The equivalence of general set-covering and implicit integer programming formulations for shift scheduling

In a recent article we demonstrated that implicit optimal modeling for shift scheduling (P2) has inherent size and execution time advantages over the general set-covering formulation for shift scheduling (P1) [11, 13]. We postulated that the absence of extraordinary overlap (EO) was a requirement for the equivalence of P1 and P2. We have defined EO as the condition in which the earliest and latest starts for a break in one shift are earlier and later than the earliest and latest starts for a break in any other shift(s). In this article, we prove that our earlier postulate was accurate. Additionally, we discuss research extensions and note other scheduling problems for which implicit modeling may be appropriate. © 1996 John Wiley & Sons, Inc.     

Optimal control of continuous-time terminal-value birth-and-death processes and airline overbooking

Consider a continuous-time airline overbooking problem that relates to a single-leg flight and a single service class with a stationary fare. Passengers may cancel their reservations at any time and receive a full refund. Therefore fares can be thought of as being paid at flight time. At that time, the airline bumps passengers in excess of flight capacity and pays a penalty for so doing. The wflight-time revenue, that is, fares received less bumping penalties paid, is quasiconcave in the number of reservations at that time. We model the reservations process as a continuous-time terminal-value birth-and-death process. A more general model than is necessary for an airline reservations system is considered, in which the airline controls both the reservation acceptance (birth) and the cancellation (death) rates. In current practice airlines do not control cancellation rates (though other industries do exercise such control, e.g., hotels) and control reservation acceptance rates by declining reservation requests. The more general model might be applied to other targeting applications, such as steering a vehicle through space toward a target location. For the general model a piecewise-constant booking-limit policy is optimal; that is, at all times the airline accepts reservation requests up to a booking limit if the current number of reservations is less than that booking limit, and declines reservation requests otherwise. When the airline is allowed to decline all reservation requests, as is the case in practice, the booking-limit optimal policy defined by using the greatest optimal booking limit at all times is piecewise constant. Moreover, these booking limits fall toward flight time. © 1996 John Wiley & Sons, Inc.     

Scheduling to minimize release-time resource consumption and tardiness penalties

We consider the problem of scheduling a set of jobs with a common due-date on a single-machine where the release time of a job is related to the amount of resource consumed. The objective is to minimize the total resource consumption and the total tardiness. While the problem is strongly NP-hard in general, we discuss two different special cases for which special properties are identified and used to develop efficient pseudo-polynomial time algorithms. © 1995 John Wiley & Sons, Inc.     

Order-statistic calculation,costs, and service in an (s,Q) inventory system

A retailer or distributor of finished goods, or the manager of a spare-parts inventory system, must generally forecast the major portion of demand. A specific customer-service level p (fraction of replenishment intervals with no stockout) implies two challenges: achieve the service within a small interval plus or minus, and do so with a minimum-cost investment in inventory. The pth fractile of lead-time demand (LTD) is the reorder point (ROP) for this service measure, and is often approximated by that fractile of a normal distribution. With this procedure, it is easy to set safety stocks for an (s, Q) inventory system. However, Bookbinder and Lordahl [2] and others have identified cases where the normal approximation yields excessive costs and/or lower service than desired. This article employs an order-statistic approach. Using available LTD data, the ROP is simply estimated from one or two of the larger values in the sample. This approach is sufficiently automatic and intuitive for routine implementation in industry, yet is distribution free. The order-statistic method requires only a small amount of LTD data, and makes no assumptions on the form of the underlying LTD distribution, nor even its parameters μ and ρ. We compare the order-statistic approach and the normal approximation, first in terms of customer service and then using a model of expected annual cost. Based upon characteristics of the available LTD data, we suggest a procedure to aid a practitioner in choosine between the normal and order-statistic method. © 1994 John Wiley & Sons, Inc.     

Optimizing the allocation of components to kits in small-lot,multiechelon assembly systems

The kitting problem in multiechelon assembly systems is to allocate on-hand stock and anticipated future deliveries to kits so that cost is minimized. This article structures the kitting problem and describes several preprocessing methods that are effective in refining the formulation. The model is resolved using an optimizing approach based on Lagrangian relaxation, which yields a separable problem that decomposes into a subproblem for each job. The resulting subproblems are resolved using a specialized dynamic programming algorithm, and computational efficiency is enhanced by dominance properties devised for that purpose. The Lagrangian problem is resolved effectively using subgradient optimization and a specialized branching method incorporated in the branch-and-bound procedure. Computational experience demonstrates that the specialized approach outperforms the general-purpose optimizer OSL. The new solution approach facilitates time-managed flow control, prescribing kitting decisions that promote cost-effective performance to schedule. © 1994 John Wiley & Sons. Inc.     

The two-machine permutation flow shop with state-dependent processing times

If the processing time of each job in a flow shop also depends on the time spent prior to processing, then the choice of a sequence influences processing times. This nonstandard scheduling problem is studied here for the minimum makespan schedule in a flow shop with two machines. The problem is NP-hard in the strong sense and already contains the main features of the general case [10]. Restricting to the case of permutation schedules, we first determine the optimal release times of the jobs for a given sequence. Permutation schedules are evaluated for this optimal policy, and the scheduling problem is solved using branch-and-bound techniques. We also show the surprising result that the optimal schedule may not be a permutation schedule. Numerical results on randomly generated data are provided for permutation schedules. Our numerical results confirm our preliminary study [10] that fairly good approximate solutions can efficiently be obtained in the case of limited computing time using the heuristics due to Gilmore and Gomory [7]. © 1993 John Wiley & Sons, Inc.     

Realignment in the National Football League: Did they do it right?

The National Football League (NFL) in the United States expanded to 32 teams in 2002 with the addition of a team in Houston. At that point, the league was realigned into eight divisions, each containing four teams. We describe a branch‐and‐cut algorithm for minimizing the sum of intradivisional travel distances. We consider first the case where any team can be assigned to any division. We also consider imposing restrictions, such as aligning the AFC (American Football Conference) and the NFC (National Football Conference) separately or maintaining traditional rivalries. We show that the alignment chosen by the NFL does not minimize the sum of intradivisional travel distances, but that it is close to optimal for an alignment that aligns the NFC and AFC separately and imposes some additional restrictions. © 2003 Wiley Periodicals, Inc. Naval Research Logistics 50: 683–701, 2003.     

北京沧达农工商公司草垛火灾引发的深思

火灾预防和火灾扑救不仅仅是消防部门自身的职责，必须依靠社会综合力量，政府是处置各类突发事件的强势者。从北京沧达农工商公司草垛火灾谈起，对政府职责、单位消防安全责任、社会应急机制等存在的问题做了进一步阐述。     

通用对潜搜索作战模型效能计算方法

对潜搜索模型有很多种,并且这些搜索模型可能因为进一部的完善、优化而发生改变;根据装备的发展及部队作战、训练的需要,也可能有新的模型不断加入.这些模型的作战效果指标是决定其是否可用的重要依据之一,而作战效果的计算应基于统一的方法,而不能各自不同,这样,得出的结论才具有可比性.为了实现这个目的,建立了基于蒙特卡罗法的通用计...