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This chapter presents the survey of selected linear and mixed integer programming multi-objective portfolio optimization. The definitions of selected percentile risk measures are presented. Some contrasts and similarities of the different types of portfolio formulations are drawn out. The survey of multi-criteria methods devoted to portfolio optimization such as weighting approach, lexicographic approach, and reference point method is also presented. This survey presents the nature of the multi-objective portfolio problems focuses on a compromise between the construction of objectives, constraints, and decision variables in a portfolio and the problem complexity of the implemented mathematical models. There is always a trade-off between computational time and the size of an input data, as well as the type of mathematical programming formulation with linear and/or mixed integer variables.

This chapter presents two optimization multicriteria models (bi and triple objective) using a lexicographic approach. Solved models are formulated as assignment of workers to different jobs or services of a real hospital, taking into account the available budget and requirements of each job. Presented problems have been solved using AMPL programming language with solver CPLEX v9.1, with the use of branch and bound method for mixed integer mathematical programming.

In this chapter, four bi-objective vehicle routing problems are considered. Weighted-sum approach optimization models are formulated with the use of mixed-integer programming. In presented optimization models, maximization of capacity of truck versus minimization of utilization of fuel, carbon emission, and production of noise are taken into account. The problems deal with real data for green logistics for routes crossing the Western Pyrenees in Navarre, Basque Country, and La Rioja, Spain.

Heterogeneous fleet of trucks is considered. Different types of trucks have not only different capacities, but also require different amounts of fuel for operations. Consequently, the amount of carbon emission and noise vary as well. Modern logistic companies planning delivery routes must consider the trade-off between the financial and environmental aspects of transportation. Efficiency of delivery routes is impacted by truck size and the possibility of dividing long delivery routes into smaller ones. The results of computational experiments modeled after real data from a Spanish food distribution company are reported. Computational results based on formulated optimization models show some balance between fleet size, truck types, and utilization of fuel, carbon emission, and production of noise. As a result, the company could consider a mixture of trucks sizes and divided routes for smaller trucks. Analyses of obtained results could help logistics managers lead the initiative in environmental conservation by saving fuel and consequently minimizing pollution. The computational experiments were performed using the AMPL programming language and the CPLEX solver.

Resource capacity and product changeovers must be both considered in the preparation of a realistic production plan. The purpose of this paper is to present a heuristic for enforcing resource availability and the accompanying changeover realities into a continuous‐variable linear programming formulation that would otherwise require a mixed‐integer model. The results from both approaches are compared in terms of objective function values and computational requirements; the effectiveness of the heuristic approach is demonstrated.

A case study search was conducted to identify relevant data sets that could be used to exercise the optimization and heuristic models. The case studies found in the literature were too small and simple compared to the problem complexity desired. The authors developed a case study based on the development of a production plan for a typical flashlight. It includes two end‐products that differ in their bills of materials and process requirements. Basic processes include plastic part preparation and final assembly; various raw materials with pre‐defined lead times are purchased from external suppliers. The results of the LP‐based heuristic and the mixed‐integer programming (MIP) optimization algorithm are then compared through a statistical experiment. The experiment includes four factors: number of products, number of periods, number of machines, and percentage line capacity utilization.

When a MIP algorithm is applied to obtain the results, most of the time the planner would have to wait days or even weeks for the algorithm to provide a solution. However, the authors' linear programming‐based procedure provides the same quality of solution in minutes and for some problems in seconds.

The originality of the heuristic approach resides on the avoidance of the lengthy MIP computer runs. At each iteration, the authors solve the LP production planning problem without changeover considerations, and then subtract from the original capacity the time associated with the changeovers resulting from the last LP solution. After a small number of iterations the heuristic always converges to the optimal MIP solution. The contribution of this research can be appreciated by someone who is using this tool to generate a production plan in a real world factory where setups are important and the results can immediately suggest changes to some of the assumptions or parameters used in the planning exercise.

The supply chain (SC) of the fast-moving consumer goods (FMCG) sector in India witnessed a significant change soon after introducing the Goods and Services Tax (GST). With the initiation of this tax, companies started moving from individual state-wise warehouses to consolidation warehouses model to save costs. This paper proposes a model that frames a mathematical formulation to optimize the distribution network in the downstream SC by considering the complexities of multi-product lines, multi-transport modes and consolidated warehouses.

The model is designed as mixed-integer linear programming (MILP), and an algorithm is developed that works on the feedback loop mechanism. It optimizes the transportation and warehouses rental costs simultaneously with impact analysis.

Total cost is primarily influenced by the critical factor transportation price rather than the warehouse rent. The choice of warehouses at prime locations was a trade-off between a lower distribution cost and higher rent tariffs.

The study enables FMCG firms to plan their downstream SC efficiently and to be in line with the recent trend of consolidation of warehouses. The study will help SC managers solve complexities such as multi-product categories, truck selection and consolidation warehouse selection problems and find the optimum value for each.

The issues addressed in the proposed work are transporting products with different sizes and weights, selecting consolidated warehouses, selecting suitable vehicles for transportation and optimizing distance in the distribution network by considering consolidated warehouses.

The purpose of this paper is to figure out in which way a hinterland-based inland depot model can help a shipping company in solving the empty container problem at a regional level. The repositioning of empty containers is a very expensive operation that does not generate profits. Consequently, it is very important to provide an efficient empty container management.

In this paper, the empty container problem is discussed at a regional repositioning level. For solving this problem, a mixed-integer linear optimization model is developed and validated by using the German hinterland as a case.

The findings show that the hinterland-based solution is able to reduce the total system costs by 40 per cent. In addition, total of truck kilometres could be reduced by more than 30 per cent too.

This research is based on German data only.

This paper closes the gap in empty container repositioning research by looking at the hinterland dimension from a single shipping company point of view.

This paper seeks to construct a model for inventory management for multiple periods. The model considers not only the usual parameters, but also price quantity discount, storage and batch size constraints.

Mixed 0‐1 integer programming is applied to solve the multi‐period inventory problem and to determine an appropriate inventory level for each period. The total cost of materials in the system is minimized and the optimal purchase amount in each period is determined.

The proposed model is applied in colour filter inventory management in thin film transistor‐liquid crystal display (TFT‐LCD) manufacturing because colour filter replenishment has the characteristics of price quantity discount, large product size, batch‐sized purchase and forbidden shortage in the plant. Sensitivity analysis of major parameters of the model is also performed to depict the effects of these parameters on the solutions.

The proposed model can be tailored and applied to other inventory management problems.

Although many mathematical models are available for inventory management, this study considers some special characteristics that might be present in real practice. TFT‐LCD manufacturing is one of the most prosperous industries in Taiwan, and colour‐filter inventory management is essential for TFT‐LCD manufacturers for achieving competitive edge. The proposed model in this study can be applied to fulfil the goal.

Fortification-interdiction models provide system designers with a broader perspective to identify and protect vital components. Based on this concept, the authors examine how disruptions impact critical supply systems and propose the most effective protection strategies based on three levels of decision-makers. This paper aims to investigate location and fortification decisions at the first level. Moreover, a redesign problem is presented in the third level to locate backup facilities and reallocate undisrupted facilities following the realization of the disruptive agent decisions at the second level.

To address this problem, the authors develop a tri-level planner-attacker-defender optimization model. The model minimizes investment and demand satisfaction costs and alleviates maximal post-disruption costs. While decisions are decentralized at different levels, the authors develop an integrated solution algorithm to solve the model using the column-and-constraint generation (CCG) method.

The model and the solution approach are tested on a real supply system consisting of several hospitals and demand areas in a region in Iran. Results indicate that incorporating redesign decisions at the third level reduces maximum disruption costs.

The paper makes the following contributions: presenting a novel tri-level optimization model to formulate facility location and interdiction problems simultaneously, considering corrective measures at the third level to reconfigure the system after interdiction, creating a resilient supply system that can fulfill all demands after disruptions, employing a nested CCG method to solve the model.

This paper aims to design an optimal supply chain network and to develop a suitable distribution planning under uncertainty for perishable product's supply chain. The ultimate goal is to help in making decisions under uncertain environments.

In this paper, stochastic programming is used under conditions of demand, supply and process uncertainties, and a non-linear mathematical model is developed for perishable product’s supply chain. Authors’ study considers disruptions in transportation routes and also within the facilities and investigates optimal facility location and shipment decisions while minimising the total supply chain cost. A scenario-based approach is used to model these disruptions. The retailer level uncertainty due to demand-supply mismatch is handled by incorporating the newsvendor model into the last echelon of supply chain network. In this paper, two policies are proposed for making decisions under uncertain environments. In the first one, the expected cost of the supply chain is minimised. To also consider the risk behaviour of the decision maker, authors propose the second policy through a conditional value-at-risk approach.

Authors discuss the model output through various examples that are provided via a case study from the milk industry. The supply chain design and planning of the disruption-free model are different from those of the resilient model.

Authors’ research benefits the perishable products industries which encounter the disruption problems in their transportation routes as well as in the facilities. Authors have demonstrated the research through a real-life case in a milk industry.

The major contribution of authors’ work is the design of the supply chain network under disruption risks by incorporating aspects of product perishability. This work provides insight into areas such as the simultaneous consideration of demand, supply and process uncertainties. The amalgamation of newsvendor model and the approximation of the non-linearity of retailer level cost function especially in the context of supply chain under uncertainty is the first of its kind. We provide a comprehensive statistical study of uncertainties that are present in the supply chain in a unique manner.

Annual influenza epidemics cause great losses in both human and financial terms. The purpose of this paper is to propose a model for optimizing a large-scale influenza vaccination program (VP). The goal is to minimize the total cost of the vaccination supply chain while guaranteeing a sufficiently high level of population protection. From a practical point of view, the analysis returns the number of shipments and the quantity of vaccines in each periodic shipment that should be delivered from the manufacturers to the distribution center (DC), from the DC to the clinics, and from the clinics to each sub-group of customers during the vaccination season.

A mixed-integer programming optimization model is developed to describe the problem for a supply chain consisting of vaccine manufacturers, the healthcare organization (HCO) (comprising the DC and clinics), and the population being vaccinated (customers). The model suggests a VP that implemented by a nation-wide HCO.

The benefits of the proposed approach are shown to be particularly salient in cases of limited resources, as the model distributes demand backlogs in an efficient manner, prioritizing high-risk sub-groups of the population over lower-risk sub-groups. In particular, the authors show a reduction in direct medical burden of consumers, such as the need for doctors, hospitalization resources, and reduction of indirect, non-medical burden, such as loss of workdays.

Drawing from the extended enterprise paradigm, and, in particular, taking consumer benefits into account, the authors suggest an operational-strategic model that creates impressive added value in a highly constrained supply chain. The model constitutes a powerful decision tool for the deployment of large-scale seasonal products, and its implementation can yield multiple benefits for various consumer segments.

The model proposed herein constitutes a decision support tool comprising operational-tactical and tactical-strategic perspectives, which logistics managers can utilize to create an enterprise-oriented plan that takes into account medical and non-medical costs.