An Optimization Approach for Medical Waste Treatment and Landfilling

Solid waste containing hazardous materials is dumped simply into landfills where the rag pickers are exposed to contamination. The disease's prevalence, which may be transmitted by hospital waste, has been alarming in cities near landfills. A mathematical model has been developed to predict the weights of medical waste for the next years (until 2035) using theartificial neural network (ANN). Predicted future medical waste weights of future plan hospitals are found to be up (55444) ton as per bed occupancies 100%. Predicted medical waste weights are used later to determine the required treatment plants and landfills capacities and select the optimal number and location of treatment plants and landfills by applying an optimization approach. A total of (2047) optimization subproblems within (11) scenario are solved to choose the optimum number of landfills and its locations. The overall minimum treatment and transportation cost is found to be gained by scenario (6), which tests the decision of using (6) landfill sites.Succeeded landfills are located atAlexandria, Imam, AbiGharaq, Hilla, Medhatia, and Shomaly districts, where have acapacity of (9240) ton for each landfill. It is clear to seen scenario (7) and (8) have a slight difference in cost with that for theoverall minimum cost in scenario (6) and they can be selectedif the optimal solution is not applicable for any reasonwithin a permission 10% and 20% of total cost. Keyword Medical waste, Prediction model, ANN,Optimization, Transportation problem.

tory variables output sigmoi s for hidden la the connection the connection values of hidde wo groups: the ears) is used fo epending on t t (R 2 ) and the os. The scenar his scenario g B.C) represen while bed oc of the input pa    Jurf Al-Nasr Alexandria  Many criteria, like environmental, political, economic, hydrological and hydrogeological criteria, are specified landfill selection. Many limitations are put to ensure these criteria, like:

IV. DESIGN, SITING AND OPERATION OF TREATMENT PLANTS AND LANDFILLS
 Landfills should be placed farther than 1000 ft. (304.8 m) up gradient from water wells [Sener, 2004] [6] .  Due to the movement of leachate and rock slope failure which can be influenced by thegeologic structure of dump layer, the best location of thelandfillis flat rolling hills that not underwent to floods.  Landfills should be constructed on a distance farther than 5000m from urban centers unless there are natural barriers [Al-Anbari et al., 2013] [7] .  A buffer zone of 500m is acceptable for roads around landfill site, despite that, the distance greater than 1 km from roads and highways should be avoided because the expensive cost of constructing road networks [Allen et al., 2001] [8] .  The buffer zone is determined as 500m for rivers or lakes and up to 250m swamp areas [Al-Anbari et al., 2013] [7] .  Distance from sensitive lands as cemeteries, historical sites, and religious sites must be more than 1500 m [Gisi, 2010] [9] .  The distance of 3030 m must be taken as a buffer zone from theairport [El-Alfy et al., 2010] [10] . Siting of treatment plants and landfills is implemented into two stages. In the first stage, siting considerations are appointed on the available sites in Babil Governorate to elect all sites that satisfy criteria such as governmental regulations, ground water, hydrogeological, geological, soil characteristics, topographical and natural resources criteria.In the second stage, a constrained optimization model is constructed to choose the best number of landfills and their locations. The objective function of the optimization model aims to minimize the total cost of treatment plants, supplying and installing, and medical waste transportation costs. Figure  Within the first stage, the buffer zones criteria are limited to 5000, 250, 500, 30, 75, 250, 1500, 3000 and 500m away from urban centers, swamp areas, roads, power lines, oil pipes, liquid gas, religion site, airports and railways, respectively. Accordingly, eleven sites within Babil Governorate borders pass the siting limitations. Succeeded sites from the first stage that shown in figure (6) will be optimized in the second stage.

A. Simplex Linear Programming
Linear program solver LiPS 1.11.1 is used. The solver is intended for solving linear, integer and goal programming problems. In thecase of large input data, the solver will use LU factorization method. In this study, 11 scenarios have been tested to reach the minimum cost of treatment and landfilling for themedical waste of Babil Governorate. Each scenario will mathematically evaluate the cost due to choosing a certain number of landfills. As example, scenario 1 tests the decision of using one landfill, scenario 2 tests the decision of using two landfill sites, and so on. A total of (2047) optimization sub-problems are solved to choose the optimum number of landfills and its locations.

B. Treatment Plants and Transportation Costs
The cost of supplying and installing treatment plants are assumed depending on the utilizing of machinery and equipment prices at sales services via web portals. The prices of treatment units according to the total input weight rates of medical waste are detailed in table (3). Transportation costs are estimated based on the assumption that truck yielding a total of 3-8 ton per transit. The total transportation costs can be approximated depending on the following: If the distance between the source and the destination is less than 30 miles (48.3 km), the transportation cost will be 0.46 $/km.ton. If the distance varies between 30 to 200 mile (48.3-321.8 km), the transportation cost will be 0.38 $/km.ton. The transportation cost will be 0.31 $/km.ton if the distance is more than 200 mile (321.8 km) [ (Feizollahi et al., 1995) [12] and (Directorate of Al-Musayeb municipality, unpublished reports, 2016) [13] ].

C. Formulation of Treatment Plants and Landfills Siting Problem
To determine  optimal  locations  for  treatment  plants  and  landfills  within Babil Governorate, the transportation in addition to treatment plant units' cost must be minimized. Hospitals (assumed to be at the centre of their own district) products an amount of medical waste to supply destinations, each landfill has a potential capacity for maximum weights of previously predicted medical waste. The objective function of present study problem can be reprostate as: The objective function is objected to supply and demand constraints: = Medical wasteweighs from source (i). The solution of theproblem is implemented for (2047) sub-problems for (11) scenario, landfills capacities are assumed to be equal in the same scenario. The overall minimum between this (2047) sub-problems (δ) is considered as the optimum solution and the corresponding number of thetreatment plant and their locations are the optimum between other experimented scenarios.Table (5) shows a summary of the results of the linear programming problem of landfills siting in Babil Governorate.   (7) shows the variation of minimum cost with the number of landfills. The overall minimum is found to be gained by scenario (6) with landfills located at Alexandria (L2), Imam (L4), Abi-Gharaq (L6), Hilla (L7), Medhatia (L9) and Shomaly (L11). It is important to record that scenario (7) with landfills located at Alexandria (L2), Imam (L4), Abi-Gharaq (L6), Hilla (L7), Medhatia (L9), Kifl (L10) and Shomaly (L11) and scenario (8) with landfills located at Alexandria (L2), Sadda (L3), Imam (L4), Abi-Gharaq (L6), Hilla (L7), Medhatia (L9), Kifl (L10) and Shomaly (L11), have a slight difference in cost with that for overall minimum cost in scenario (6) and they can be considered as succeeded scenarios. Figure (8) shows the (462) sub-problems solved in present study for scenario (6) to reach the minimum scenario cost.   Figure (10) shows the succeeded optimization sub-problem that solved corresponding to scenario 6. It can also be noticed that outgoing medical waste proportion contributes the total capacity of thelandfill.

D. The Inability to Satisfy the Optimum Scenario:
There are many reasons make the optimum scenario cannot satisfy, this inability may be due to the changes in land use, overestimated or unexpected population growth because of exceptional conditions or immigration, whether or not the structural future plan is accomplished, financial considerations and other reasons else.Alternative for such cases is studied to produce new choices that minimize the cost, this analysis done by assuming that there is up to 10% and 20% of total cost of scenario (6) is permitted. All scenarios of a cost increment less than 10% and 20% of the total cost are suggested to be alternatives if a shortage of optimum scenario site will occur to provide the required flexibility to the decision maker.
Permission of 10% of total cost for succeeded landfills corresponding to scenario 6 brings out 13 alternative sites (each consists of 6 active landfills) distributed over all districts, selected landfills for scenario (7) also validate at cost release 10% of total cost. Likewise, 58 alternative sites are brought up a cost release of 20% distributed to all districts in thegovernorate. It can be seen that alternative sites if there is a release to 10% and 20% increment in the total cost, will appear in scenario (7) and (8), while no other scenario produce alternative sites. Figure (11  VI. CONCLUSION Based on the results obtained from this study, many conclusions can be inferred. For medical waste prediction model, it can be seen that the generated model is influenced significantly by the order of consecutive monthsforbed capacity, area, population and bed occupation. Also, Landfills locations play an essential role in solid waste management cost where the cost of treatment and landfilling of medical waste are not directly proportionalto the number of landfills, i.e. if landfills number increase, it is not necessary to result in an increase in medical waste management cost. One also can conclude that the optimum solution is not unique if slight differences in scenarios costs are ignored.  (7) (11-C) Succeeded sites from scenario (8) (11-A) Succeeded sites from scenario (6) For the case study focused throughout this study, medical waste weights are predicted until 2035 as per bed occupancies (100%) for health care facilities according to government future plan. The developedANN model succeeded model to match historical records with R 2 equal to (98%) and RMSE of (258.67 kg). Results and comparisons showed that using an optimization approach with ANN prediction seem to be beneficial to provide the decision makers multiple, flexible and economic choices for medical waste treatment and management.