Decision Support
Flexible waste management under uncertainty

https://doi.org/10.1016/j.ejor.2013.09.026Get rights and content

Highlights

  • We determine the optimal recycling policy within a flexible waste management program.

  • We determine the optimal time for investing in a flexible waste management program.

  • Flexibility is purchased to reduce the impact of uncertainty on investment.

  • Investment in a flexible program occurs earlier and at a higher expected NPV.

Abstract

In this paper, we use stochastic dynamic programming to model the choice of a municipality which has to design an optimal waste management program under uncertainty about the price of recyclables in the secondary market. The municipality can, by undertaking an irreversible investment, adopt a flexible program which integrates the existing landfill strategy with recycling, keeping the option to switch back to landfilling, if profitable. We determine the optimal share of waste to be recycled and the optimal timing for the investment in such a flexible program. We find that adopting a flexible program rather than a non-flexible one, the municipality: (i) invests in recycling capacity under circumstances where it would not do so otherwise; (ii) invests earlier; and (iii) benefits from a higher expected net present value.

Introduction

The design of effective solid waste management strategies is a crucial issue for policy makers not only at the (inter)national level, where guidelines, targets, and strategies are set (US EPA, 2002, European Commission, 2010), but also at the local level, where waste is actually produced, collected, and treated.

In the last decades, the amount of municipal solid waste produced by industrialized societies has been increasing (Eurostat, 2011, EPA, 2011). This trend, together with growing attention on environmental pollution, human health, and resource recovery, has stimulated a wide debate on the strategies to be implemented to reduce the amount of waste produced and treat the waste collected in an effective and sustainable way (OECD, 2007, EC, 2008).1 In particular, starting from the late 1970s, the US first, and later the EU, introduced a stricter regulation for the construction and operation of landfills2 in order to promote recycling and incineration as alternative disposal methods (EEA, 2009, Kinnaman, 2006). Incinerators are expensive, however, and their effect on human health is controversial. As a consequence, citizens seem more willing to spend time sorting their waste for recycling than accepting the operation of an incinerator in their neighborhood (Giusti, 2009).3 Thus, although their profitability is still debated, an increasing number of municipalities have introduced recycling programs (in order) to meet citizens’ preferences (see, e.g., Kinnaman, 2006).

In this paper, we consider a municipality designing a new waste management program that integrates the preexistent landfilling with recycling as an alternative waste disposal method.4 We assume that a price is paid to the municipality for recycled materials and that such a price follows a geometric Brownian motion. We also assume that recycling has higher operative costs than landfilling. The municipality can choose between a non-flexible and a flexible waste management program.

By investing in a non-flexible program (hereafter NFP), the municipality may partially or totally substitute landfilling with recycling. This decision is irreversible and implies that, irrespective of a change in the relative convenience of recycling with respect to landfilling, the purchased recycling capacity must always be fully used.

In contrast, by investing in a flexible program (hereafter FP), the municipality purchases recycling capacity but keeps the option to fully use the preexisting landfilling capacity whenever changes in the relative convenience make it profitable. By combining the two disposal methods, the FP guarantees a certain degree of operational flexibility, which may be beneficial under uncertainty about the price for recycled materials. This flexibility, however, comes at a cost. More specifically, we assume that the FP setup requires a sunk investment cost which depends on the chosen recycling capacity, i.e., the chosen degree of flexibility.

The problem faced by the municipality is twofold, and we solve it in two steps. First, the municipality must determine the recycling capacity, taking into account its uncertain profitability and the option of landfilling whenever recycling becomes unprofitable. Second, the municipality must set the investment time threshold, triggering the adoption of the optimally designed FP.

Having designed the optimal FP, we compare the investment in such a program with the investment in an NFP where, as stated above, the option to switch back to landfilling is not available. We find that adopting an FP rather than an NFP gives the municipality two main advantages. First, we show that the municipality may be willing to invest in recycling capacity under circumstances where investment in an NFP would not be undertaken. Second, we show that an investment in an FP may be undertaken earlier than one in an NFP and also provide a higher expected net present value (hereafter NPV).

The intuition behind these results is that the municipality that adopts the FP, by holding the option to switch back to landfilling, may, if needed, adjust the waste disposal operations and so optimally hedge against uncertainty about the profit from recycling. This hedging policy may prove particularly valuable when net revenues from recycling remain low and/or are volatile. In contrast, when net revenues are high and stable, the exercise of the option to switch back to landfilling becomes unlikely and the value of the hedging policy vanishes. Hence, the municipality may, by investing in an FP that guarantees operational flexibility, start recycling when the relative net revenues are too low to justify the investment in an NFP instead. Moreover, this may also occur with a higher payoff in terms of NPV.

Several papers have studied the design of waste management programs in the presence of alternative disposal strategies. In a deterministic frame, some pioneer investigations have been conducted by Huhtala, 1997, Highfill and McAsey, 1997, Highfill and McAsey, 2001b. Huhtala uses an optimal control model to determine the optimal recycling rate for municipal solid waste. He shows that landfilling is more costly than other disposal alternatives, once the monetary costs of recycling, the social costs of landfilling, and consumers’ environmental preferences have been accounted for. Under endogenous waste stream, Highfill and McAsey (1997) study a municipality which must choose between using an (existing and exhaustible) landfill or recycling at higher cost. The authors show that a municipality that recycles will always simultaneously use its landfill. This will last for some time when since landfill use is declining while recycling is increasing. Highfill and McAsey (2001b) extend previous works by including in their analysis a growing income stream. Income is optimally split between consumption and expenditures for waste disposal. Waste disposal must be optimally allocated between recycling, which is considered (as) a backstop technology, and landfilling. The authors show that landfill capacity and initial income have a considerable impact on the optimal recycling program and recommend considering these factors when designing a waste management program. Recently, Lavee et al. (2009) have analyzed the choice of a municipality that can switch forward and backward between landfilling and recycling but cannot combine them. The choice is determined by taking into account a sunk switching cost and uncertainty about prices for recycled materials. Their main finding is that recycling, due to its uncertain profitability, may not be adopted even when it is less expensive than landfilling. Hence, their analysis advises policy intervention in favor of price stabilization as a tool for enhancing recycling. Finally, it is worth noticing that an alternative approach for tackling waste management decision problems under uncertainty and multiplicity of objectives is represented by fuzzy mathematical programming5 (see Zadeh, 1965). As shown by,6 for instance, Koo et al. (1991) and Chang and Wang, 1996a, Chang and Wang, 1997, the practical implementation of this approach to real-world cases may provide valuable support to policy makers when comparing waste disposal alternatives characterized by different economic and environmental impacts.

Our paper contributes to the literature adopting a stochastic programming approach in two respects. First, under uncertainty about profit from recycling, we study the optimal design of a program where the simultaneous combination of two disposal strategies, i.e., landfilling and recycling, is feasible. Second, we consider how the presence of landfilling as a preexisting and residual method affects (i) the degree of operational flexibility in the waste management program and (ii) the timing of its adoption.7

The remainder of the paper is organized as follows. In Section 2, we present the basic setup of our model. In Section 3, we determine the optimal recycling capacity. In Section 4, we study investment value and timing. In Section 5, we use some numerical examples to illustrate our findings. Section 6 concludes. All proofs are available in Appendix A.

Section snippets

The basic setup

Consider a municipality currently using landfilling as a waste disposal method and contemplating the opportunity of integrating it with recycling. Following Highfill and McAsey (2001b), we restrict our analysis to the recycling programs offered by the municipality and do not consider any recycling activity undertaken by individuals on their own initiative. By integrating these two disposal methods, the collected waste may be partially or totally recycled, with the municipality still holding the

The optimal waste management program

In this section, we determine the recycling capacity, α, that a municipality must purchase to ensure an optimal waste management program. As discussed above, when an FP, W, has been adopted, the municipality holds the options to switch to recycling and back to landfilling. These options are particularly valuable under uncertain profit from recycling since they provide the flexibility needed to conveniently rearrange the waste disposal operations. As can be seen from Eq. (7.1–7.2), the value of

Investment value and adoption timing

In this section, we study the timing of the investment in an optimal waste management program. To this end, we derive the value of the option to invest and then determine the conditions characterizing an optimal investment time strategy.

First, let us define by W and W^ the flexible and the non-flexible program where the recycling capacity has been set at its optimal level, α(pt). Second, we consider the option to invest in the continuation region 0<pt<p̃ where p̃ is the price threshold

Numerical examples

In this section, we use some numerical examples to illustrate the effect of operational flexibility on the investment timing and on the value of a waste disposal program. We start our calculations by setting d = 1. This is equivalent to normalizing our frame with respect to the additional cost of disposal incurred when recycling.

Conclusion

The design of a waste management program is a crucial choice for a municipality. This must be made by taking into account, on the one hand, the constraints fixed on the disposal methods available and, on the other hand, the economic profitability of the adopted program. Despite the increasing popularity of recycling programs, their actual economic profitability remains weak. This is mainly due to the level of prices paid for recycled materials, which, for some specific materials, do not even

Acknowledgement

We wish to thank Michele Moretto for helpful comments. We are also grateful for comments and suggestions to seminar participants at FOI (University of Copenhagen) and University of Brescia. The usual disclaimer applies.

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