Vaughan Jones, Kolmogorov Complexity, and the New Complexity Landscape around Circuit Minimization

We survey recent developments related to the Minimum Circuit Size Problem and time-bounded Kolmogorov Complexity.

Multi-Item Production Lot Sizing with Postponement, External Source for Common Parts, and Adjustable Rate for End Products

This study considers a multi-item production lot-size problem incorporating postponement, an external source for common parts, and an adjustable-rate for end products. Dealing with product variety, timely requirements, and limited in-house capacity has led production managers to seek manufacturing schemes and utilization-reduction strategies that can help them meet customer needs, smoothen fabrication schedules, and lower overall manufacturing expenses. We propose a two-stage manufacturing scheme. The first stage produces common parts for multiproduct incorporating a partial supply from an outside contractor to reduce utilization/uptime. Stage two fabricates all end products using an adjustable-rate to reduce the uptime further. We build a model to characterize the problem’s features and use optimization methods to derive the optimal rotation cycle time in order to help managers make cost-effective lot-size decisions and allow manufacturers to gain competitive advantages. A numerical illustration validates the model’s capability and applicability. This study makes two important contributions: (1) It offers a decision-support model for studying such a particular batch-size problem and deciding the optimal rotation cycle time, and (2) it identifies the individual/collective influence of dual uptime-reduction strategies on the operating policy and various performance indexes to help facilitate managerial decision-making.

Models and Solution Algorithms for Efficient Truck Scheduling at Cross-docking Terminals with Time-sensitive Products

This dissertation focuses on the scheduling of trucks (both in- and outbound trucks) at a CDT, where some of the delivered products are perishable in nature. The short lifespan of perishable products (i.e., foods and drugs) poses critical challenges to the CDT operations management. Perishable goods are time-sensitive products that require minimal handling time to preserve their quality and profitability. Cross-docking is expected to facilitate the distribution of perishable products within supply chains. There are many challenges involved in the management of the cross-docking terminals with perishable products, including determination of the service order of the trucks (inbound and outbound) carrying perishable products, selection of preemption strategies for certain trucks (i.e., a given truck can leave the door, so another truck can be docked for service), allocation of suitable temporary storage space for products, quality loss due to late delivery or errors in temperature control.This dissertation aims to develop a mathematical model for scheduling the arriving trucks at a cross-dock terminal, taking product decay into consideration throughout the handling process. The objective of the mathematical model minimizes the total truck service cost, which includes (1) waiting cost; (2) service cost; (3) cost of product storage; (4) cost of delay in truck departure; and (5) the cost associated with the decay of products that are perishable in nature. A number of linearization techniques are discussed in order to linearize the original nonlinear mathematical model (where the nonlinearity is caused by the adopted product decay function). The complexity of the linearized model is evaluated in this dissertation. Moreover, the candidate solution approaches for the proposed mathematical model are described.The developed model was solved using the exact optimization technique. In particular, the model was solved to optimality using CPLEX. However, it was observed that the computational time increased as the problem size increased due to the model complexity. Four alternative solution approaches namely: (1) Evolutionary Algorithm (EA); (2) Variable Neighborhood Search (VNS); (3) Tabu Search (TS); and (4) Simulated Annealing (SA), which are common metaheuristic algorithms, were developed and compared with CPLEX using small-size problem instances. These metaheuristics were able to achieve optimal solutions for the small-size problem instances and required relatively low computational times. The metaheuristic algorithms were further compared, and EA was found to outperform the others (VNS, TS, and SA) based on the balance between the objective function and computational time values. A set of analyses were carried out using EA, and managerial insights that could be of interest to supply chain stakeholders were drawn. The proposed mathematical model, the developed EA, and the managerial insights could assist the CDT manager in making efficient and timely truck scheduling decisions in any planning horizon.