Springer Science and Business Media LLC

In a queueing systemM/M/c let the number of actual serversχ≤c be chosen depending on the statey (number of customers in the system). We consider an opportunity costw per server per unit of time and a waiting costh per customer per unit of time. Using Dynamic Programming the optimal policy forc=1 is found to be as follows. Use no server wheny1 under certain conditions.

In this paper we explore tramp ship routing and scheduling. Tramp ships operate much like taxies following the available demand. Tramp operators can determine some of their demand in advance by entering into long-term contracts and then try to maximise profits from optional voyages found in the spot market. Routing and scheduling a tramp fleet to best utilise fleet capacity according to current demand is therefore an ongoing and complicated problem. Here we add further complexity to the routing and scheduling problem by incorporating voyage separation requirements that enforce a minimum time spread between some voyages. The incorporation of these separation requirements helps balance the conflicting objectives of maximising profit for the tramp operator and minimising inventory costs for the charterer, since these costs increase if similar voyages are not performed with some separation in time. We have developed a new and exact branch-and-price procedure for this problem. We use a dynamic programming algorithm to generate columns and describe a time window branching scheme used to enforce the voyage separation requirements which we relax in the master problem. Computational results show that our algorithm in general finds optimal solutions very quickly and performs much faster compared to an earlier a priori path generation method. Finally, we compare our method to an earlier adaptive large neighbourhood search heuristic and find that on similar-sized instances our approach generally uses less time to find the optimal solution than the adaptive large neighbourhood search method uses to find a heuristic solution.

We consider single-level uncapacitated and capacitated lot-sizing problems with product substitution, where products may be substituted by certain other products to satisfy demand. The models incorporate initial inventories and general substitution structures. We formulate the problems as mixed-integer linear programs and develop Simple Plant Location-based reformulations as well as new valid inequalities. Computational results on generated problem instances show that the reformulations are superior to the original formulations and those with valid inequalities added a priori, except for instances with multiple resources and downward substitution. In most cases, the running times of a mixed-integer programming solver on approximate extended formulations that only contain a subset of the disaggregated constraints were almost as good as on complete Simple Plant Location-based reformulations.

In this paper, we consider the resource-constrained project scheduling problem with partially renewable resources and general temporal constraints. For the first time, the concept of partially renewable resources is embedded in the context of projects with general temporal constraints. While partially renewable resources have already broadened the area of applications for project scheduling, the extension by general temporal constraints allows to consider even more relevant aspects of real projects. We present a branch-and-bound procedure for the problem with the objective to minimize the project duration. To improve the performance of the solution procedure, new consistency tests, lower bounds, and dominance rules are developed. Furthermore, new temporal planning procedures, based on forbidden start times of activities, are presented which can be used for any project scheduling problem with general temporal constraints independent on the considered resource type. In a performance analysis, we compare our branch-and-bound procedure with the mixed-integer linear programming solver IBM CPLEX 12.8.0 on adaptations of benchmark instances from the literature. In addition, we compare our solution procedure with the only available branch-and-bound procedure for partially renewable resources. The results of the computational experiments prove the efficiency of our branch-and-bound procedure.

We consider the incentive characteristics of optimal linear contracts based on relative performance evaluation (RPE) for managers under moral hazard in imperfectly competitive product markets. Each contract influences the quantity choices of all competing agents causing contract externalities that affect the principals’ contracting game. We analyze the relations between the optimal extent of RPE and several firm and market characteristics, allowing for heterogeneous firms and idiosyncratic firm risk. In general, we find non-monotonic comparative static results regarding the influence of market and firm-specific risk, the industry’s competitiveness, and the correlation of the firms’ profit.

In der Arbeit wird gezeigt, wie mit Hilfe der Theorie der unscharfen Mengen geeignete Angebote aus Datenbanken bestimmt werden können. Zur Berechnung wird jedes der einzelnen Entscheidungskriterien durch den Kunden eingeschätzt. Seine Präferenzen werden in Zugehörigkeitsfunktionen umgesetzt. Ein geeignetes Angebot erhält man nun durch Maximierung einer Funktion, die sich als Komposition der einzelnen Zugehörigkeitsfunktionen ergibt. Für diese Verknüpfung schlagen wir den Werners-Operator vor, da er Dieser Zugang ist auch möglich bei nur verbal formulierbaren Kriterien und größeren Datenbanken.