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In this paper, we study the impact of corruption in the context of a game involving a manager and a controller. We propose a model where the controller initiates the bribe demand from the manager. We identify the structure of three potential subgame perfect Nash equilibria, and show their uniqueness. Next, we analyze the influence of the corruption parameters (bribery amount, reciprocity bonus and reputation gain) and the manager’s and the controller’s bonuses/penalties on the equilibria. Finally, we explain how the manager and the controller may increase, decrease or maintain their performance, when the bribery amount, the reciprocity bonus or the reputation gain index increase.

This paper studies the equality generalized symmetric traveling salesman problem (EGSTSP). A salesman has to visit a predefined set of countries. S/he must determine exactly one city (of a subset of cities) to visit in each country and the sequence of the countries such that s/he minimizes the overall travel cost. From an academic perspective, EGSTSP is very important. It is NP-hard. Its relaxed version TSP is itself NP-hard, and no exact technique solves large difficult instances. From a logistic perspective, EGSTSP has a broad range of applications that vary from sea, air, and train shipping to emergency relief to elections and polling to airlines' scheduling to urban transportation. During the COVID-19 pandemic, the roll-out of vaccines further emphasizes the importance of this problem. Pharmaceutical firms are challenged not only by a viable production schedule but also by a flawless distribution plan especially that some of these vaccines must be stored at extremely low temperatures. This paper proposes an approximate tree-based search technique for EGSTSP. It uses a beam search with low and high level hybridization. The low-level hybridization applies a swap based local search to each partial solution of a node of a tree whereas the high-level hybridization applies 2-Opt, 3-Opt or Lin-Kernighan to the incumbent. Empirical results provide computational evidence that the proposed approach solves large instances with 89 countries and 442 cities in few seconds while matching the best known cost of 8 out of 36 instances and being less than 1.78% away from the best known solution for 27 instances. © The authors. Published by EDP Sciences, ROADEF, SMAI 2021.

In this paper, we investigate FRB, which is the single facility Euclidean location problem in the presence of a (non-)convex polygonal forbidden region where travel and location are not permitted. We search for a new facility’s location that minimizes the weighted Euclidean distances to existing ones. To overcome the non-convexity and non-differentiability of the problem’s objective function, we propose an equivalent reformulation (RFRB) whose objective is linear. Using RFRB, we limit the search space to regions of a set of non-overlapping candidate domains that may contain the optimum; thus we reduce RFRB to a finite series of tight mixed integer convex programming sub-problems. Each sub-problem has a linear objective function and both linear and quadratic constraints that are defined on a candidate domain. Based on these sub-problems, we propose an efficient bounding-based algorithm (BA) that converges to a (near-)optimum. Within BA, we use two lower and four upper bounds for the solution value of FRB. The two lower and two upper bounds are solution values of relaxations of the restricted problem. The third upper bound is the near-optimum of a nested partitioning heuristic. The fourth upper bound is the outcome of a divide and conquer technique that solves a smooth sub-problem for each sub-region. We reveal via our computational investigation that BA matches an existing upper bound and improves two more.