QUOPLAN: A System for Optimizing Sales Quota-Bonus Plans

This paper describes an IBM-PC menu-driven and user-friendly procedure which can help sales management in setting up optimal quota-bonus plans. For a given sales force, the resulting quotabonus plan maximizes the firm's current profits subject to (1) keeping every individual sales-force member at least at his/her current level of satisfaction (or eventually, increasing this level), and (2) being consistent and harmonious across sales representatives. The QUOPLAN system is composed of two submodels. The first submodel is used by salespersons for eliciting their own utility functions, and is essentially based upon the principles of conjoint analysis. The second submodel is used by management for reconciling all the individuals' judgements and the company's objectives into a consistent quota-bonus plan.     

Multi-Item Scheduling by Benders' Decomposition

Scheduling the production of several items requires the determination of production quantities in different periods in the presence of resource constraints. Several approximate and heuristic algorithms have been proposed to solve this problem. However, no method for finding an optimal solution has as yet been developed. It is shown that the problem may be solved advantageously using Benders' decomposition. The subproblem in Benders' decomposition is shown to be a transportation problem, and some strategies for solving the master problem are indicated. The paper concludes with a sample problem demonstrating the application of the method.     

Interactive Compromise Programming

The purpose of this paper is to introduce a solution method for multiple objective linear programming (MOLP) problems. The method, called interactive compromise programming (ICP), offers a practical solution to MOLP problems by combining judgement with an automatic optimization technique in decision-making. This is realised by using the method of compromise programming and the method of a two-person zero-sum game in an iterative way. The method is illustrated by a numerical example.     

Cost Comparisons for Out-of-Phase Inventory Models

Inventory costs for a fixed time period have traditionally been determined by allocating total costs per cycle uniformly throughout that cycle as well as any partial cycles. This procedure for cost allocation has led to the solution of numerous inventory problems, most notable of which is the anticipated price-increase model. When comparing two out-of-phase inventory models, if costs are accounted for when they occur over a fixed planning horizon, inventory policies should be changed to reflect the impact of this different cost-allocation procedure. For the anticipated price-increase model, the ‘optimal’ order quantity as well as the implied savings in inventory costs will be different when cost models are developed based on these different cost-allocation methods. If the objective is to maximize over a fixed planning horizon the actual savings in inventory costs as they occur, the cost models presented here should be used.     

Combined Routeing and Scheduling for the Transportation of Containerized Cargo

A tractor-trailer problem, with full load, from the class of combined routeing and scheduling problems is described. Distinctive features of the problem are: movements must be carried out within certain time windows; subsets of movements are linked in the sense that they must be executed in a certain order; and different priorities are attached to different movements. A new bidirectional sequential constructive heuristic is developed for the solution of this problem. The method constructs routes and schedules for the available tractor fleet. The algorithm attempts to minimize the total time for all the movements by minimizing the time taken up by unproductive movements (so-called deadhead) and waiting time between movements. Some practical aspects of the implementation of the approach are discussed.     

Boundary layer solutions for some nonlinear elastic membrane problems

Summary The method of matched asymptotic expansions is used to describe finite axisymmetric deformations of two thin elastic membrane problems: a circular membrane with a small radial traction at the edge, an annular membrane with a small circular hole at the center. In both problems, the surface load is assumed to be an axial pressure. There is a boundary layer at the outer edge in the first problem, and at the hole in the second problem.

---

Zusammenfassung Mit Hilfe der in der singulären Störungsrechnung benutzten Methode einer inneren und äußeren asymptotischen Entwicklung werden endliche, axialsymmetrische Deformationen bei zwei Membranproblemen beschrieben: eine dünne elastische Kreismembran mit kleiner radialer Zugspannung am Rande, und eine Kreisringmembran mit einem kleinen konzentrischen Loch. In beiden Problemen wird die Belastung als ein axial gerichteter Oberflächendruck angenommen. Im ersten Problem zeigt die Lösung am äußeren Rand Grenzschichtverhalten, welches im zweiten Problem am Lochrand vorliegt.

     

Interval estimation of the critical value in a general linear model

Summary This paper concerns interval estimation of the critical value θ which satisfies under the general linear model,Y _i =μ(x _i )+ε _i (i=1,2,···), where for and the functional forms off _j ^′ s are known. From an asymptotic expansion it is shown that, under reasonable conditions, the limiting distribution of is normal. Thus in the large-sample case a confidence interval for θ can be obtained. Such a result is useful when one is interested in carrying out a retrospective analysis rather than designing the experiment (as in the Kiefer-Wolfowitz procedure). In Section 3 a sequential procedure is considered for confidence intervals with fixed width 2d. It is shown that, for a given stopping variableN, is also asymptotically normal asd→0. Thus the coverage probability converges to 1−α (preassigned) asd→0. An example of application in estimating the phase parameter in circadian rhythms is given for the purpose of illustration. Research partially supported by the NSF Grant DMS-8502346.     

Some sufficient conditions for the E- and MV-optimality of block designs having blocks of unequal size

Summary In this paper we consider experimental situations in which ν treatments are to be tested inb blocks whereb _i blocks containk _i experimental units,i=1,...,p, k ₁<k ₂<...<k _p . The idea of a group divisible (GD) design is extended to that of a group divisible design with unequal block sizes (GDUB design) and then a number of results concerning the E- and MV-optimality of GD designs are generalized to the case of GDUB designs.     

Asymptotic properties of Rao's test for testing hypotheses in discrete parameter stochastic processes

Summary In this note some asymptotically optimum tests for testing hypotheses concerning parameters when the observations are dependent are obtained. Test statistics based on the score functions, similar to the one proposed by Rao in the case when the observations are i.i.d. are proposed. Asymptotically UMP tests for one sided hypotheses against one sided alternatives and asymptotically UMP unbiased test for a simple hypothesis against two sided alternatives are derived. In the multiparameter case tests for simple hypotheses that have asymptotically best constant power on some family of surfaces in the parameter space are derived.