Supply Chain Network Design with Concave Costs: Theory and Applications

Many practical decision models can be formulated as concave minimization problems. Supply chain network design problems (SCNDP) that explicitly account for economies-of-scale and/or risk pooling often lead to mathematical problems with a concave objective and linear constraints. In this thesis, we propose new solution approaches for this class of problems and use them to tackle new applications. In the first part of the thesis, we propose two new solution methods for an important class of mixed integer concave minimization problems over a polytope that appear frequently in SCNDP. The first is a Lagrangian decomposition approach that enables a tight bound and a high quality solution to be obtained in a single iteration by providing a closed-form expression for the best Lagrangian multipliers. The Lagrangian approach is then embedded within a branch-and-bound framework. Extensive numerical testing, including implementation on three SCNDP from the literature, demonstrates the validity and efficiency of the proposed approach. The second method is a Benders approach that is particularly effective when the number of concave terms is small. The concave terms are isolated in a low dimensional master problem that can be efficiently solved through enumeration. The subproblem is a linear program that is solved to provide a Benders cut. Branch-and-bound is then used to restore integrality if necessary. The Benders approach is tested and benchmarked against commercial solvers and is found to outperform them in many cases. In the second part, we formulate and solve the problem of designing a supply chain for chilled and frozen products. The cold supply chain design problem is formulated as a mixed-integer concave minimization problem with dual objectives of minimizing the total cost, including capacity, transportation, and inventory costs, and minimizing the global warming impact that includes, in addition to the carbon emissions from energy usage, the leakage of high global-warming-potential refrigerant gases. Demand is modeled as a general distribution, whereas inventory is assumed managed using a known policy but without explicit formulas for the inventory cost and maximum level functions. The Lagrangian approach proposed in the first part is combined with a simulation-optimization approach to tackle the problem. An important advantage of this approach is that it can be used with different demand distributions and inventory policies under mild conditions. The solution approach is verified through extensive numerical testing on two realistic case studies from different industries, and some managerial insights are drawn. In the third part, we propose a new mathematical model and a solution approach for the SCNDP faced by a medical sterilization service provider serving a network of hospitals. The sterilization network design problem is formulated as a mixed-integer concave minimization program that incorporates economies of scale and service level requirements under stochastic demand conditions, with the objective of minimizing long-run capacity, transportation, and inventory holding costs. To solve the problem, the resulting formulation is transformed into a mixed-integer second-order cone programming problem with a piecewise-linearized cost function. Based on a realistic case study, the proposed approach was found to reach high quality solutions efficiently. The results reveal that significant cost savings can be achieved by consolidating sterilization services as opposed to decentralization due to better utilization of resources, economies of scale, and risk pooling

Integrated procurement and reprocessing planning for reusable medical devices with a limited shelf life

We present a new model formulation for a multiproduct dynamic order quantity problem with product returns and a reprocessing option. The optimization considers the limited shelf life of sterile medical devices as well as the capacity constraints of reprocessing and sterilization resources. The time-varying demand is known in advance and must be satisfied by purchasing new medical devices or by reprocessing used and expired devices. The objective is to determine a feasible procurement and reprocessing plan that minimizes the incurred costs. The problem is solved in a heuristic manner in two steps. First, we use a Dantzig-Wolfe reformulation of the underlying problem, and a column generation approach is applied to tighten the lower bound. In the next step, the obtained lower bound is transformed into a feasible solution using CPLEX. Our numerical results illustrate the high solution quality of this approach. The comparison with a simulation based on the first-come-first-served principle shows the advantage of integrated planning

Análise do desempenho de um centro de reprocessamento de dispositivos médicos recorrendo à simulação

Uma das atividades com maior impacto operacional nas unidades de saúde, i.e., nas clínicas e nos hospitais, é o reprocessamento de dispositivos médicos que, muito sucintamente, são instrumentos utilizados por profissionais de saúde para prevenir, diagnosticar ou tratar uma doença humana. Nos últimos anos, as unidades de saúde têm optado, de uma forma crescente, pela subcontratação desta atividade a centros de reprocessamento de dispositivos médicos (RUMEDs), pelos benefícios económicos e de segurança associados. Os RUMEDs têm como missão (i) garantir a fiabilidade e aptidão para uso de um dispositivo médico estéril e (ii) transportar tais dispositivos desde as unidades de saúde até às suas instalações. Atualmente, os RUMEDs enfrentam desafios de eficiência relacionados com a previsibilidade do que chega às suas instalações, sincronização dos processos de reprocessamento e elevados tempos de espera. O estudo de caso apresentado incide sobre um RUMED sediado em Lisboa e tem como objetivo avaliar o seu desempenho atual no que diz respeito ao cumprimento do nível de serviço acordado com as unidades de saúde suas clientes. Com base nesta avaliação, ainda era objetivo melhorar o desempenho global do reprocessamento de dispositivos médios. A simulação foi a ferramenta utilizada para avaliar o desempenho atual do RUMED e testar o impacto das propostas de melhoria. As propostas de melhoria desenvolvidas baseiam-se na filosofia Lean, assentes na eliminação de desperdícios, como os tempos de espera, e foram agregadas em seis cenários de três tipos. O Cenário do tipo A tem como base o nivelamento das chegadas dos dispositivos médicos ao RUMED e os Cenários do tipo B e C têm como finalidade testar a resposta do RUMED ao aumento do número de técnicos operacionais de esterilização nas zonas de descontaminação e de inspeção e embalamento, respetivamente. O cenário que, do ponto de vista operacional, mais beneficia o RUMED propõe (i) o nivelamento das chegadas dos dispositivos médicos; (ii) a alocação de mais dois técnicos operacionais de esterilização à zona de descontaminação para os turnos da manhã e noite face à situação atual e (iii) a alocação de apenas sete técnicos operacionais de esterilização à zona de inspeção e embalamento nos 3 turnos. Estima-se que ao adotar estas propostas, o RUMED cumpra o nível de serviço acordado com todas as unidades de saúde. No final, é realizada uma análise crítica dos cenários à luz dos objetivos enunciados e são propostas sugestões para utilizar em trabalhos futuros.Over the last years, reprocessing procedures have loomed to be the achilles heel of healthcare providers and facilities. This has forged many healthcare facilities to seek reprocessing units for medical devices. Medical devices can very briefly be defined as instruments used by healthcare professionals to prevent, diagnosis and treat a medical condition. These are specialized centers that have in place appropriate policies and procedures that are consistent with current healthcare standards and guidelines. Their mission is to (i) guarantee reliability and aptitude of sterile medical devices and (ii) to secure a safe transportation to their corresponded healthcare unit. Currently, reprocessing units for medical devices challenges are related to predictability of what arrives at its centers, synchronization of reprocessing processes and long waiting times. The present study aimed to investigate a reprocessing unit for medical devices based in Lisbon, on its service-level agreement with costumer healthcare units. The work sought to determine if the agreement between the two parties, the reprocessing unit for medical devices and the healthcare unit, was fulfilled, to what extent and potential refinement strategies. Considering the previous evaluation, further research was conducted to improve the global performance of the reprocessing of medical devices. Simulation was the tool used to appraise reprocessing unit for medical devices’ actual execution and the impact that improvement proposals. The proposals were developed using a Lean-based methodology which is based on one guiding tenet, creating value to the customer by optimizing resources. This means reducing waste and adding customer defined value to products and services, such as the waiting time. The proposals were grouped into six scenarios of three types. The type A Scenario is established on levelling medical devices arrivals to the reprocessing unit for medical devices, while Scenarios from types B and C intend to test the reprocessing unit for medical devices’ response to an increase in the number of operational sterilization technicians in the decontamination, inspection and packaging zones, respectively. The scenario that proved to be the most beneficial to the reprocessing unit for medical devices proposes (i) levelling medical devices arrivals to the reprocessing unit for medical devices; (ii) the allocation of two more operational sterilization technicians to the decontamination zone, for the morning and night shifts and (iii) the allocation of only seven operational sterilization technicians to the inspection and packaging area during the 3 shifts. We anticipate that by adopting the proposals comprised, the reprocessing unit for medical devices is able to comply with the service level agreement agreed between all healthcare units. To conclude, a critical analysis of the scenarios was carried out emphasizing the work objectives and suggestions for future work were proposed