Management Science

Aldrich, Carole; Morton, Thomas E.

doi: 10.1287/mnsc.21.5.491pmid: N/A

The problem of financing risky R&D projects over time has been stated as an optimal control problem by Hess [Hess, S. W. 1962. A dynamic approach to R&D budgeting and project selection. IRE Transactions on Engineering Management EM-9 (December) 170178.], Lucas [Lucas, Robert E. 1971. Optimal management of a research and development project. Management Sci. 17 (11, July) 679697.], and Kamien and Schwartz [Kamien, M. I., N. L. Schwartz. 1971. Expenditure patterns for risky R&D projects. J. Appl. Probab. VIII (1, March) 6072.]. In this paper, the model is extended to allow the possibility of time dependent returns. The authors restate the problem as a finite horizon continuous time dynamic programming problem, and demonstrate uniform convergence to a unique, autonomous (infinite horizon) solution for the present value of the project and optimal spending rate as a function of expended effort. Further conclusions are shown for the time dependent model with exponential completion probability and for the time independent model.

Lavenberg, Stephen S.

doi: 10.1287/mnsc.21.5.501pmid: N/A

We derive an expression for the Laplace-Stieltjes transform of the steady-state distribution of the queueing time for the M/G/1 finite capacity queue. The derivation proceeds in terms of a related 2-stage closed cyclic queueing network. The resulting expression is a rational function of the steady-state probabilities of the imbedded Markov chain at departure epochs and of the Laplace-Stieltjes transform of the service time distribution. The expression can be differentiated readily in order to obtain moments of the steady-state queueing time and some numerical results for the mean and coefficient of variation are presented.

Fryer, John S.

doi: 10.1287/mnsc.21.5.507pmid: N/A

This paper describes a simulation study that examines the influence of system size and labor flexibility on the performance effects of dispatching and labor control decision rules in labor and machine limited production systems. Four production systems are useda small job shop, a medium job shop, a large job shop in which workers may be transferred between major organizational divisions, and a large job shop in which workers cannot be transferred between divisions. For each system the decision rules for dispatching and labor control are varied. Comparisons are made of the relative effects of the decision rules, for the different systems, on mean flow-time, flow-time variance and number of worker transfers.Results indicate that the effects of dispatching and labor control decision rules on flow-time measures are consistent for different size and labor flexibility combinations. With one exception, the effects on labor transfer measures are also consistent. Consistency here means that the directions of change in performance measures are the same for the different systems. The magnitudes of both actual and percentage changes do vary for the different systems.

Kalymon, Basil A.

doi: 10.1287/mnsc.21.5.516pmid: N/A

This paper explores the normative theory of simulation within the context of an optimization algorithm for a linear programming model of the experimental setting. The simulation is viewed as a random generalized mathematical function which provides an uncertain evaluation of any policy within a specified constraint set. A sequential experimental design aimed at identifying the feasible levels of the policy variables which provide the optimal level of expected response is presented and analyzed. The results of numerical tests of the proposed procedure are discussed.

Ratliff, H. Donald; Sicilia, G. Thomas; Lubore, S. H.

doi: 10.1287/mnsc.21.5.531pmid: N/A

The n most vital links of a flow network are defined as those n arcs whose simultaneous removal from the network causes the greatest decrease in the throughput capability of the remaining system between a specified pair of nodes. These n arcs are shown to be the n largest capacity arcs in a particular cut. A solution procedure is developed which involves sequentially modifying the network so as to make this cut eventually become the cut with smallest capacity. An algorithm with computational results is presented.

Schrage, Linus

doi: 10.1287/mnsc.21.5.540pmid: N/A

There are a finite number of jobs to be scheduled on a single machine. All jobs are available from the start and the objective is to sequence the jobs so that the time-in-system (or equivalently, the completion time) variance is minimized. A number of necessary conditions for an optimal sequencing (which for small jobsets turn out to be sufficient) are presented.

Smith, M. L.; Panwalkar, S. S.; Dudek, R. A.

doi: 10.1287/mnsc.21.5.544pmid: N/A

A flowshop sequencing problem having an ordered processing time matrix is defined. Job and machine characteristics resulting in processing time relationships that have logical and practical bases are discussed. An optimizing solution procedure for a special class of ordered matrix problem is presented along with proof of optimality.

Dirickx, Yvo M. I.; Jennergren, L. Peter

doi: 10.1287/mnsc.21.5.550pmid: N/A

A sufficient condition for the optimality of myopic policies is derived for a class of sequential decision problems. A necessary condition is also derived. The usefulness of the sufficient condition is illustrated in the context of a dynamic portfolio selection problem, a matched sampling problem, and a multi-item inventory model.

Blin, J. M.; Whinston, Andrew B.

doi: 10.1287/mnsc.21.5.557pmid: N/A

This paper is based on the notion of discriminatory power of a pattern classifier acting over a feature space. Discriminant functions are normally used to trace out regions of the feature space corresponding to specific pattern classes. Indeterminate cases occur whenever a pattern lies on a class boundary. The number of occurrences of such indeterminacies measures the relative discriminatory power of a family of discriminant functions. In this paper these concepts are applied to majority voting decisions. It is first shown how regular majority voting leads to discriminant functions with insufficient discriminatory power whenever intransitive social ordering occurs. An (improved) family of discriminant functions is proposed to resolve such cases.

Gal, Tomas

doi: 10.1287/mnsc.21.5.567pmid: N/A

The rim multiparametric linear programming problem (RMPLP) is a parametric problem with a vector-parameter in both the right-hand side and objective function (i.e., in the rim). The RMPLP determines the region K E such that the problem, maximize z() cT()x, subject to Ax b(), x 0, has a finite optimal solution for all K.Let Bi be an optimal basis to the given problem, and let Ri, be a region assigned to Bi such that for all Ri the basis Bi is optimal. The goal of the RMPLP problem is to cover K by the Ri such that the various Ri do not overlap.The purpose of this paper is to present a solution method for finding all regions Ri that cover K and do not overlap. This method is based upon an algorithm for a multiparametric problem described in an earlier paper by Gal and Nedoma.