Allocation in Life Cycle Inventory Analysis for Joint Production

Allocation in joint production is still one of the unresolved and often discussed methodological issues in Life Cycle Inventory Analysis. Using the many years of experience of man agement sciences, a new classification scheme is proposed. It is postulated that companies perform allocation in joint production in view of optimising the products’ performance (economic and/ or environmental), which helps them to maximise their profits. Therefrom it is derived that value judgements and negotiations are inevitable. The proposed classification scheme differentiates between the number of decision-makers involved, and the type of markets for joint products. Several decision-makers have to find fair allocation factors for their commonly operated joint production, whereas individual decision-makers may choose allocation factors considering the (economic and/ or environmental) competitiveness of their joint products. Applied on the case of a small-scale gas-fuelled combined heat and power plant, the methodology proposed shows a strong dependency on the disutility function, i.e., private costs, environmental damage costs or a combination of the two. Presentation and Introduction of this set of articles see Int. J. LCA 4 (3) 175–179 (1999)     

Average-Cost Optimal Policies for an Unreliable Flexible Multiproduct Machine

This paper is concerned with optimal production planning on a single failure-prone flexible machine that produces N distinct part types. The machine is flexible in the sense that no setup is required for switching from production of one part type to another. We consider the problem of controlling production rates to minimize the expected long-run average cost of product surpluses over time. We assume constant unit holding and shortage costs and constant demand rates for the part types. Moreover, the costs are assumed to be the same for all products. We provide an explicit optimal solution for the problem.     

Optimal allocation between nutrient uptake and growth in a microbial trichome

 A microbial trichome grows by assimilating nutrients from its environment, and converting these into catalytic macro-molecular machinery. This machinery may be divided into assimilatory machinery and proliferative machinery. The former type is involved in nutrient uptake, whereas the latter type enables the trichome to grow. The cells in the trichome are faced with an allocation problem: given the availability of nutrients in the environment, how many macro-molecular building blocks should be allocated to the synthesis of assimilatory machinery, and how many to the synthesis of proliferative machinery? We answer this question for a particular model, which is a generalization of the Droop quota model. We formulate a two-dimensional non-linear optimal control problem, corresponding to this model. An optimal allocation regime with a singular segment is derived, based on Pontryagin’s maximum principle. We give a direct proof of optimality. We discuss how actual biological cells might implement this optimal regime. Received: 16 December 1996 / Revised version: 14 September 1997     

Optimal resource allocation in perennial plants: A continuous-time model

A continuous-time model, similar to W. M. Schaffer's (1983, Amer. Nat. 121, 418–431), of growth and reproduction for a perennial herb with discrete growing seasons is considered. Assuming that metabolic rates of reproductive and storage structures are equal, it was possible, through the reduction of the continuous model to a discrete one, to find the optimal allocations to the vegetative, reproductive, and reserve structures. The main feature of the optimal strategy is the existence of an optimal reserve size. The allocation to vegetative structures is, every growing season, the allocation which maximizes the total of reproductive and reserve structures at the end of the season. The relative allocation between reserve and reproductive structures is given, when reproductive success is a linear function of investment, by the fastest growth to the optimal size: no reproduction until the optimal size is reached, and, afterwards, allocation to reproduction of everything beyond what is needed to maintain size R*. Asymptotic growth to the equilibrium and cycles are possible, when reproductive success is a nonlinear function of investment (A. Pugliese, 1988, in “Biomathematics and Related Computational Problems” (L. M. Ricciardi, Ed.), Reidel, Dordrecht, to appear). It has therefore been possible to solve the “general life history problem” ( Schaffer, 1983) when growth is in general a concave function of body size. In the Discussion discrete and continuous-time models are compared; if the real dynamics is described by a continuous model of the type analyzed here, life history predictions made by analyzing the system with a discrete model are upheld.     

Dynamic optimization of host defense, immune memory, and post-infection pathogen levels in mammals

When attacked by pathogens, higher vertebrates produce specific immune cells that fight against them. We here studied the host's optimal schedule of specific immune cell production. The damage caused by the pathogen increases with the pathogen amount in the host integrated over time. On the other hand, there is also a cost incurred by the production of specific immune cells, not only in terms of the energy needed to produce and maintain the cells, but also with respect to damages sustained by the host's body as a result of immune activity. The optimal strategy of the host is the one that minimizes the total cost, defined as a weighted sum of the damage caused by pathogens and the costs caused by the specific immune cells. The problem is solved by using Pontryagin's maximum principle and dynamic programming. The optimal defense schedule is typically as follows: In the initial phase after infection, immune cells are produced at the fastest possible rate. The amount of pathogen increases temporarily but is eventually suppressed. When the pathogen amount is suppressed to a sufficiently low level, the immune cell number decreases and converges to a low steady level, which is maintained by alternately switching between fastest production and no production. We examine the effect of time delay required to have fully active immune cells by comparing cases with different number of rate limiting steps before producing immune cells. We examine the effect of the duration of time (time delay) required before full-scale production of active immune cells by comparing cases with different numbers of rate-limiting steps before immune-cell production. We also discuss the role of immune memory based on the results of the optimal immune reaction.     

Evolution of life history strategies for an asexual annual plant model

At any given moment in time a plant is partitioning total growth mass into its various component parts such as leaves, roots, reproductive material, etc. The view is taken that the plant has evolved a life history strategy to control this partitioning process. This paper illustrates the utility of optimal control theory for use in determining life history strategies which maximize fitness for a given asexual plant model. The optimal control methods are first used on a model previously analyzed by Professor Dan Cohen, who used a different method. His results of a change from 100% vegetable growth to 100% reproductive growth at a fixed switching time is again obtained. This 100% switching result is shown to be more generally applicable by using a qualitatively described model. However the switching time in general is shown to be a function of both leaf mass and time remaining to the end of the growing season. The allocation to toxin production is also considered. It is shown that under this model an inequality between system parameters must be satisfied before the plant should allocate growth to toxin production. Although the particular model explored here may rarely be realistic in nature, these same methods of optimal control theory can be applied in a similar fashion to many other proposed models of plant resource allocation.     

Life-history consequences of investment in free-spawned eggs and their accessory coats

The optimal trade-off between offspring size and number can depend on details of the mode of reproduction or development. In marine organisms, broadcast spawning is widespread, and external coats are a common feature of spawned eggs. Egg jelly coats are thought to influence several aspects of fertilization and early development, including the size of the target for sperm, fertilization efficiency, egg suspension time, polyspermy, embryo survival, and fecundity. These costs and benefits of investment in jelly result in trade-offs that can influence optimal reproductive allocation and the evolution of egg size. I develop an optimization model that sequentially incorporates assumptions about the function of egg coats in fertilization. The model predicts large variation in coat size and limited variation in ovum size under a broad range of conditions. Heterogeneity among spawning events further limits the range of ovum sizes predicted to evolve under sperm limitation. In contrast, variation in larval mortality predicts a broad range of optimal ovum sizes that more closely reflects natural variation among broadcast-spawning invertebrates. By decoupling physical and energetic size, egg coats can enhance fertilization, maintain high fecundity, and buffer the evolution of ovum size from variation in spawning conditions.     

An Optimal Strategy for Energy Allocation in a Multiple Resource Environment

We consider a model for a population in discrete time with nonoverlapping generations that has fecundity proportional to the amounts of two essential resources obtained up to a saturating level. A population’s strategy defines how individuals divide their total available energy between efforts to obtain the two resources. We assume that the total amount of each resource obtained is a positive, increasing, concave down function of the total energy exerted toward the resource. By considering two competing subpopulations that have different energy allocation strategies, we characterize the stability of all possible equilibria and find a unique optimal strategy where a fixed subpopulation resists invasion by a small competing subpopulation using any other strategy. Except when one of the resources is readily obtained above the saturation level, this optimal strategy is to divide effort equally between the resources. We illustrate the behavior of the model, directly showing the effects of an invading subpopulation with pairwise invasibility plots.     

Optimal surveillance strategy for invasive species management when surveys stop after detection

Invasive species are a cause for concern in natural and economic systems and require both monitoring and management. There is a trade‐off between the amount of resources spent on surveying for the species and conducting early management of occupied sites, and the resources that are ultimately spent in delayed management at sites where the species was present but undetected. Previous work addressed this optimal resource allocation problem assuming that surveys continue despite detection until the initially planned survey effort is consumed. However, a more realistic scenario is often that surveys stop after detection (i.e., follow a “removal” sampling design) and then management begins. Such an approach will indicate a different optimal survey design and can be expected to be more efficient. We analyze this case and compare the expected efficiency of invasive species management programs under both survey methods. We also evaluate the impact of mis‐specifying the type of sampling approach during the program design phase. We derive analytical expressions that optimize resource allocation between monitoring and management in surveillance programs when surveys stop after detection. We do this under a scenario of unconstrained resources and scenarios where survey budget is constrained. The efficiency of surveillance programs is greater if a “removal survey” design is used, with larger gains obtained when savings from early detection are high, occupancy is high, and survey costs are not much lower than early management costs at a site. Designing a surveillance program disregarding that surveys stop after detection can result in an efficiency loss. Our results help guide the design of future surveillance programs for invasive species. Addressing program design within a decision‐theoretic framework can lead to a better use of available resources. We show how species prevalence, its detectability, and the benefits derived from early detection can be considered.     

Parasites shape the optimal investment in immunity

The evolution of optimal functioning and maintenance of the immune system is thought to be driven by the costs arising from the allocation of resources to immune functions rather than to growth and reproduction and by the benefits arising from higher defence if an infection occurs. In young animals there is a high premium for fast growth and competitiveness and a parasite-mediated trade-off is thus predicted between the allocation of resources to growth versus immune function. In a field study on nestling great tits (Parus major), we manipulated simultaneously the level of immune defence by a dietary supplementation of the immunostimulant methionine and ectoparasite (Ceratophyllus gallinae) abundance in the nest and thereby assessed both the costs and benefits of investing in immune defence. Nestlings supplemented with methionine grew slower during the experimental boost of their immune system compared to controls. Thereafter, however, nestlings with a boosted immune system grew at faster rates under parasite pressure compared to unstimulated birds. It experimentally shows the costs and benefits of investment in immunity and suggests that the evolution of optimum host defence is governed by a parasite-mediated allocation trade-off between growth and immune function.     

Environmental heterogeneity generates fluctuating selection on a secondary sexual trait

In any population in which resources are limiting, the allocation of resources toward increased reproductive success may generate costs to survival [1-8]. The relationship between a sexually selected trait and fitness will therefore represent a balance between its relative associations with fecundity versus viability [3, 6, 7]. Because the risk of mortality in a population is likely to be heavily determined by ecological conditions, survival costs may vary as a function of the prevailing environment [7]. As a result, for populations experiencing heterogeneous ecological conditions, there may not be a single optimal level of allocation toward reproduction versus survival [9]. Here, we show that early viability and fecundity selection act in opposing directions on a secondary sexual trait and that their relative magnitude depends upon ecological conditions, generating fluctuating selection. In a wild population of Soay sheep (Ovis aries), phenotypic and genetic associations between male horn growth and lifetime reproductive success were positive under good environmental conditions (because of increased breeding success) and negative under poor environmental conditions (because of reduced survival). In an unpredictable environment, high allocation to early horn growth is a gamble that will only pay off if ensuing conditions are favorable. Such fluctuating selection may play an important role in preventing the erosion of genetic variance in secondary sexual traits.     

Resource allocation for epidemic control over short time horizons

We present a model for allocation of epidemic control resources among a set of interventions. We assume that the epidemic is modeled by a general compartmental epidemic model, and that interventions change one or more of the parameters that describe the epidemic. Associated with each intervention is a 'production function' that relates the amount invested in the intervention to values of parameters in the epidemic model. The goal is to maximize quality-adjusted life years gained or the number of new infections averted over a fixed time horizon, subject to a budget constraint. Unlike previous models, our model allows for interacting populations and non-linear interacting production functions and does not require a long time horizon. We show that an analytical solution to the model may be difficult or impossible to derive, even for simple cases. Therefore, we derive a method of approximating the objective functions. We use the approximations to gain insight into the optimal resource allocation for three problem instances. We also develop heuristics for solving the general resource allocation problem. We present results of numerical studies using our approximations and heuristics. Finally, we discuss implications and applications of this work.     

Optimising investments from elephant tourist revenues in the Maputo Elephant Reserve, Mozambique

Private enterprises are active in conservation initiatives in Africa. Some of these enterprises have long-term licences for the development of conservation areas. The motivation of these organisations to participate in conservation is ultimately determined by the economic output of their activities. An electric fence is being constructed in the Maputo Elephant Reserve, Mozambique. A costs-benefit analysis was carried out, in order to assist in the optimisation of the management activities of the elephant population, based on elephant population size, fence costs, crop raid costs, elephant poaching, and benefits derived from tourism (game-viewing and hunting). Tourist numbers increased with increasing elephant density through a concave utility function. Optimal harvest/hunting strategies were calculated from optimal control theory, using dynamic optimisation (Pontryagin's Maximum Principle). Poaching and raid costs could be compared to fence construction costs at different elephant population sizes. Costs generated through elephant poaching and elephant crop raid costs were higher than fence construction costs at a population size >100. Elephant hunting was a less favourable activity, economically and ecologically, than elephant viewing, due to the large game-viewing profits per elephant. Only if the licence fee increases from US$6500 to 28,500 would hunting become attractive, although ecological and economical constraints would probably prevent the development of hunting activities in the area. The assumed resource price of elephant (US$5000) was lower than the marginal value derived from tourism, indicating that elephants should be bought until the maximum stocking rate is reached.     

Analysis of a two-stage, flexible production system with unreliable machines, finite buffers and non-negligible setups

We analyze a Markov model of a two-stage production system capable of producing two part types. Each stage consists of an unreliable machine and the different stages are decoupled by two intermediate buffers of finite capacity, one for each part type. Unlike previous work, we specifically consider non-negligible machine setup times during changeovers and also assume that machine failure probabilities are dependent on the part type being produced. We assume that machine processing times, repair/failure times and setup times are exponentially distributed and may have different mean rates for each machine and for each part-type. We describe a solution method to evaluate the system performance that reduces the total number of equations to be solved from a multiplicative function to an additive function of buffer sizes. This model may then be integrated with a new decomposition method for analyzing longer lines. The results show the relative influence of different factors on system performance and thus provide guidance to the optimal choice of system parameters such as buffer sizes.     

Scheduling algorithms for a two-machine flexible manufacturing system

The flexible manufacturing system (FMS) considered in this paper is composed of two CNC machines working in series—a punching machine and a bending machine connected through rollers acting as a buffer system of finite capacity. The main difference between the present problem and the standard two-machine flow shop problem with finite intermediate capacity is precisely the buffer system, which in our problem consists of two stacks of parts supported by rollers: the first stack contains the output of the punching machine, while the second stack contains the input for the bending machine. When the second stack is empty, the first stack may be moved over. Furthermore, the capacity of each stack depends on the particular part type being processed. The FMS can manufacture a wide range of parts of different types. Processing times on the two machines are usually different so that an unbalance results in their total workload. Furthermore, whenever there is a change of the part type in production, the machines must be properly reset—that is, some tools need to be changed or repositioned. A second important difference between the present problem and the usual two-machine flow shop problem is the objective. Given a list ofp part types to be produced in known quantities, the problem considered here is how to sequence or alternate the production of the required part types so as to achieve various hierarchical targets: minimize the makespan (the total time needed to complete production) and, for instance, compress the idle periods of the machine with less workload into a few long enough intervals that could be utilized for maintenance or other reasons. Although Johnson's rule is optimal in some particular cases, the problem addressed in the paper isNP-hard in general: heuristic procedures are therefore provided.     

Sequence comparison with concave weighting functions

We consider efficient methods for computing a difference metric between two sequences of symbols, where the cost of an operation to insert or delete a block of symbols is a concave function of the block's length. Alternatively, sequences can be optimally aligned when gap penalties are a concave function of the gap length. Two algorithms based on the ‘candidate list paradigm’ first used by Waterman (1984) are presented. The first computes significantly more parsimonious candidate lists than Waterman's method. The second method refines the first to the point of guaranteeingO(N ² lgN) worst-case time complexity, and under certain conditionsO(N ²). Experimental data show how various properties of the comparison problem affect the methods' relative performance. A number of extensions are discussed, among them a technique for constructing optimal alignments inO(N) space in expectation. This variation gives a practical method for comparing long amino sequences on a small computer. This work was supported in part by NSF Grant DCR-8511455.     

Design of optimal cancer chemotherapy using a continuous-time state model of cell kinetics

A continuous bilinear model in state space is used to describe the cell kinetics of a tumor-cell population under the effects of chemotherapy. Firstly, the time-course behavior of a Chinese-hamster-ovary (CHO) cell population is simulated to demonstrate the utility of the model. Then, an optimal strategy for cancer treatment is derived, based on the need to balance the effects on both cancerous and normal tissues. The performance index minimized is the sum of the weighted tumor population and the weighted total drug dosage. The optimization problem has resulted in a two-point boundary-value problem (TPBVP) with a bang-bang control policy, which is solved by the switching-time variation method (STVM). Computer simulation of CHO cells is also carried out as a numerical example of determining optimal cancer chemotherapy.     

Community dynamics, trade-offs, invasion criteria and the evolution of host resistance to microparasites

A hybrid cellular automaton model is described and used to simulate early tumor growth and examine the roles of host tissue vascular density and tumor metabolism in the ability of a small number of monoclonal transformed cells to develop into an invasive tumor. The model incorporates normal cells, tumor cells, necrotic or empty space, and a random network of native microvessels as components of a cellular automaton state vector. Diffusion of glucose and H(+)ions (the latter largely resulting from the tumor's excessive reliance on anaerobic metabolism) to and from the microvessels, and their utilization or production by cells, is modeled through the solution of differential equations. In this way, the cells and microvessels affect the extracellular concentrations of glucose and H(+)which, in turn, affect the evolution of the automaton. Simulations of the model demonstrate that: (i) high tumor H(+)ion production is favorable for tumor growth and invasion; however for every H(+)ion production rate, there exists a range of optimal microvessel densities (leading to a local pH favorable to tumor but not to normal cells) for which growth and invasion is most effective, (ii) at vascular densities below this range, both tumor and normal cells die due to excessively low pH, (iii) for vascular densities above the optimal range the microvessel network is highly efficient at removing acid and therefore the tumor cells lose their advantage over normal cells gained by high local H(+)concentration. While significant spatial gradients of glucose formed, no regions of detrimentally poor glucose perfusion (for either cell type) were observed, regardless of microvessel density. Depending on metabolic phenotype, a variety of tumor morphologies similar to those clinically observed were realized in the simulations. Lastly, a sharp transition (analogous to that of the adenoma-carcinoma sequence) between states of initial tumor confinement and efficient invasiveness was observed when H(+)production reached a critical value.     

Different effects of mating group size as male and as female on sex allocation in a simultaneous hermaphrodite

Sex allocation theory predicts that the optimal sexual resource allocation of simultaneous hermaphrodites is affected by mating group size (MGS). Although the original concept assumes that the MGS does not differ between male and female functions, the MGS in the male function (MGSm; i.e., the number of sperm recipients the focal individual can deliver its sperm to plus one) and that in the female function (MGSf; the number of sperm donors plus one) do not always coincide and may differently affect the optimal sex allocation. Moreover, reproductive costs can be split into “variable” (e.g., sperm and eggs) and “fixed” (e.g., genitalia) costs, but these have been seldom distinguished in empirical studies. We examined the effects of MGSm and MGSf on the fixed and variable reproductive investments in the sessilian barnacle Balanus rostratus. The results showed that MGSm had a positive effect on sex allocation, whereas MGSf had a nearly significant negative effect. Moreover, the “fixed” cost varied with body size and both aspects of MGS. We argue that the two aspects of MGS should be distinguished for organisms with unilateral mating.