Contribution of robust optimization on handling agricultural processed products supply chain problem during Covid-19 pandemic

This research aims to show how decision sciences can make a significant contribution on handling the supply chain problem during Covid-19 Pandemic. The paper discusses how robust optimization handles uncertain demand in agricultural processed products supply chain problems within two scenarios during the pandemic situation, i.e., the large-scale social distancing and partial social distancing. The study assumes that demand and production capacity are uncertain during a pandemic situation. Robust counterpart methodology is employed to obtain the robust optimal solution. To this end, the uncertain data is assumed to lie within a polyhedral uncertainty set. The result shows that the robust counterpart model is a computationally tractable through linear programming problem. Numerical experiment is presented for the Bandung area with a case on sugar and cooking oil that is the most influential agricultural processed products besides the main staple food of the Indonesian people, rice.

Extending the Scope of Robust Quadratic Optimization

We derive computationally tractable formulations of the robust counterparts of convex quadratic and conic quadratic constraints that are concave in matrix-valued uncertain parameters. We do this for a broad range of uncertainty sets. Our results provide extensions to known results from the literature. We also consider hard quadratic constraints: those that are convex in uncertain matrix-valued parameters. For the robust counterpart of such constraints, we derive inner and outer tractable approximations. As an application, we show how to construct a natural uncertainty set based on a statistical confidence set around a sample mean vector and covariance matrix and use this to provide a tractable reformulation of the robust counterpart of an uncertain portfolio optimization problem. We also apply the results of this paper to norm approximation problems. Summary of Contribution: This paper develops new theoretical results and algorithms that extend the scope of a robust quadratic optimization problem. More specifically, we derive computationally tractable formulations of the robust counterparts of convex quadratic and conic quadratic constraints that are concave in matrix-valued uncertain parameters. We also consider hard quadratic constraints: those that are convex in uncertain matrix-valued parameters. For the robust counterpart of such constraints, we derive inner and outer tractable approximations.

Adjustable Robust Optimization for Multi-Period Water Allocation in Droughts under Uncertainty

Optimal, rational water resource allocation can go some way to overcoming water deficiencies; however, its achievement is complex due to conflicting hierarchies and uncertainties, such as water availability (WA) and water demand (WD). This study developed a robust water withdrawal scheme for arid and semi-arid regions that balanced the trade-offs between the sub-areas and water use participants, ensured sustainable regional system development, and guaranteed robust solutions for future uncertainties. A bi-level affinely adjustable robust counterpart (AARC) programming framework was developed, in which the regional authority as the leader allocates water to the sub-areas to maximize the intra- and intergenerational equity, and the sub-areas as the followers allocate water to their respective water departments to maximize their economic benefits and minimize water shortages. This method used affine functions between the decision variables (water allocation amount) and the uncertain parameters (WA, WD) to deal with the computationally intractable (NP-hard) robust counterpart for the multi-period water resources management. To illustrate the applicability and feasibility of this framework, a case study from Neijiang, China, is given. This model can assist regional authorities develop more robust water resource allocation solutions for multi-period planning responses to uncertain water deficiencies.

Heuristic Approach For Robust Counterpart Open Capacitated Vehicle Routing Problem With Time Windows

Garbage is one of the environmental problems. The process of transporting garbage sometimes occurs delays such as congestion and engine failure. Robust optimization model called a robust counterpart open capacitated vehicle routing problem (RCOCVRP) with time windows was formulated to get over this delays. This model has formulated with the limitation of vehicle capacity and time windows with an uncertainty of waste volume and travel time. The RCOCVRP model with time windows is solved by a heuristic approach. The heuristic approach used to solve the RCOCVRP model with time windows uses the nearest neighbor and the cheapest insertion heuristic algorithm. The RCOCVRP with time windows model is implemented on the problem of transporting waste in Sako sub-district. The solutions of these two heuristic approaches are compared and analyzed. The RCOCVRP model with time windows to optimize the route problems of waste transport vehicles that is solved using the cheapest insertion heuristics algorithm is more effective than the nearest neighbor method.

Robust Solutions for Uncertain Continuous-Time Linear Programming Problems with Time-Dependent Matrices

The uncertainty for the continuous-time linear programming problem with time-dependent matrices is considered in this paper. In this case, the robust counterpart of the continuous-time linear programming problem is introduced. In order to solve the robust counterpart, it will be transformed into the conventional form of the continuous-time linear programming problem with time-dependent matrices. The discretization problem is formulated for the sake of numerically calculating the ϵ-optimal solutions, and a computational procedure is also designed to achieve this purpose.

Two-Stage Robust Counterpart Model for Humanitarian Logistics Management

In the early stages of a major public emergency, decision-makers were troubled by the timely distribution of a large number of donations. In order to distribute caring materials reasonably and efficiently, considering the transportation cost and time delay cost, this paper takes the humanitarian logistics management as an example to study the scheduling problem. Based on the actual situation of insufficient supply during the humanitarian logistics management, this paper using optimization theory establishes a two-stage stochastic chance constrained (TS-SCC) model. In addition, due to the randomness of emergency occurrence and uncertainty of demand, the TS-SCC model is further transformed into the two-stage robust counterpart (TS-RC) model. At the same time, the validity of the model and the efficiency of the algorithm are verified by simulations. The result shows that the model and algorithm constructed are capable to obtain the distribution scheme of caring materials even in worst case. In the TS-BRC (with box set) model, the logistics service level increased from 89.83% to 93.21%, while in the TS-BPRC (with mixed box and polyhedron set) model, it increases from 90.32% to 94.96%. Besides, the model built in this paper can provide a more reasonable dispatching plan according to the actual situation of caring material supply.

Linearized Robust Counterparts of Two-Stage Robust Optimization Problems with Applications in Operations Management

In this article, we discuss an alternative method for deriving conservative approximation models for two-stage robust optimization problems. The method mainly relies on a linearization scheme employed in bilinear programming; therefore, we will say that it gives rise to the linearized robust counterpart models. We identify a close relation between this linearized robust counterpart model and the popular affinely adjustable robust counterpart model. We also describe methods of modifying both types of models to make these approximations less conservative. These methods are heavily inspired by the use of valid linear and conic inequalities in the linearization process for bilinear models. We finally demonstrate how to employ this new scheme in location-transportation and multi-item newsvendor problems to improve the numerical efficiency and performance guarantees of robust optimization.

Demand robust counterpart open capacitated vehicle routing problem time windows and deadline model of garbage transportation with LINGO 13.0

Demand robust counterpart-open capacitated vehicle routing problem with time windows and deadline (DRC-OCVRPtw,d) model formed and explained in this paper, is the model used to find the minimum distance and the time needed for vehicles to transport garbage in Sukarami Sub-District, Palembang that consists of the time it takes for the vehicle to pass through the route. Time needed to transport garbage to the vehicle is called time windows. Combination of the thoses times is called deadline. The farther the distance passed by vehicle and the more garbage transported, the longer the deadline is needed. This DRC-OCVRPtw,d model is completed by LINGO 13.0 to obtain the optimal route and time deadline for Sukarami Sub-District. The model shows that the improved model of open vehicle routing problem involving the robustness, time windows and deadline can achieve the optimal routes that enable driver to save operational time in picking up the garbage compared to similar problem not involving no-time windows and deadline stated in previous research.