Properties of a source location estimator in the plane

The statistical properties of an estimator of a source location were established by simulation for the case in which the source location is estimated—using transformation of lines to points—from the angles in which different observers see the source, and both the assumed locations of the observer points and the observed angles are subject to error. It was found that for normal error distributions the estimator is unbiased, and the resulting estimates are approximately normally distributed with a small standard deviation. An easy-to-use and reliable forecasting formula was suggested to forecast the parameters of the distributions of the estimates for different observer-source relationships. © 1993 John Wiley & Sons, Inc.     

Optimizing disaster relief: Real-time operational and tactical decision support

We introduce a real-time decision support system which uses optimization methods, simulation, and the judgement of the decision maker for operational assignment of units to tasks and for tactical allocation of units to task requirements. The system, named ARES for the Greek god of war, accommodates a high degree of detail in the logistics of unit movements during operations, yet separates the assignment and allocation activities in a fashion which naturally accommodates human intervention and judgement—ARES is designed to assist the decision maker, not to replace him. ARES is demonstrated with a hypothetical scenario constructed for 14 Engineering Battalions of the Hellenic Army which are assigned 20 tasks employing 25 resource types in repairing major damage to public works following a great earthquake. (This hypothetical data was prepared prior to the earthquake in Kalamata near Athens on 13 September, 1986, and exhibits uncanny, but coincidental, resemblance to that real situation.) ARES is designed for use in real time, and quick data preparation is aided by the provision from published sources of standard data for many foreseeable tasks; this data can be quickly accessed via visual icons on a computer screen and customized for the actual work at hand. © 1993 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.     

Real-time task scheduling with overheads considered

n periodic tasks are to be processed by a single machine, where each task i has a maximum request rate or periodicity F_i, a processing time E_i, a deadline D_i, relative to each request of task i, a task-request interrupt overhead I_i, and a task-independent scheduling overhead S. Two scheduling strategies are considered for sequencing the execution of an arbitrary arrangement of task requests in time: the preemptive and the nonpreemptive earliest-deadline algorithms. Necessary and sufficient conditions are derived for establishing whether a given set of tasks can be scheduled by each scheduling strategy. The conditions are given in the form of limited simulations of a small number of well-defined task-request arrangements. If all simulations succeed, the schedule is feasible for the given set of tasks. If any simulation fails, the schedule is infeasible. While interrupt handling and scheduling overheads can be handled by such simulations, context switching overhead resulting from preemption cannot. A counterexample illustrates how the simulations fail to uncover unschedulable task sets when context switching overhead is considered.     

A new heuristic solution method in resource-constrained project scheduling

A new heuristic method is presented for the resolution of multiresource constrained conflicts in project scheduling. In attempting to find a minimal makespan solution, the algorithm employs a simple procedure to generate a feasible solution with no backtracking. A postanalysis phase then applies a hill-climbing search. The solution method is different from existing heuristic methods in that it repairs resource conflicts rather than constructs detailed schedules by dispatching activities. Resource-violating sets of activities are identified which must be prevented from concurrent execution because this would violate resource constraints. Repairs are made by imposing an arc to sequence two activities in such a resource violating set. Computational results are compared with those of existing heuristics for the minimal makespan problem.     

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.     

Integrating multiple criteria decision making models into the decision support system framework for marketing decisions

A large number of multiple criteria decision making (MCDM) models have evolved over the past decade. This field now seems to have reached a stage of maturity. However, the managerial community has not yet extensively adopted these models in solving practical decision problems. The present article focuses on integrating the MCDM models within the decision support system (DSS) framework to encourage greater use of these models. A DSS framework and the criteria used for the choice of a model is discussed. Based on these criteria MCDM models generally used in the marketing field are evaluated. The possibility of using a mixture of MCDM models within the DSS framework is also explored. Following this, the role of the MCDM models in DSS is delineated. It is argued that, within the problem-solving process, the confluence of MCDM models and DSS plays a vital role in developing high-quality solutions.