Jaya Singhal

Supply chains and compatibility among components in product design

Abstract Two problems in designing and developing a product are directly tied into effective management of the marketing/operations interface. We first consider technological incompatibility between pairs of alternatives for different components to identify feasible product designs at various stages of product-development, from screening to the final design. We then consider experts’ judgment on compatibility between pairs of alternatives for different attributes to generate product ideas and to perform a preliminary screening. This expert-based approach can be used in conjunction with other expert-based approaches or consumer-based approaches to identify potentially desirable product ideas. The methodology developed here includes explicit simultaneous consideration of product, process, and supply chain development and it is applicable to the entire spectrum of product novelty, from radical to incremental innovation. We also describe a real-world application.

Fixed Order Branch-and-Bound Methods for Mixed-Integer Programming: The zoom System

A branch-and-bound algorithm for mixed-integer programming (MIP) is presented in which a different integer variable is designated for branching at each depth in the search tree. This is done in order to achieve economies of scale in solving the linear programming relaxations to obtain bounds for the (MIP) algorithm. This algorithm is the foundation for the zoom software system, which is briefly described. Illustrative computational experience is included. INFORMS Journal on Computing, ISSN 1091-9856, was published as ORSA Journal on Computing from 1989 to 1995 under ISSN 0899-1499.

Alternate approaches to solving the Holt et al. model and to performing sensitivity analysis

Abstract The staircase structure of the recurrence relations for the Holt et al. model can be used to develop simple and efficient computational approaches for obtaining the optimal solution. The computational approaches are noniterative. We deal with finite planning horizon cases in which one or more terminal boundary conditions are not specified. The computation time varies linearly with the number of periods in the planning horizon. A framework is also developed for sensitivity analysis on the terminal values and for generation of alternate production plans. The alternate plans provide considerable flexibility to the decision maker because they can be evaluated in the context of (a) constraints not included in the model, (b) plant capacity, (c) actual costs, and (d) implications beyond the planning horizon. The results should be of interest for real world applications as well as for research because the Holt et al. model continues to be used as a benchmark to evaluate the performance of other aggregate production planning models.

The number of feasible designs in a compatibility matrix

Abstract Many design and planning problems consist of a number of distinct subsystems. Generally, there are several possible alternatives for design of a subsystem. However, an alternative for one subsystem may be incompatible with an alternative for another subsystem. Thus, a feasible design is one that incorporates one alternative for each subsystem such that no pairwise incompatibilities exist. Several such design and planning problems have been formulated as compatibility matrices. The feasible designs can be identified by using an efficient algorithm. This paper shows that, in general, the exact number of feasible designs decreases exponentially with the increase in the number of incompatible pairs. This finding should motivate more potential users to employ the compatibility matrix approach.

Structural Properties Of The Compatibility Matrix: Existence Of Mathematical Relationships

AbstractA project network consists of activities that have many alternatives and pairwise compatibility relationships. This paper employs the compatibility matrix approach and derives statistical relationships for the estimation of the mean and standard deviation number of feasible alternsitives plans.

On the noniterative multiproduct multiperiod production planning method

Bahl and Zionts [H.C. Bahl, S. Zionts, A noniterative multiproduct multiperiod production planning method, Operations Research Letters 1 (1982) 219-221] formulated a problem for planning multiproduct multiperiod production on a single facility. They developed a column-minima noniterative method and claimed that it gave an optimal solution. We show that the claim is incorrect.

A Noniterative Algorithm for the Linear-Quadratic Profit-Maximization Model for Smoothing Multiproduct Production

In multiproduct-production and workforce-smoothing problems, the objective is to determine the levels of employment and production for each product in each period that will maximize the total profit over a planning horizon of N periods given quadratic revenue and cost functions for M products. The planned levels of production, in turn, determine the planned levels of inventory or backorders for each product in each period. A real-world problem may involve 20,000 products and 12 periods, leading to over 480,000 variables. This requires solving simultaneous equations with as many variables. We exploited the staircase structure of optimality conditions to develop an algorithm that requires solving, without iterations, simultaneous equations with only three variables. The computation time, regardless of the number of variables in the model, is of the order of one second on a Vax 11/780. This algorithm also facilitates sensitivity analysis and generation of alternate plans for production, the workforce, and sales.