This paper presents a new integer programming model for optimal shift scheduling with multiple rest and lunch breaks, and break windows. A set-covering approach for this problem was originally developed by Dantzig (1954). Since then, a number of set-covering-based formulations have been proposed in the literature. These formulations require an integer variable for every shift type, shift start time, and rest/lunch break placement combination. Unfortunately, the number of integer variables required is rather large, making them impractical to solve for an optimal solution in most applications. We present a new approach in which a set of break variables is introduced for every shift-break type combination to determine the break placements. This approach leads to a significantly improved integer programming model requiring substantially smaller number of variables and computer memory. We tested the proposed approach with 40 test problems involving between 1,728 and 8,640 shift variations, and five demand patterns. Our results showed that the proposed formulation is very useful in solving large shift scheduling problems optimally.manpower scheduling, service operations management, integer programming
Recently, hub-and-spoke networks employing central hub facilities to channel flows between interacting nodes have become popular with successful applications in ground and air transportation. In this paper, we introduce a framework for the design of this type of distribution network with networking policies and models together with exact and heuristic solution procedures. We consider two networking policies: (i) Nonstrict hubbing, in which channeling flows through hubs is not required but chosen if found cost efficient and (ii) strict and restrictive hubbing, in which all flows to/from a node are channeled through the same hub. Variations of these policies are discussed together with various aspects of air passenger and cargo transportation, effects of network organization on demand and network design under continuous economies of scale. The performances of the proposed algorithms and the effects of the networking policy implemented on the hub locations and the route structure are studied using data on air passenger flows between the top forty U.S. cities in 1989.
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