Stochastic leadtimes in two-level distribution-type networks

Shortages of assembly parts often arise from late arrivals of one or more batches of components. We address the problem of determining planned leadtimes in two-level assembly systems with stochastic leadtimes, with the objective of minimizing the sum of inventory holding costs and tardiness costs. An algorithm is developed which exploits properties of the objective function to find optimal solutions. Computational results indicate that optimal solutions often have negative safety times for at least one of the components, as well as substantial safety times for the assembly stage.

We consider the NP-hard problem of scheduling jobs on a single machine about an unrestricted due date to minimize total weighted earliness and tardiness cost. Jobs are grouped into families where jobs in the same family share a setup; a setup time is required between the processing of two jobs from different families. Each job has an earliness penalty rate and a tardiness penalty rate that are allowed to be arbitrary. These rates are assessed on a per-period basis when the completion time deviates from its due date. In this paper, we generalize properties from the literature that characterize the structure of an optimal schedule, present a lower bound, propose a branch and bound algorithm and a beam search procedure, and report results from a computational experiment. We find that optimal solutions can be quickly obtained for smaller problem instances. For large problems, we find high quality solutions within a few minutes of CPU time.

We consider the problem of scheduling n jobs on a single machine. Each job i has a processing time p/sub i/, a weight w/sub i/, and a due date D/sub i/, which is a fuzzy number with a triangular membership function. The problem is to determine: (i) a job sequence, and (ii) a set of idle times each before one job, so as to minimize the total weighted earliness and tardiness cost under the fuzzy due dates. We first introduce a fuzzy distance function to measure the deviation of the completion time of a job from its fuzzy due date. We show that, given a job sequence, the problem of determining the optimal idle times is a continuous and convex optimization problem with a differentiable objective function, although the objective function after applying the fuzzy distance measure becomes nonlinear. We devise a genetic algorithm (GA) to tackle the problem, using a pigeon-hole coding scheme to represent a sequence and a nonlinear optimizer to determine the idle times. We evaluate the solutions obtained by such a GA as compared to the solutions obtained by treating the due dates as crispy numbers equal to the mean values of its fuzzy partners.

We consider production allocation in a discrete manufacturing system formulated as an open queueing network (OQN) composed of some GI/G/1 queueing systems. The lead time performance, such as expectation and variance, in the manufacturing system has been analyzed and discussed using the OQN theory in the previous works. Through the improvement of lead time performance, we can discuss the decrease of the tardiness cost for delivery in the manufacturing system. Then, although the distribution of lead time is frequently required in order to evaluate the tardiness cost for delivery, it is difficult to understand the distribution of lead time exactly. In this article, we have a challenge of assessing the tardiness cost by using only the limited information, such as the expectation and variance of lead time. Concretely, we evaluate the upper bound of tardiness cost by combining the distribution free approach (DFA) with the OQN analysis. Then, a new optimal allocation policy for the production and tardiness costs is proposed.

We study the scheduling of multiple tasks under varying processing costs and derive a priority rule for optimal scheduling policies. Each task has a due date, and a non‐completion penalty cost is incurred if the task is not completely processed before its due date. We assume that the task arrival process is stochastic and the processing rate is capacitated. Our work is motivated by both traditional and emerging application domains, such as construction industry and freelance consulting industry. We establish the optimality of Shorter Slack time and Longer remaining Processing time (SSLP) principle that determines the priority among active tasks. Based on the derived structural properties, we also propose an effective cost‐balancing heuristic policy and demonstrate the efficacy of the proposed policy through extensive numerical experiments. We believe our results provide operators/managers valuable insights on how to devise effective service scheduling policies under varying costs.

Mathematical model for dynamic suppliers’ selection strategy in multi-period supply planning with lead-times uncertainty

We develop a queuing model to evaluate production and subcontracting policies commonly used in an assembled-to-order manufacturing system with service level constraints. The manufacturer determines production and inventory levels for the components using a base stock policy, and inventory is replenished from suppliers that have stochastic lead times. Customer demands for the assembled products can be satisfied only when all the required components are available and unsatisfied demands are backordered. The manufacturer offers high level of service to the customer and reserves the option, if necessary, to produce components internally at a faster rate and higher cost. Using queuing models we compare the performance of two policies: on-hand inventory based policy and leadtime based policy and compare these policies to obtain the condition where each policy is better than the other.

This paper considers the problem of real-time dispatching of a fleet of automated guided vehicles (AGVs) with battery constraints. AGVs must be immediately assigned to transport requests, which arrive randomly. In addition, the AGVs must be repositioned and recharged, awaiting future transport requests. Each transport request has a soft time window with late delivery incurring a tardiness cost. This research aims to minimize the total costs, consisting of tardiness costs of transport requests and travel costs of AGVs. We extend the existing literature by making a distinction between parking and charging nodes, where AGVs wait idle for incoming transporting requests and satisfy their charging needs, respectively. Also, we formulate this online decision-making problem as a Markov decision process and propose a solution approach based on deep reinforcement learning. To assess the quality of the proposed approach, we compare it with the optimal solution of a mixed-integer linear programming model that assumes full knowledge of transport requests in hindsight and hence serves as a lower-bound on the costs. We also compare our solution with a heuristic policy used in practice. We assess the performance of the proposed solutions in an industry case study using real-world data.

In this paper, we study a two-dimensional vehicle loading and routing problem in which customer orders with deadlines become available for dispatch as per their release dates. The objective is to minimize the sum of transportation, inventory, and tardiness costs while respecting various loading and routing constraints. This scenario allows us to study various tradeoffs that tend to arise due to temporal order aggregation across release dates. We thereby propose an integrated mathematical formulation to simultaneously model both the routing and loading requirements of the problem at hand. Specifically, as the problem is NP-hard, we propose a scatter search-based heuristic approach to solve large-size instances. Further, its performance is enhanced using problem-specific procedures and strategic oscillation approaches. Additionally, the numerical experiments illustrate the influence of cost structures on both the optimal loading configurations along with the optimal routes. Importantly, our experiments also suggest that the proposed scatter search method can produce good-quality solutions in less time.

In this study, we consider a scheduling extension for the two-stage cutting stock problem with the integration of order due dates. The two-stage cutting stock problem arises when technical restrictions inhibit demanded items to be cut from stock rolls directly, and hence require the cutting process to be done in two subsequent stages. The mathematical model proposed for the due date extension aims to determine a cutting plan which not only minimizes the number of stock rolls used but also reduces tardiness and earliness costs incurred. Preliminary results have shown that the modeling approach used is capable of overcoming difficulties caused by the dependencies between stages.

Several distributed scheduling policies are analyzed for a large semiconductor manufacturing facility, where jobs of wafers, each with a desired due date, follow essentially the same route through the manufacturing system, returning several times to many of the service centers for the processing of successive layers. It is shown that for a single nonacyclic flow line the first-buffer-first-serve policy, which assigns priorities to buffers in the order that they are visited, is stable, whenever the arrival rate, allowing for some burstiness, is less than the system capacity. The last-buffer-first-serve policy (LBFS), where the priority ordering is reversed, is also stable. The earliest-due-date policy, where priority is based on the due date of a part, as well as another due-date-based policy of interest called the least slack policy (LS), where priority is based on the slack of a part, defined as the due date minus an estimate of the remaining delay, are also proved to be stable.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Multi-objective scheduling in labor-intensive manufacturing systems

Optimal and Near Optimal Control of a Two-Part-Type Stochastic Manufacturing System with Dynamic Setups

Malaria is a major health concern for many developing countries. Designing strategies for efficient distribution of malaria medications, such as Artemesinin Combination Therapies, is a key challenge in resource constrained countries. This paper develops a solution methodology that integrates strategic‐level and tactical‐level models to better manage pharmaceutical distribution through a three‐tier centralized health system, which is common to sub‐Saharan African countries. At the strategic level, we develop a two‐stage stochastic programming approach to address the problem of demand uncertainty. In the first stage, an initial round of shipments is sent before the malaria season to each local clinic from district hospitals, which receive medications from regional warehouses. After the malaria season begins, a recourse action is triggered to avoid shortages in the form of (i) lateral transshipment or (ii) delayed shipment. The optimal solutions developed by the strategic model identify small clinic clusters possessing exclusive transshipment policies. Therefore, we decompose the problem at the tactical level, solving each clinic cluster independently using a Markov decision process approach to determine optimal periodic transshipment policies. A case study of our proposed distribution system is performed for 290 facilities controlled by the Malawi Ministry of Health. Numerical analysis of Malawi's distribution system indicates that our proposed cluster‐based decomposition method could near optimally reduce shortage incidents. Moreover, such an approach is robust to challenges of developing countries such as slow paper‐based inventory review, uncertain transportation infrastructure, the need for equitable distribution, and seasonal and correlated demand associated with malaria transmission dynamics.

Open market and e-commerce change the environment of the manufacturing system. In fact, nowadays, vendors are facing a more and more flexible demand. At the same time, we have more accurate tools to study demand evolution and characteristics. This paper reports a methodology to adopt for optimizing the supply chain inventory management (SCIM) taking into account parameters characterizing this uncertain environment. This approach tends to reduce the cost of parameters changing when dealing with a flexible demand. We focus on the management of stochastic parameters characterizing the demand such as stochastic lead time, quantity and rate and other parameters such as delivery time. The objective fixed is to optimize the profit composed of unsatisfied demand, backlog, inventory and production costs. Since an analytical formula of the profit isn't possible, we use Monte Carlo simulation and genetic algorithms. Numerical results are given for two cases.