ABSTRACTConsumer choice among multiattributed products is modeled as a two‐stage process in which a conjunctive stage (that eliminates products with one or more "totally unacceptable" attribute levels) is followed by a compensatory stage (that trades off remaining products on multiple attributes). A self‐explicated preference measurement procedure based on the two‐stage model yielded a slightly larger predictive validity compared to conjoint analysis.
Abstract Since 1971 conjoint analysis has been applied to a wide variety of problems in consumer research. This paper discusses various issues involved in implementing conjoint analysis and describes some new technical developments and application areas for the methodology.
AbstractWe consider the transportation problem of determining nonnegative shipments from a set of m warehouses with given availabilities to a set of n markets with given requirements. Three objectives are defined for each solution: (i) total cost, TC, (ii) bottleneck time, BT (i.e., maximum transportation time for a positive shipment), and (iii) bottleneck shipment, SB (i.e., total shipment over routes with bottleneck time). An algorithm is given for determining all efficient (pareto‐optimal or nondominated) (TC, BT) solution pairs. The special case of this algorithm when all the unit cost coefficients are zero is shown to be the same as the algorithms for minimizing BT. provided by Szwarc and Hammer. This algorithm for minimizing BT is shown to be computationally superior. Transportation or assignment problems with m=n=100 average about a second on the UNIVAC 1108 computer (FORTRAN V)) to the threshold algorithm for minimizing BT. The algorithm is then extended to provide not only all the efficient (TC, BT) solution pairs but also, for each such BT, all the efficient (TC, SB) solution pairs. The algorithms are based on the cost operator theory of parametric programming for the transportation problem developed by the authors.
AbstractIn this paper we consider a multiperiod deterministic capacity expansion and shipment planning problem for a single product. The product can be manufactured in several producing regions and is required in a number of markets. The demands for each of the markets are non‐decreasing over time and must be met exactly during each time period (i.e., no backlogging or inventorying for future periods is permitted). Each region is assumed to have an initial production capacity, which may be increased at a given cost in any period. The demand in a market can be satisfied by production and shipment from any of the regions. The problem is to find a schedule of capacity expansions for the regions and a schedule of shipments from the regions to the markets so as to minimize the discounted capacity expansion and shipment costs. The problem is formulated as a linear programming model, and solved by an efficient algorithm using the operator theory of parametric programming for the transporation problem. Extensions to the infinite horizon case are also provided.
AbstractThis paper considers a logistics system modelled as a transportation problem with a linear cost structure and lower bounds on supply from each origin and to each destination. We provide an algorithm for obtaining the growth path of such a system, i. e., determining the optimum shipment patterns and supply levels from origins and to destinations, when the total volume handled in the system is increased. Extensions of the procedure for the case when the costs of supplying are convex and piecewise linear and for solving transportation problems that are not in "standard form" are discussed. A procedure is provided for determining optimal plant capacities when the market requirements have prespecified growth rates. A goal programming growth model where the minimum requirements are treated as goals rather than as absolute requirements is also formulated.
AbstractThis paper investigates the effect on the optimum solution of a (capacitated) transportation problem when the data of the problem (the rim conditions‐i. e., the warehouse supplies and market demands‐the per unit transportation costs and the upper bounds) are continuously varied as a (linear) function of a single parameter. An operator theory is developed and algorithms provided for applying rim and cost operators that effect the transformation of optimum solution associated with changes in rim conditions and unit costs. Bound operators that effect changes in upper bounds are shown to be equivalent to rim operators. The discussion in this paper is limited to basis preserving operators for which the changes in the data are such that the optimum basis structures are preserved.
AbstractThis paper models a k‐unit service system (e.g., a repair, maintenance, or rental facility) with Poisson arrivals, exponential service times, and no queue. If we denote the number of units that are busy as the state of the system, the state‐dependent pricing model formalizes the intuitive notion that when most units are idle, the price (i.e., the service charge per unit time) should be low, and when most units are busy, the price should be higher than the average. A computationally efficient algorithm based on a nonlinear programming formulation of the problem is provided for determination of the optimal state‐dependent prices. The procedure ultimately reduces to the search on a single variable in an interval to determine the unique intersection point of a concave increasing function and a linear decreasing function. The algorithm takes, on the average, only about 1/2 second per problem on the IBM 360/65 (FORTRAN G Compiler). A discrete optimal‐control approach to the problem is shown to result in essentially the same procedure as the nonlinear‐programming formulation. Several properties of the optimal state‐dependent prices are given. Comparisons of the optimal values of the objective function for the state‐dependent and state‐independent pricing policies show that the former is on the average, only about 0.7% better than the latter, which may explain partly why state‐dependent pricing is not prevalent in many service systems. Potential generalizations of the model are discussed.
Summary Background Comprehensive and comparable estimates of health spending in each country are a key input for health policy and planning, and are necessary to support the achievement of national and international health goals. Previous studies have tracked past and projected future health spending until 2040 and shown that, with economic development, countries tend to spend more on health per capita, with a decreasing share of spending from development assistance and out-of-pocket sources. We aimed to characterise the past, present, and predicted future of global health spending, with an emphasis on equity in spending across countries. Methods We estimated domestic health spending for 195 countries and territories from 1995 to 2016, split into three categories—government, out-of-pocket, and prepaid private health spending—and estimated development assistance for health (DAH) from 1990 to 2018. We estimated future scenarios of health spending using an ensemble of linear mixed-effects models with time series specifications to project domestic health spending from 2017 through 2050 and DAH from 2019 through 2050. Data were extracted from a broad set of sources tracking health spending and revenue, and were standardised and converted to inflation-adjusted 2018 US dollars. Incomplete or low-quality data were modelled and uncertainty was estimated, leading to a complete data series of total, government, prepaid private, and out-of-pocket health spending, and DAH. Estimates are reported in 2018 US dollars, 2018 purchasing-power parity-adjusted dollars, and as a percentage of gross domestic product. We used demographic decomposition methods to assess a set of factors associated with changes in government health spending between 1995 and 2016 and to examine evidence to support the theory of the health financing transition. We projected two alternative future scenarios based on higher government health spending to assess the potential ability of governments to generate more resources for health. Findings Between 1995 and 2016, health spending grew at a rate of 4·00% (95% uncertainty interval 3·89–4·12) annually, although it grew slower in per capita terms (2·72% [2·61–2·84]) and increased by less than $1 per capita over this period in 22 of 195 countries. The highest annual growth rates in per capita health spending were observed in upper-middle-income countries (5·55% [5·18–5·95]), mainly due to growth in government health spending, and in lower-middle-income countries (3·71% [3·10–4·34]), mainly from DAH. Health spending globally reached $8·0 trillion (7·8–8·1) in 2016 (comprising 8·6% [8·4–8·7] of the global economy and $10·3 trillion [10·1–10·6] in purchasing-power parity-adjusted dollars), with a per capita spending of US$5252 (5184–5319) in high-income countries, $491 (461–524) in upper-middle-income countries, $81 (74–89) in lower-middle-income countries, and $40 (38–43) in low-income countries. In 2016, 0·4% (0·3–0·4) of health spending globally was in low-income countries, despite these countries comprising 10·0% of the global population. In 2018, the largest proportion of DAH targeted HIV/AIDS ($9·5 billion, 24·3% of total DAH), although spending on other infectious diseases (excluding tuberculosis and malaria) grew fastest from 2010 to 2018 (6·27% per year). The leading sources of DAH were the USA and private philanthropy (excluding corporate donations and the Bill & Melinda Gates Foundation). For the first time, we included estimates of China's contribution to DAH ($644·7 million in 2018). Globally, health spending is projected to increase to $15·0 trillion (14·0–16·0) by 2050 (reaching 9·4% [7·6–11·3] of the global economy and $21·3 trillion [19·8–23·1] in purchasing-power parity-adjusted dollars), but at a lower growth rate of 1·84% (1·68–2·02) annually, and with continuing disparities in spending between countries. In 2050, we estimate that 0·6% (0·6–0·7) of health spending will occur in currently low-income countries, despite these countries comprising an estimated 15·7% of the global population by 2050. The ratio between per capita health spending in high-income and low-income countries was 130·2 (122·9–136·9) in 2016 and is projected to remain at similar levels in 2050 (125·9 [113·7–138·1]). The decomposition analysis identified governments' increased prioritisation of the health sector and economic development as the strongest factors associated with increases in government health spending globally. Future government health spending scenarios suggest that, with greater prioritisation of the health sector and increased government spending, health spending per capita could more than double, with greater impacts in countries that currently have the lowest levels of government health spending. Interpretation Financing for global health has increased steadily over the past two decades and is projected to continue increasing in the future, although at a slower pace of growth and with persistent disparities in per-capita health spending between countries. Out-of-pocket spending is projected to remain substantial outside of high-income countries. Many low-income countries are expected to remain dependent on development assistance, although with greater government spending, larger investments in health are feasible. In the absence of sustained new investments in health, increasing efficiency in health spending is essential to meet global health targets. Funding Bill & Melinda Gates Foundation.
