this model in the context of a materials requirements planning (MRP) system.

Four simple greedy heuristics are presented to find solutions to the model. A six-factor experiment with 192 test problems is used to evaluate the heuristics. The factors in the experiment included the procedures, number of items, capacity tightness, degree of commonality, setup cost to carrying cost ratio, and setup time to run time ratio. For smaller problems the heuristics are compared with optimal solutions found with an exact branch-and-bound algorithm. For larger problems, the heuristics are compared with a lower bound.

The results of the experiment show that the heuristics provide excellent solutions across all experimental factors. Computing times for the proposed heuristics appear to be practical even for realistic MRP environments with many thousands of items.     

Incorporating a delay mechanism in ordering policies into multi-echelon distribution systems

In this paper, we devise a framework for obtaining the optimal ordering policy in a single location, continuous-review inventory system with arbitrary inter-demand times. We show that it is optimal to order at demand arrival epochs only if the inter-demand time has a constant or decreasing failure rate. When the inter-demand time has an increasing failure rate, we show that the optimal policy is to delay the order. We then extend this policy to multi-echelon distribution systems consisting of one supplier and many retailers. Both decentralized and centralized systems are considered. We derive expressions and procedures for the evaluation of the total cost and the computation of optimal delay in all the considered settings. More importantly, we study the impact of our delay policy in all the settings. The numerical results indicate that for the single-location model, the optimal delay can significantly reduce the total cost. Results from the single-location model can be applied to the decentralized multi-echelon system, where the upstream supplier acts as a single-location system. The supplier order delay can also have a significant impact (either positive or negative) on the retailers' total cost as well as the system's total costs. Finally, the impact of supplier order delay is minimal in the centralized multi-echelon setting. We offer an intuitive explanation for this observation.     

Routing problem under the shared storage policy for unit-load automated storage and retrieval systems with separate input and output points

In this study the routing problem for unit-load automated storage and retrieval systems (AS/RSs) with separate input and output points is considered under the shared storage policy. The problem is to find an optimal travel route of a S/R (storage and retrieval) machine to process given storage and retrieval requests so that the total travel time is minimised, where the input and output points are possibly separate and the shared storage policy is assumed. We first give two types of formulations as 0–1 integer linear programming problems corresponding to two types of dwell point settings: the dwell point is the input point and the output point. Next, we propose a simple but efficient exact solution algorithm based on the formulations that utilises a general MILP (Mixed Integer Linear Programming) solver. Its efficiency is then demonstrated by numerical experiments. Instances with 400 items (200 for each storage and retrieval) are solved within 100 s.     

A heuristic for multi-item production with seasonal demand

A heuristic is developed for a common production/inventory problem characterized by multiple products, stochastic seasonal demand, lost sales, and a constraint on overall production. Heuristics are needed since the calculation of optimal policies is impractical for real-world instances of this problem. The proposed heuristic is compared with those in current use as well as optimal solutions under a variety of conditions. The proposed heuristic is both near optimal and superior to existing heuristics. The heuristic deviated from optimality by an average of 1.7% in testing using dynamic programming as a benchmark. This compares favorably against linear-programming-based heuristics and practitioner heuristics, which deviated from optimality by 4.5 to 10.6%.     

Multi-product inventory planning with downward substitution, stochastic demand and setup costs

In this paper we consider a single period multi-product inventory problem with stochastic demand, setup cost for production, and one-way product substitution in the downward direction. We model the problem as a two-stage integer stochastic program with recourse where the first stage variables determine which products to produce and how much to produce, and the second stage variables determine how the products are allocated to satisfy the realized demand. We exploit structural properties of the model and utilize a combination of optimization techniques including network flow, dynamic programming, and simulation-based optimization to develop effective heuristics. Through a computational study, we evaluate the performance of our heuristics by comparison with the corresponding optimal solution obtained from a large scale mixed integer linear program. The computational study indicates that our solution methodology can be very effective (98.8% on average) and can handle industrial-sized problems efficiently. We also provide several new qualitative insights on issues such as the effect of demand variance and cost parameters on the optimal number of products setup, the amount produced or inventoried, and the benefits of allowing substitution.