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We study server scheduling in multiclass service systems under uncertainty in the customer arrival volumes. Common practice in such systems is to first identify staffing levels and then determine schedules for the servers that cover these levels. We propose a new stochastic integer programming (SIP) model that integrates these two decisions, which can yield lower scheduling costs by exploiting the presence of alternative server configurations that yield similar quality of service. We find that a branch-and-cut algorithm based on Benders decomposition may fail due to the weakness of the relaxation bound. We propose a novel application of mixed-integer rounding to improve the Benders cuts used in this algorithm, a technique that is applicable to any SIP with integer first-stage decision variables. Numerical examples illustrate the computational efficiency of the proposed approach and the potential benefit of solving the integrated model compared to considering the staffing and scheduling problems separately. This paper was accepted by Yinyu Ye, optimization. [ABSTRACT FROM AUTHOR]

We examine how different characteristics of product demand and market impact the relative sales volume in the forward and spot markets for a commodity whose aggregate demand is uncertain. In a setting where either the forward contracts are binding quantity commitments between buyers and suppliers or the forward production takes place before the uncertainty in demand is resolved, we find that a combination of factors that include market concentration, demand risk, and price elasticity of demand will determine whether a commodity will be sold mainly through forward contracts or in the spot market. Previous findings in the literature show that when participants are risk neutral, the ratio of forward sales to spot sales is a function of market concentration alone; also, the lower the concentration, the higher this ratio. These findings hold under the assumption that demand is either deterministic or, if demand is uncertain, all production takes place after uncertainty is fully resolved and production plans can be altered instantaneously and costlessly. In our setting, however, we find that even a low level of demand risk can reverse the nature of supply in a highly competitive (low concentration) market, by shifting it from predominantly forward-driven to predominantly spot-driven supply. In markets with high concentration, the price elasticity of demand will determine whether the supply will be predominantly spot-driven or forward-driven. Our analysis suggests various new hypotheses on the structure of supply in commodity markets. [ABSTRACT FROM AUTHOR]

Airlines are continually faced with the challenge of efficient utilization of their cockpit crew resources. In addition to regular flying crews, airlines maintain significant reserve staffing levels to meet contractual obligations and provide smooth daily operations. Most airlines also depend on voluntary and involuntary flying by regular crews to cover trips that fall out of work schedules due to conflicts and disruptions (open time trips). These open time trips, combined with expected levels of voluntary and involuntary flying, affect reserve staffing levels; airlines must plan crew staffing in advance to meet resulting training and new-hire requirements. Inefficient operational reserve utilization can further affect long-range crew staffing, resulting in higher training and new-hire costs. The proposed optimization strategy to estimate long-range crew staffing combines operational reserve utilization and premium operational costs due to voluntary and involuntary flying with long-range business needs. [ABSTRACT FROM AUTHOR]

In this paper we formulate and efficiently solve staff scheduling problems for large organizations that provide continuous services to customers. We describe an integer programming approach for a class of such problems, where solutions have to obey a number of constraints related to workload balancing, shift compatibility, and distribution of days off. The formulation of the constraints is general and can be extended to different personnel management problems where staff members must cover shifts, and management must assign a fixed number of days off per week. The model maximizes staff satisfaction, expressed by positive weights for pairs of shifts in consecutive days. We consider the associated polytope and study its structure, determining some classes of inequalities that are facet inducing for special subproblems and other valid classes. We also identify a particular subproblem whose solution can be used to determine strong cuts for the complete problem. In addition, we design special branching rules that break the symmetries that arise in the solution space and have a large impact in the efficiency of the method. The validity of this approach has been ascertained by extensive computational tests; moreover, the operations research (OR) department of an airline has implemented the method to solve ground staff management problems. [ABSTRACT FROM AUTHOR]

This paper develops a model for allocating cross-trained workers at the beginning of a shift in a multidepartment service environment. It assumes departments are trying to maximize objective functions that are concave with respect to the number of workers assigned. Worker capabilities are described by parameters that range from zero to one, with fractional values representing workers who are less than fully qualified. The nonlinear programming model presented is a variant of the generalized assignment problem.The model is used in a series of experiments to investigate the value of cross-utilization as a function of factors such as demand variability and levels of cross-training. Results show that the benefits of cross-utilization can be substantial, and in many cases a small degree of cross-training can capture most of the benefits. Beyond a certain amount additional cross-training adds little additional value, and the preferred amount depends heavily on the level of demand variability. [ABSTRACT FROM AUTHOR]

A model is introduced to examine the long-term planning associated with the purchase and implementation of information technologies (IT) that indirectly contribute to output through enhancement of an organization's knowledge workers. For example, architectural firms in the service industry and manufacturers developing new or modified products invest in computer-aided design systems (CAD) to increase the volume of output generated by the engineering specialist. A critical element of the IT-knowledge worker model introduced is the inclusion of implementation-related dynamics. In particular we model both the short-term disruption to output that typically occurs at the start of the implementation period and the effect of worker learning during implementation The ability of the organization to generate output is examined in relation to the levels of workforce, information technology, worker skill, and a variety of features of the IT. Seven production function attributes are introduced to quantify the manner in which output is generated for the IT-knowledge worker system The production function is embedded into an optimization model in which profit is maximized. The formulation is dynamic in order to capture important elements of the decision-making environment, including the learning process, technological change, increasing wages, and changes in the labor supply. Optimal policies are obtained depicting the manner in which an organization should hire and fire its workforce and acquire information technology over time. A fundamental result is obtained establishing the existence of a complementary relationship between IT and knowledge workers. It is shown that a greater level of effective IT increases the desirability of hiring additional workers. In addition, as the ability of the IT to enhance knowledge worker productivity improves (reflecting IT features such as ease of use, functionality, connectivity, etc.), the desirability of hiring additional workers increases. Similarly, due to a high volume of workforce or a high level of worker skill, the desirability of acquiring IT increases. It is also shown that if an organization ignores the nature of the lagged effect of workforce learning, or if the impact of workforce learning on output is underestimated, then the projected volume of output over time is largely exaggerated. These results have important implications to management decision making with respect to effective implementation practices, technology choice issues, and workforce selection. Numerical results are generated to explore the effect of organizational size. It is shown that a smaller organization (as measured by the size of its workforce) relies more heavily on information technology to enhance worker productivity and generate output. Lastly, in response to higher wages, analytic results are derived demonstrating that an organization should reduce its level of hiring and its purchase of IT. Furthermore, numerical results show that an organization paying higher wages should allocate a greater amount of IT per worker to enhance productivity. [ABSTRACT FROM AUTHOR]

The dynamic nature of an operating environment, such as machine utilization and break-down frequency results in changing preventive maintenance (PM) needs for manufacturing equipment. In this paper, we present an approach to generate an adaptive PM schedule which maximizes the net savings from PM subject to workforce constraints. The approach consists of two components: (a) task prioritization based on a multi-logit regression model for each type of PM task, and (b) task rescheduling based on a binary integer programming (BIP) model with constraints on single-skilled and multi-skilled workforce availability. The task prioritization component develops a multi-logit regression for machine failure probability associated with each type of PM task at the beginning of the year, using historical data on machine utilization, PM, and machine breakdowns. At the start of each PM time-bucket (e.g., a month), we use the updated machine failure probability for each candidate PM task to compute its current contribution to net PM savings, which indicates its current priority. The task rescheduling BIP model incorporates the priorities in selecting tasks for the current bucket to maximize PM effectiveness subject to workforce availability, yielding an adaptive and effective PM schedule for each time-bucket of the master PM schedule. We examine the effect of using multi-skilled workforce on the overall PM effectiveness, and also provide an illustration from a newspaper publishing environment to explain the use of the approach. We have developed four heuristic algorithms to yield good solutions to large scale versions of this scheduling problem. The heuristics perform extremely well, and the best heuristic solution is within 1.4% of optimality on an average. [ABSTRACT FROM AUTHOR]

A new crew scheduling optimization system has been developed for United Airlines. The system was developed to permit quick response to schedule changes and to reduce crew scheduling costs. It was designed to work efficiently for both the medium sized problems (300 flights daily) and the very large problems (1,700 flights daily) that United must solve. The system has two main components, a generator and an optimizer. The generator creates pairings (candidate crew trips) which are fed as variables to the optimizer as an elastic embedded set partitioning integer programming problem. The optimizer then seeks to find a set of pairings that covers all of the flight segments exactly once with minimal cost. Once a disjoint solution has been found, the system cycles between the generator and the optimizer to improve it. Savings of $16,000,000 annually in crew scheduling costs have been obtained [ABSTRACT FROM AUTHOR]

The crew scheduling problem is one that has been studied almost continually for the past 40 years but all prior approaches have always approximated the problem of finding an optimal schedule for even the smallest of an airline's fleets. The problem is especially important today since costs for flying personnel of major U.S. carriers have grown and now often exceed $1.3 billion a year and are the second largest item (next to fuel cost) of the total operating cost of major U.S. carriers. Thus even small percentage savings amount to substantial dollar amounts. We present a branch-and-cut approach to solving to proven optimality large set partitioning problems arising within the airline industry. We first provide some background related to this important application and then describe the approach for solving representative problems in this problem class. The branch-and-cut solver generates cutting planes based on the underlying structure of the polytope defined by the convex hull of the feasible integer points and incorporates these cuts into a tree-search algorithm that uses automatic reformulation procedures, heuristics and linear programming technology to assist in the solution. Numerical experiments are reported for a sample of 68 large-scale real-world crew scheduling problems. These problems include both pure set partitioning problems and set partitioning problems with side constraints. These "base constraints" represent contractual labor requirements and have heretofore not been represented explicitly in the construction of crew schedules thus making it impossible to provide any measure of how far the obtained solution was from optimality. An interesting result of obtaining less costly schedules is that the crews themselves are happier with the schedules because they spend more of their duty time flying than waiting on the ground. [ABSTRACT FROM AUTHOR]

In this paper we consider a type of bias which stems from the mathematical algorithm often used to determine an optimal match between two groups. We compare two different solution concepts for the matching assignment problem: the traditionally stable solution vs. a multiplicative utility approach that should avoid the bias. Simulation modeling leads us to conclude that: (1) With respect to all sizes compared in our experiment, applicants and employers groups were always treated far more equally under the multiplicative utility approach than the stable approach. (2) When using the stable algorithm, the size of the bias is affected by the size of the problem (i.e., the larger the problem size is, the larger the performance discrepancy between two groups of participants). Further analyses of the sensitivity of the finding to different assumptions (e.g., correlation in the preference orderings of the two groups, or use of nonlinear conversion from ranks to utilities) also resulted in a superior performance of the multiplicative utility algorithm in terms of a more equitable outcome. [ABSTRACT FROM AUTHOR]

This research focuses on the effect of setup time on lot sizing. The setting is the Capacitated Lot Sizing Problem (the single-machine lot sizing problem) with nonstationary costs, demands, and setup times. A Lagrangian relaxation of the capacity constraints of CLSP allows it to be decomposed into a set of uncapacitated single product lot sizing problems. The Lagrangian dual costs are updated by subgradient optimization, and the single-item problems are solved by dynamic programming. A heuristic smoothing procedure constructs feasible solutions (production plans) which do not require overtime. The algorithm solves problems with setup time or setup cost. Problems with extremely tightly binding capacity constraints were much more difficult to solve than anticipated. Solutions without overtime could not always be found for them. The most significant results are that (1) the tightness of the capacity constraint is a good indicator of problem difficulty for problems with setup time; and (2) the algorithm solves larger problems better than smaller problems, although they are more time consuming to solve. This indicates that larger problems may be easier despite the greater computational effort they require. [ABSTRACT FROM AUTHOR]

Previous lower bounds on workforce size have been derived from the consideration that the number of working shifts which can be provided by the workers over a given period of time must be at least as large as the number of working shifts required by the staffing demands over that period. None of those bounds incorporates the effect of constraints on the changing of shifts in a multiple shift manpower scheduling problem. This paper utilizes a network model of the problem to model its multiple shift aspect and provide new lower bounds on workforce size. For some common special cases of constraints these lower bounds can be calculated by hand. For some common special cases of demands the multiple shift lower bounds degenerate to the single shift lower bounds. [ABSTRACT FROM AUTHOR]

In a study of 56 food processing firms, respondents reported on manpower flows that had an important influence on innovation decision making. Positive gain manpower flows appear to be a relatively rare occurrence. Only 23 (41%) of these 56 firms report any significant, innovation-impact, personnel additions, and 15 of these involve management positions. Four propositions were tested that focus on the relationship between manpower flows and innovative outcomes of an organization, i.e., offering new products and incorporating new processes. Moderate support was found for the proposition that net gain manpower flows are more likely to be related to radical as opposed to incremental process adoption. Evidence suggests that there is an inverted "u" shaped relationship between, net manpower flows and innovation outcomes. New blood stimulates innovation up to a point after which there is disruption to the innovation process. Adding too many people at once who all have a significant influence on the process may be unwise. The impact of manpower flows on innovative outcomes appears to be moderated by organization structure and the availability of slack resources for innovating. In particular, net manpower flows were significantly more likely to be positively correlated with the sum of the staged adoption behaviors for the retort pouch in decentralized (p < 0.05) and complex (p < 0.01) organizations. This and other evidence suggest that structural autonomy and new job titles with substantial visibility in the firm can go far to accommodate newcomers and capture the innovative benefits of their arrival. The availability of slack resources strengthens the relationship between the adoption of the retort pouch and net manpower flows although the effects were not as strong (p < 0.10) as for the structural moderators. This supports the common sense notion that newcomers who have had a significant effect on innovative decision making will see these decisions implemented in organizations that allocate resources to innovating. [ABSTRACT FROM AUTHOR]

In recent years, labour negotiations for seven-day-week organizations such as hospitals, mining companies and chemical industries have seen an increased emphasis on improving shift schedules. This paper gives an exact lower bound on the number of workers required to satisfy such primary contractual commitments as ensuring that each employee receives at least A out of every B weekends off, everyone works exactly five days per week, and no one works more than six consecutive days. The model addressed is general in that it allows the number of workers required each day to vary. The proof that the bound is the best possible is constructive. A linear time algorithm is presented that generates schedules satisfying all the primary objectives. Extensions discuss means of incorporating secondary objectives such as giving pairs of adjacent days off. [ABSTRACT FROM AUTHOR]

This paper first presents a brief reveiw of the multicriteria problems faced by the United States Army, Navy, and Marine Corps in making enlisted personnel assignment decisions. Then for the most complex of these military assignment problems, the Marine Corps problem, a new modeling and solution approach is presented with computational results for a problem having eleven criteria and approximately 10,000 constraints and 780,000 variables. Other contributions of this paper include: (a) New insights into the effects on model structure and solution efficiency of handling preemptive multiple criteria sequentially versus simultaneously. (b) Derivation of an excellent convex proportional fill function. (c) Providing multicriteria researchers with a class of large-scale test problems. [ABSTRACT FROM AUTHOR]

In manpower planning, as in all other kinds of planning, an important choice is the level of aggregation. The proper level of aggregation depends on the flexibility (mobility) of the personnel. This dependency is investigated in this paper. The manpower system considered is characterized by two dimensions, level and function group. Conditions are derived for aggregate long-term planning (aggregation over function group) combined with one-period disaggregation being optimal. [ABSTRACT FROM AUTHOR]

Shift and days-off scheduling problems have received much attention in the literature of integer programming approaches to workforce scheduling. A typical managerial use would be to schedule full-time employees to minimize the number of labor hours while satisfying variable workforce requirements of a service delivery system. We present computational experience to show that an easily implemented application of linear programming frequently produces optimal solutions to these problems. When the context progresses toward a continuous operating environment (service delivery over 24 hours a day, 7 days a week) we stress the need to shed the myopic views of the shift and days-off scheduling formulations in favor of an integrative tour scheduling formulation. For this problem we observe that a simple heuristic initiated by rounding down the associated LP solution consistently produces near optimal solutions. This observation is based on experiments over varying workforce requirement patterns. [ABSTRACT FROM AUTHOR]

Engineering manpower constitutes an important national resource where demand and supply must be in reasonable balance to assure continued economic growth. The paper establishes a demand analysis to predict the need for engineers in 15 industry groups through 1987, subject to various economic scenarios. It is shown that for total engineering employment in any industry segment the constant dollar gross national product fraction per engineer is only a slowly varying function of time. A least-square fit of this ratio versus time is shown to be an adequate predictor of employment and can be used for extrapolation with confidence. A parallel analysis is also developed for engineers employed in research and development. It is shown that, in general, the need for new engineers due to economic growth is smaller than the need to make up for attrition due to death, retirement, promotions out of engineering and voluntary leaving of the profession. The high mobility rate of engineers out of the profession is significant and its importance has not previously been documented. The paper concludes with a preliminary discussion of the balance between supply and demand. Even with a healthy economic growth the nation is likely to produce a small excess of engineering graduates over the near future. However, there will be a shortage of engineers holding advanced degrees for entry into research and development, even if R & D sees only a moderate growth. Better industry-university cooperation is called for to encourage engineers to undertake advanced degrees, to assess actual future needs and to advise students to select appropriate engineering disciplines. [ABSTRACT FROM AUTHOR]

This paper investigates the relationship between the size of an organization and the number of its administrative personnel drawing upon information from 46 local electricity distribution divisions. Traditionally size has been treated as a uni-dimensional concept, and various single measures/indicators have been used to represent it. In contrast to this view the present study considers size as multi-dimensional. An array of indicators is used and factor analysis is employed to uncover underlying distinct dimensions. In a further step the relationship between the administrative component, i.e. the number of administrative personnel, and the revealed distinct dimensions of size is examined. Results show that the administrative component increases less than proportionately with output-related dimensions of size, thus suggesting that here there are economies of scale. On the other hand the administrative component appears to be weakly related or unrelated to other dimensions expressing fixed assets, market characteristics and growth. Theoretical and practical implications of the analysis are discussed. [ABSTRACT FROM AUTHOR]

Work force scheduling research over the last few years has concentrated on the shift scheduling problem in service oriented firms (telephone operators, postal employees, bank encoders, etc.). In all cases, the authors were primarily interested in the evaluating procedures (optimal and heuristic) to determine the appropriate number of workers to be assigned to the available set of work schedules to meet fluctuating work volumes. However, more attention should be given to how the available shift schedules were defined (start times, durations, etc.) and their impact on maintaining good productivity levels. This paper analyzes the impact of six different approaches in defining the available weekly tour-shift schedules. Tests are conducted to evaluate the performance of the six approaches using operating data from Ohio National Bank for the check proof and encoding activity. The results of this study provide some useful managerial insights into the issues of effectively staffing personnel on a weekly basis. First, restrictive employment policies/customs can substantially increase costs. Second, structured procedures can be used to identify and build good employment schedules for a weekly assignment. And third, the structured procedures presented here provide useful cost and productivity information for evaluating various staffing decisions, and weighing these decisions with other intangible factors such as employee morale and turnover. [ABSTRACT FROM AUTHOR]

In this paper we present data concerning the accuracy of firm's forecasts of engineering employment and suggest a simple model that may be of use in improving their accuracy. The results, which pertain to 54 firms in the aerospace, electronics, chemical, and oil industries, should be of use to managers, because the formulation of proper manpower policies clearly depends on the precision of such forecasts. Our approach also may be applicable to personnel other than engineers: better forecasts may result from the application of this simple model. [ABSTRACT FROM AUTHOR]

We present a greedy heuristic for the n job/1 machine scheduling problem with precedence constraints. This method is useful whenever the manager's optimization criteria is the sum of weighted or unweighted completion times, the sum of weighted or unweighted flow times, (with or without release dates), the sum of weighted or unweighted working times, the sum of weighted or unweighted lateness, average completion time, average flow time, average waiting time or average lateness. The greedy heuristic found the optimal solution for 58 of 68 test problems for which a branch and bound method was used to find the optimal solution. The heuristic is, of course, much easier to implement (and executes in less time). The greedy heuristic fared well in comparison with a simple myopic heuristic presented by Morton and Dharan [4]. [ABSTRACT FROM AUTHOR]

The recruitment of enlisted men and officers under the All-Volunteer Force concept costs approximately $620 million per year; of this amount approximately $100 million are in advertising expenditures. However, recently Congress and the General Accounting Office have expressed considerable concern over the lack of justification for such expenditures. The issue is further complicated by the recent recruiting shortfalls by all the services and the debate surrounding registration and a possible return to the draft. Finally, results of most profit-oriented sales research are difficult to apply to improving military recruiting efficiency due to the difference in the levels of rapport and credibility necessary to convince a potential recruit to invest several years of his life. This paper reports on modeling and implementation experience geared towards determining the proper allocation of resources between advertising and recruiters. This mix is especially crucial since Congress does not permit funds appropriated for advertising to be used for manpower or vice versa. The study consists of two parts: generation of response functions to estimate the number and mix of enlistments over time and geographically as a function of the various demographics, advertising expenditures and the number of recruiters; a nonlinear programming resource allocation model to improve the budget generation and budget execution capabilities in meeting and assessing the impact of the various multi-faceted quantity and quality goals. The basic model, with updating of the response function parameters, is being used by the Navy to aid in the generation and defense of its annual budget appropriations. Numerical results are given which are compared to the past allocations of the Navy and to results observed in industrial product marketing. [ABSTRACT FROM AUTHOR]

In this paper we compare the performance of one-officer and two-officer police patrol units using travel time as the measure of performance. We estimate travel times under two different models of dispatch operations. The first model reflects most existing dispatch systems in which patrol units are assigned to specific beats. Under this beat system, the dispatcher does not know the precise location of each police unit, so he often does not dispatch the closest unit. The second model treats a dispatch operation that is supported by an automatic vehicle monitoring system (AVM). With this system, police units can patrol an overlapping region and the closest available unit to a call can always be dispatched. Probabilistic models are used to derive formulae for estimating travel times to calls requiring only one officer (Type 1) and to calls requiring two officers (Type 2) for each of the two dispatch models. We compared the deployment of the same number of officers in either one or two-officer units over a wide range of unavailability rates. The general findings are summarized as follows: 1. The average travel time of one-officer units to Type 1 calls is at least 30% less than the average travel time of two-officer units. The difference between the two average travel times increases as the unavailability rate increases. 2. The average travel rime of the first-arriving one-officer unit at a Type 2 call is at least 40% less than that of the first-arriving two-officer unit. 3. With non-AVM dispatching and normal patrol beats, the difference between the average travel time of the second-arriving one-officer unit and the first-arriving two-officer unit is sensitive to the unavailability rate. For low unavailability rates the two-officer unit is preferred and for high unavailability rates two one-officer units are preferred. 4. With AVM dispatching and no beats, the average travel time of the second-arriving one-officer unit to a Type 2 call is almost always less than the average travel time of the first-arriving two-officer unit. Again the difference between the two travel times increases as the unavailability rate increases. We also used our models to explore the impact of manpower reductions that accompany a switch to one-officer units. Our results suggest that the existence of an AVM system can be a critical factor when considering manpower reductions. Without an AVM system, the changeover is likely to have mixed results; shorter average travel times for the first-arriving officer and longer travel times for the second-arriving officers. In addition, the results suggest that the existence of an AVM system can significantly affect the average time between the first and second one-officer units. This statistic is a measure of the exposure to danger of the first officer to arrive at the scene. Thus, it may be attractive for a police decision-maker to consider the introduction of an AVM system combined with a changeover from two-officer to one-officer units and a manpower reduction. This is one of the few examples in which new technology can be used to reduce the manpower needs of a police department. At the close of the paper some of the results of our analysis are illustrated with an example. For this specific example we estimate travel time statistics for both dispatch models and discuss manpower reductions and tradeoffs among different travel time measures. We conclude with a discussion of future research directions. [ABSTRACT FROM AUTHOR]

A highly automated, real-time dispatch system is described which uses embedded optimization routines to replace extensive manual operations and to reduce substantially operating costs for a nation-wide fleet of petroleum tank trucks. The system is currently used in daily operations by the Order Entry and Dispatch segment of the Chevron U.S.A. Marketing System. Refined petroleum products valued at several billion dollars per year are dispatched from more than 80 bulk terminals on a fleet exceeding 300 vehicles in approximately 2600 loads per day. Centralized use of the dispatch system required its design and implementation as a set of transaction modules within a large management information system. This environment presents special challenges for the optimization methods; an heuristic sequential network assignment was developed for certified performance on these dispatch models in lieu of their solution as integer programs. Objectives include minimizing transportation costs (approaching $100 million annually) while maintaining equitable man and equipment workload distribution, safety standards, and customer service, and satisfying equipment compatibility restrictions. [ABSTRACT FROM AUTHOR]

Two models are presented as aids in setting realistic numerical goals for the employment of women and minority persons, and in evaluating progress towards meeting such goals. By modelling personnel flows in terms of hiring and persistence rates for various job categories, we develop a consistent structure for projecting future employment patterns as a function of hiring goals. These hiring goals themselves are made to depend on the growth-rate of staff size, the relative availability of women and minority candidates in the potential pool of job applicants, and the organization's policies towards equity in hiring. The second model considers a small organizational unit with fixed staff size. By formulating the process of attrition and replacement with new hires as a Markov chain, we are able to make probability statements about the number of positions that will be occupied by women and/or minority persons at some future time. The relationship of the these probabilities to the distribution among job applicants is made explicit. Applications of these models to faculty and staff planning at Stanford University are briefly discussed. [ABSTRACT FROM AUTHOR]

A goal programming model for planning officer accessions to the U.S. Navy from various commissioning sources is developed and described. Present and future requirements for different career specialty areas in the Navy are considered in terms of years of commissioned service and related to various "choke points" where inventories fall short of requirements in officer force structure. An illustration of the use of this model is provided which involves assessments of the effects of phasing out one comissioning source. Other uses and possible further extensions are also indicated for this model, which now forms a part of the Navy's manpower planning procedures. [ABSTRACT FROM AUTHOR]

This paper develops a balanced growth fractional flow model for the opportunities for promotion, length of service, and career earnings of personnel in a hierarchical manpower organization, and relates these characteristics to the expenditures needed to maintain the system for a specified period of operation. The primary controls available in the model are the proportions of rank members promoted to higher ranks during each period, the proportions of personnel in each rank who are promoted on the basis of seniority, and the growth rate of the size of the system. Using an analytical approach, we investigate the responses to different emphases on seniority in the promotion process, and determine the effect of alternative system growth rates on these responses. Among significant findings are: (i) in systems of stable size, mobility, time-in-service and some career earnings characteristics are independent of the emphasis on seniority in the promotion process; (ii) both the maximum possible periods of service in each rank and the average levels of experience in each rank decrease as promotions-by-seniority increase and as the system growth rate increases; (iii) the total time served in each rank decreases as the system growth rate increases, but decreases as promotions-by-seniority increase only in systems that are stable or growing in size; in contracting systems, total line served in each rank increases as promotions-by-seniority increase; (iv) the trends for changes in the mobility of members in each rank are opposite to those for total time served in the rank; (v) the rank support costs decrease as the promotion rates, the system growth rate, and promotions-by-seniority increase, although these costs are much less sensitive to different emphases on seniority than to changes in the growth rate. [ABSTRACT FROM AUTHOR]

The two duty period scheduling problem is an integer programming problem with 0-1 constraint coefficients. It is recognized that the problem can be reformulated as a one duty period problem with side constraints. Since the one duty period problem can be solved as a minimal cost network flow problem, we dualize with respect to the side constraints, forming a Lagrangean relaxation which is easily solved. Subgradient optimization is used to maximize the Lagrangean. Computational results are reported for several large problems. [ABSTRACT FROM AUTHOR]

A practical conceptual framework for sales resource allocation modeling is presented in this paper. A literature review of sales resource allocation models is described in terms of this framework. The conceptual framework also lends itself to several integer programming models which may be used to address the variety of sales resource allocation decisions faced by every sales organization. A general model for sales resource allocation is developed which incorporates multiple sales resources, multiple time periods and carryover effects, non-separability, and risk. Several actual model implementations are discussed which illustrate the practical application of the integer programming models. The model implementations utilize recent advances in integer programming theory which enables sales managers and sales representatives to quickly develop and evaluate alternative sales resource allocation strategies. [ABSTRACT FROM AUTHOR]

This paper presents a successful application of integer programming to the scheduling of flight crews for a cargo airline. The crew planning process is discussed, the role of the set partitioning model is explained, and representative computational experience is reported. The success of this application is shown to rest upon improved problem conceptualization and decomposition rather than on any advances in solution techniques. [ABSTRACT FROM AUTHOR]

The literature on the decomposition of mathematical programs as models for organizational design and resource allocation in decentralized organizations is extensive. Although models differ in detail, all conceptualize the allocation problem as a multi-level managerial coordination procedure, involving local (divisional) and global (organization-wide) resources, in which informational automony is to be maintained. That is, coordination of resource usage by relatively autonomous divisions is to be effected in these models without any one agent in the organization accumulating complete knowledge of the technical resource transformations, payoff or cost coefficients and detailed plans that divisions utilize in converting resources to useful ends. Unfortunately there has been little empirical investigation into the implementational problems of applying these models in decentralized organizations. This study reports on an experiment with human subjects as decision makers in a simulated decentralized organization. The formulation of the overall resource-allocation problem as a linear program permitted two forms of coordination: price-directive in which transfer pricing is used to allocate resources, and resource-directive in which a rationing or budgeting approach is used. Both schemes can be shown to solve the overall organizational problem but impose different information, communication, and decision-making structures upon the subject managers. The experiment was designed to examine comparative managerial performance by the subjects, as central coordinating agents, under the alternative transfer pricing and budgeting schemes. Within each of these schemes two levels of decision time pressure were also introduced to examine its impact upon subject performance. The purpose of the investigation was to study the influence of organizational design (allocation scheme) and situational factors (time pressure) upon human decision-making under carefully controlled experimental... [ABSTRACT FROM AUTHOR]

This paper deals with a model of the firm engaged in production to order. Models of this situation frequently conclude that the size of the order and production rate each influence the costs of production. Despite this fact, empirical work on production costs focus almost exclusively on either production rate or the size of the order as explainers of variations in costs. In this paper, a model is developed which is consistent with both these facts, the model permits production rate to be a decision variable in the manufacturer's production planning. The model is solved for an optimal production plan which requires production rate to change throughout the life of the program. The planning situation, where alternative order sizes are considered, is then contrasted with the production situation, where unit costs are related to cumulative output given a production plan. This approach provides guidance for the use of data on past programs in the estimation of cost functions and the evaluation of future production plans. [ABSTRACT FROM AUTHOR]

We examine the problem of scheduling days off in continuous (seven-day-a-week) operations under a variety of day-off policies, when demand for manpower is N on weekdays and n on weekend days. We consider a number of policies governing employee work assignments, and in each case we give a formula for the minimum workforce size and a schedule construction algorithm. [ABSTRACT FROM AUTHOR]

Alternative ways to alleviate the shortage of anesthesiologists in obstetric services have been investigated in three study stages. These were (1) a survey and detailed analysis of the existing situation in one metropolitan region of the United States, (2) the construction and validation of a computer simulation model to study the consequences of alternative practice modes with speed, with economy and requiring no human experimentation, and (3) the establishment of a methodology for selecting an optimal anesthesia team configuration. This in turn should aid administrators in establishing future manpower needs and enable more efficient allocations of existing staff. The methodology, incorporating the simulation model, provides team design charts which enable decision makers to arrive at a basis for enlightened tradeoffs between personnel-associated costs and quality of service. Service quality is measured in terms of temporary unavailability of anesthesia personnel with the proper skills for performing certain tasks when needed. This article documents the overall project mission, the data base, the methodologies used, and the study results. [ABSTRACT FROM AUTHOR]

This paper presents a stochastic technique for short-term demand forecasting of manpower requirements for a particular functional skill group. The demand model is adaptable to any organization in which the demand for services from a skill group is derived from several projects or activities. Working from these multi-project demands for skill group services, Bayesian decision analysis is used to produce a composite forecast of total skill group manpower demand. Options in the model provide for selectively varying the number and level of detail of the multi-project demand curves. The output of the model is useful for further manpower planning. [ABSTRACT FROM AUTHOR]

When a demand pattern is dominated by a seasonal effect, the concept of a steady state solution can be used in two ways in aggregate production planning. First, general policy recommendations can be made concerning the use of seasonal workforce changes versus overtime and seasonal inventory. Second, the results can be used to provide ending conditions in an intermediate range planning algorithm with a moving horizon. These ideas are explored using a linear programming model, making use of known planning horizon properties. A simulation experiment tests the efficacy of short horizon deterministic models in a stochastic environment, and demonstrates that ending conditions, derived from the steady state model, improve decisions under a variety of conditions on costs and horizon length. [ABSTRACT FROM AUTHOR]

A fire department, in order to balance equitably its resources throughout a city, must consider several often conflicting objectives, This paper describes an allocation method that avoids the difficulty of choosing an objective in advance by allowing the decision-maker to enumerate a range of criteria by varying a trade-off parameter. The method uses travel time to fires as a measure of system performance and generates allocations satisfying criteria ranging from the minimization of city-wide travel time to the equalization of average travel times in different regions. A comparison of the allocations generated by the model to the current allocation of fire companies in New York City shows that one value of the trade-off parameter produces results that correspond closely to the current allocation policy. An example of how the model can be used as a policy tool is given. [ABSTRACT FROM AUTHOR]

A mathematical model of a military manpower system is presented which seeks to determine the optimal steady state wage rate and force distribution by length of service. Accessions and retention are the transition parameters of a steady state manpower model and these are assumed to be a function of wages. A productivity function is introduced to measure effectiveness of each force structure. Gradient search is used to find the compensation plan that will produce a long-run force with maximum effectiveness within a given limited annual budget. [ABSTRACT FROM AUTHOR]

Heuristic methods are presented for scheduling telephone traffic exchange operators to meet demand that varies over a 24-hour operating period. Two types of heuristics are described: (1) for determining the work shift types to be considered in preparing an operator shift schedule and (2) for constructing an operator shift schedule from a given set of work shift types. These heuristics are evaluated both in terms of solution quality and computational efficiency, using actual operating data. [ABSTRACT FROM AUTHOR]

This paper describes the integration of a network optimization algorithm with a decision and reformation system for the Graduate School of Management at UCLA. This optimization algorithm plays an important role in the determination of the annual teaching schedule by assigning faculty to courses and other activities on the basis of their responses to course preference questionnaires. In addition, the network structure provides an ideal framework for a compact information system for the department. The system can also provide some assistance in determining faculty recruiting priorities or in studying the impacts of changes in student enrollments. Our actual experiences in implementing and using this system are described. [ABSTRACT FROM AUTHOR]

This paper concerns the analysis of two basic planning problems inherent in the building inspection operations of municipal fire prevention bureas. These problems are (1) how often to inspect each type occupancy in each area of the city, and (2) how to divide the city into "area-of-responsibility" districts, with one district for each inspector. The problems are interrelated and are represented in one model. Formulation of the model is based on the operations of the Atlanta, Georgia, Fire Prevention Bureau. The model constitutes a "controllable" analogue to the political redistricting problem. A solution procedure is presented which is a modification of the Hess and Weaver redistricting algorithm. Application of the model and solution procedure to Atlanta is given. Preliminary results indicate an improvement in districting over current practices. [ABSTRACT FROM AUTHOR]

Aggregate manpower plans can be made operational only if they are translatable into shorter range assignments of personnel to specific work groups, operations, and products or services. This paper describes a combined heuristic programming and simulation algorithm amenable to this process of decomposition. Due to the complexity of the problem and the multiplicity of objectives, optimization techniques are only of academic interest. The algorithm is adapted to a particular environment, namely the construction of tour assignments in a post office. A "tour assignment" specifies simultaneously the exact timing (days and hours) of the work week (shift or tour) as well as the particular job assignment for each employee in the workforce. After describing the problem structure, the algorithm's logic is explained along with the interactive nature of the man-machine approach. Several options can be exercised to combine the power of a computer model with the judgment of the decision maker. The application of this methodology, is illustrated with representative data, showing how the search and decision process can be conducted. [ABSTRACT FROM AUTHOR]

A manpower system is examined in which the members are organized according to rules frequently met in graded firms and industries. We determine the manpower structures possible under such conditions and specify the form of the recruitment distribution, given an initial structure. [ABSTRACT FROM AUTHOR]

This paper discusses a methodology developed for allocation of float nurses in short-term general hospitals. The severity of need for nursing care on a unit is measured from the perceptions of head nurses of the unit. A multivariate regression model is used to predict head nurses' perceptions at the beginning of a shift from certain auditable variables. The multivariate regressions are used as an objective function in a branch and bound allocation model designed to allocate float nurses before the start of a shift. The model is tested in five nursing units of a study hospital, and results are presented. [ABSTRACT FROM AUTHOR]

A recently proposed goal programming approach to aggregate planning of production rates and work force levels is reviewed and it is pointed out that there is very little difference between the "new approach" and the earlier Hanseman and Hess linear programming formulation. It is noted that the HMMS model used as a test vehicle in the original article can also be viewed as a goal programming formulation. Some more general opinions on the role of modelling in decision making are also included. [ABSTRACT FROM AUTHOR]

A patient-day of service is classified as potentially avoidable if the unique facilities and manpower of an acute care hospital are not essential to providing the services received. From a practical standpoint, not all potentially avoidable days are truly avoidable. However, norms can be established, specific to diagnosis, surgery, sex, and age, which specify an acceptable range for the percentage of potentially avoidable days. A procedure is developed for efficiently assessing potential avoidability, making it feasible to measure this concept for every patient on a daily basis. The resultant data base can then be used in utilization review screening to detect abnormal patterns of utilization by case, physician, or hospital. [ABSTRACT FROM AUTHOR]

For a seven day a week operation in which N employees are needed on each weekday and n on each weekend day, with N at least as large as n, the effects of time-off policies on the size of the work force are studied. The simplest time-off schedule considered is one in which each employee has two days off out of the week. The most complicated is the policy under which each employee gets every other weekend off, four days off in each two weeks, and all days off in two-day blocks. After the minimum necessary work force has been determined for a policy, it is then shown how any work force meeting the requirement can actually be scheduled. [ABSTRACT FROM AUTHOR]

This paper formulates a general longitudinal manpower flow model and poses the problem of scheduling the inflow of manpower for an infinite number of periods subject to constraints on the stocks and inflows of manpower and the size of the manpower system. The objective is to minimize the present value of the costs of system operation. A finite linear program is introduced which can calculate a lower bound on the optimal value of the infinite problem. The optimal solution of the finite linear program can be used to construct a sound and easily implemented policy for the infinite problem. [ABSTRACT FROM AUTHOR]

This discussion demonstrates the application of discrete optimal control theory to production planning problems. In particular we show that most of the previous models which have appeared in the literature on production planning (scheduling, smoothing and work force balancing) can be characterized as special cases of the control theory problem formulation. This more general model relaxes a number of the assumptions required by other formulations in capturing a wide spectrum of production planning policies. Computational aspects of the control theory approach are discussed and solution results included for numerical examples. [ABSTRACT FROM AUTHOR]