Optimization techniques can be employed to determine the best cropping patterns to ensure optimum net benefits, food production, and labor employment. Therefore, the current investigation employed the linear programming module in LINGO 14.0 software to develop optimal crop area allocation plans in the Right Main Canal (RMC) of the Bhimsagar irrigation project. The optimal cropping patterns (OCPs) were generated for 2013–2014 under different canal run (CR) periods in a month, i.e., 30, 24, and 21 days using three objective functions, viz., net benefit, food production, and labor-days maximization. In addition, the OCP scenarios were generated for long-term agriculture sustainability scenarios, viz., 2015, 2020, and 2025. Results revealed that the net benefit was increased by 122.2, 93.4, and 95.5% for Ratanpura (RT), Chaplada (CP), and Maraita II (MT) minor, respectively, under OCP estimated for 30-day CR in 2013–2014, whereas food production was increased by 22.4, 33.8, and 25.9% for RT, CP, and MT, respectively, under OCP over existing cropping patterns. Similarly, under OCP, labor employment had increased by 40.9, 33.8, and 33.1% for RT, CP, and MT, respectively, for 30-day CR. These findings infer that higher net benefits, food production, and labor employment may be achieved by shifting to OCPs.

  • Linear programming models were developed for net benefit, food, and labor employment maximization.

  • Water availability, area, labor, and food requirements were considered as constraints.

  • Conjunctive water use and long-term scenarios analysis was carried out.

  • Optimal cropping pattern differed from the existing cropping pattern.

  • Net benefit, food production and labor employment enhanced under optimal cropping pattern.

Water and land resource availability is declining at an alarming rate due to urbanization, climate change, and intensive irrigation worldwide (Kumari et al. 2022; Zerouali et al. 2022; Rajput et al. 2023a). India is an agricultural economy accounting for approximately 15% of GDP share but facing water resources availability (Gulati et al. 2021). Efficient use of accessible water resources is essential for a country such as India, which accounts for 17% of the global population with just 2.4% of the land resources and 4% of the freshwater resources (Jerin et al. 2020). In India, the agriculture sector utilizes 80% of the existing groundwater resources (Jain et al. 2020). In addition, agriculture's share of water usage is expected to decline by 10–20% from the current 83% of overall water use (605 × 105 million m3) due to rising industrial and domestic needs (Elbeltagi et al. 2020; Dimple et al. 2023). Population explosion and food security have resulted in an additional burden on the water resources (Jain et al. 2020; Rai et al. 2020). By 2050, India's population may reach 1.6 billion, leading to high consumption of water, food, and energy (Jain et al. 2020).

Determining the ideal cropping pattern for a given land area to limit water usage within a defined threshold is a key factor in ensuring the sustainability of water resources in agricultural production (Hacısüleyman & Özger 2024). Water and land resources planning and management under inadequate resources (such as water, land, capital investment, and human) have been critical issues globally (Dimple et al. 2022a, 2022b; Rajput et al. 2022b). Thus, the available land and water resources must be improved to achieve the sustainable development goals (SDGs) of United Nations (UN) and sustainable agriculture. Strong sustainability is accomplished when irrigation methods ensure that neither natural nor human resources are depleted (Pretty & Bharucha 2014). This implies that both environmental and economic sustainability criteria are fulfilled. This can be achieved by meeting the irrigation water demands while safeguarding environmental flows and freshwater reserves (Jägermeyr et al. 2017).

Optimum water application reduces the problem of salinization, ensures better yield, water saving, higher nutrients use efficiency and thus helps in achieving sustainable agriculture (Dimple et al. 2020). The optimization of input resources can be performed by employing modern tools and techniques (Singh 2022). For example, several researchers have utilized optimization models to obtain optimal land and water allocation plans for food production, net returns, and man-days maximization (Lange et al. 2021; Ogbolumani & Nwulu 2022; Singh 2022). Efficient and well-planned irrigation scheduling at the network level is essential not only for optimizing crop yields and maximizing the overall benefits of the irrigation system, but also for promoting the sustainable and responsible use of water and other limited resources (Elbeltagi et al. 2023; Kilic & Özçakal 2024). By implementing effective irrigation strategies, it becomes possible to balance agricultural productivity with environmental conservation, ensuring long-term sustainability in the face of growing resource constraints (Zeng et al. 2010).

Canal irrigation system inadequately managed may results into negative consequences like waterlogging, salinization, seepage, among other (Rai et al. 2020; Rajput et al. 2021a). Remote sensing and other modern tools and techniques should be employed for monitoring the current canal status and crop yield monitoring to assure better production and thus optimized use of the input resources. According to Nigam et al. (2023), barriers to the efficient canal command system are resource system, legal and constitutional, financial, capacity building, and external environment. Inefficient water distribution system has resulted in inadequacy, inequity, and untimely water availability at the farm which affected the crop yield (Rajput et al. 2021a). Adoption of the better water distribution plan, implementation of the participatory irrigation management (PIM), formulation of the water user associations (WUAs), optimal cropping pattern (OCP) selection, supplementary reservoir based micro-irrigation system, decision support system for equitable water distribution are some of the advancements employed for achieving higher water use efficiency (Singh et al. 2016; Rajput et al. 2022a). Adequate management plans need to be developed to assure irrigation under the changing climate scenarios. Climate change has caused changing in the pattern and availability of the rainfall along with change in the land use and land cover (Verma et al. 2023). Such climatic aberrations have resulted into extreme events like draught. Net-zero agriculture ensures zero sustainable balance of greenhouse gasses emission from the farming methods and the available in the atmosphere and thus no effects of climate change (Rosa & Gabrielli 2023). These farming techniques ensures balance sustainable growth and development of the irrigation sector. Site specific management technologies address the issues of nitrogenous based gas emission (Pan et al. 2022).

To eliminate the adverse impact of irrigation schemes to a certain extent, optimal water reservoir operational policies and optimization of land and water resources are of prime importance (Levidow et al. 2014; Loucks & van Beek 2017). A practical irrigation schedule guarantees potential plant growth, ensuring that all necessary agricultural inputs are delivered at an optimal rate and time. A deficit occurring at a particular stage of crop growth may result in higher yield declines than the same deficit arising at any other growth stage (Jerin et al. 2020). Irrigation system performance assessment suggests key constraint details and helps maximize irrigation efficiency and, thus, crop productivity in the canal command area, an area over which canal irrigation water flows by gravity (Rajput & Kothari 2017; Rajput et al. 2017, 2022a; Makadiya et al. 2022). Given the current facilities, improving the irrigation system's operation through a better execution plan is the only way to make such projects work in a sustainable way which can be achieved by optimizing the critical input resources and their allocation as per needs.

The optimal allocation of land and other resources involves determining which crops to grow, how much land to assign to each crop, what should be irrigation rotation plan, and which methods and combinations of inputs to apply in order to maximize farm profits, production and labor employment (Aseema et al. 2023; Angammal & Grace 2024). To achieve this, mathematical models and irrigation management strategies are crucial for crop planning. Linear programming (LP) is a commonly used technique by researchers to address irrigation planning issues in real-world case studies. It is one of the optimizations approaches commonly used to assign finite resources due to the consistent behavior of the allocation issue (Ibrahim & Alfa 2017). LP models are most widely employed for optimization techniques (Singh et al. 2016; Ammar & Emsimir 2021). Researchers in the command area domain around the world have applied optimization techniques for input resources planning. However, an optimal strategy for water distribution must be evaluated under varying socio-economic circumstances to optimize cropland decisions (Loucks & van Beek 2017; Gomez et al. 2019). Mardani et al. (2019) used a management model, considering regional planning features based on environmental, social, financial, and objectives in a combined and separated manner. In the Heihe River Basin (China), fuzzy linear fractional programming (FLFP) has been used based on the double-sided fuzziness method under uncertainty for optimal irrigation water allocation (Zhang et al. 2021). The results revealed that the FLFP was derived by incorporating DFCCP into LFP, where the FLFP could deal with ratio optimization problems based on DFCCP. Furthermore, based on the objective function of the FLFP model, the sum of groundwater and irrigated surface water equals the minimum crop water requirements. Tyagi et al. (2005) reported that a significant amount of water is lost while crop irrigation due to low irrigation efficiency. Conjunctive water use of both, i.e., combined use of groundwater and surface water supplies to meet the irrigation demand, is vital since the presence of a single water source throughout space and time may not always be adequate to satisfy all irrigation needs (Tyagi et al. 2005; Harmancioglu et al. 2013; Lalehzari & Kerachian 2020). A well-operated conjunctive use irrigation scheme can produce greater water than independently regulated groundwater and surface water systems (Zhang et al. 2021). The optimum distribution of available water sources is the key to the preparation and operation of conjunctive use, and it can be accomplished using the optimization model (Singh 2014).

According to Singh (2014), the results of management planning demonstrate that the integrated use of simulation-optimization models has been preferred for solving the issues of conjunctive water management. However, some results of management problems may not be optimally achieved. Several authors have used distinct programming methods to optimize land and water resources (Li et al. 2011; Kishan & Kumar 2020). LP is particularly well-suited for optimizing crop area allocation in canal command systems due to its simplicity, efficiency, and ability to guarantee optimal solutions. It can handle large-scale problems with numerous variables and constraints, such as water availability, land, and crop requirements, making it ideal for balancing resources in agricultural planning. It also provides deterministic, optimal solutions, ensuring the most efficient allocation of resources like land and water, which is crucial in canal systems. Additionally, LP supports sensitivity analysis, allowing for adjustments based on changes in factors like water supply or crop prices. Compared to more complex non-linear or heuristic methods, LP is reliable, scalable, and supported by well-established algorithms and software, making it a robust choice for decision-making in crop allocation. Considering these benefits, the LP techniques have been selected in the current study to develop optimal crop area allocation plan. The numerous irrigation schemes in the countries have demonstrated poor operational performance in the command areas. The current water delivery performance of the Bhimsagar canal water distribution system is poor (Rajput et al. 2022a). The Bhimasagar irrigation scheme needed immediate efforts to achieve the sustainability in utilizing the resources optimally. Therefore, the current study was undertaken with the main objective to develop LP models for optimization of net benefit, food production and labor employment in the LINGO 14.0 environment. In addition, attempt was done to derive OCP plans in the command area of the Bhimsagar irrigation scheme for long-term agricultural sustainability under varying water availability scenarios. The outcomes of the formulated plans have the potential to optimize both land and water resources by identifying the most profitable, sustainable, and efficient cropping patterns, taking into account the limitations of the available resources. The findings from this investigation can serve as a valuable guide for water management planners and policymakers as they work on developing sustainable management plans for both land and water resources, aiming to achieve comprehensive system sustainability.

Study area description

The Bhimsagar irrigation scheme is a medium irrigation project having cultivable command area (CCA) of 9,986 ha. It is located in Jhalawar district, Rajasthan, India. The water distribution network consists of the Right Main Canal (RMC) and Left Main Canal (LMC), with 19 minors off-take from these main canals to irrigate 8,903 ha. The CCA of LMC is 7,278 ha and of RMC is 2,708 ha. The topography of the command area is almost plain. The location map of the Bhimsagar Dam is displayed in Figure 1.
Figure 1

Location map of the Bhimsagar Dam, Jhalawar, India.

Figure 1

Location map of the Bhimsagar Dam, Jhalawar, India.

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Water distribution system

The distribution system comprises 19 minors with a total length of 55.27 km; 5 minors off-take from RMC and 14 from the LMC. The detail of all RMC minors is given in Table 1.

Table 1

Details of RMC minors

MinorLength, CHLocation on RMC from headwork, CHDischarge rate, (cubic meter per seconds)Area coverage, (CCA in hectare)
Ratanpura 118 L-60 0.206 286.20 
Chaplada 80 R-150 0.177 246.45 
Marayta I 53 L-380 0.244 328.72 
Marayta II 100 L-482 0.132 196.35 
Tail 108 R-537 0.148 205.26 
MinorLength, CHLocation on RMC from headwork, CHDischarge rate, (cubic meter per seconds)Area coverage, (CCA in hectare)
Ratanpura 118 L-60 0.206 286.20 
Chaplada 80 R-150 0.177 246.45 
Marayta I 53 L-380 0.244 328.72 
Marayta II 100 L-482 0.132 196.35 
Tail 108 R-537 0.148 205.26 

Note: 1 CH = 20.11 m.

Irrigation water requirement estimation

Monthly irrigation needs were determined using the CROPWAT 8.0 model (Allen et al. 1998; Rajput et al. 2021b; Rajput et al. 2023b; Rajput et al. 2023c). Reference evapotranspiration (ET0) and crop water demand were computed using CROPWAT 8.0 software for every month which uses the Penman–Monteith equation. Crop coefficients (Kc) were used for the major crops in compliance with FAO guidelines.

Net crop irrigation demand was determined as the difference between crop water requirements (ETc) and effective rainfall (Pe). Net crop irrigation requirements for each outlet (QR) were determined using each outlet. The monthly water requirement for various crops is shown in Table 2. A Box plot of the meteorological parameters (2001–2012) dataset has been displayed in Figure 2. In Figure 2, Tmax and Tmin stand for maximum and minimum temperatures in °C, and RHI (morning), RHII (afternoon), WS, SS, and Ep represent relative humidity (%), wind speed (km/day), sunshine hours (h), and evaporation (mm/day), respectively.
Table 2

Monthly water requirement of rabi crops (in cm)

MonthWheatMustardGarlicCoriander
November 1.36 1.57 3.17 3.17 
December 5.59 6.34 10.34 9.46 
January 10.76 11.21 10.80 10.69 
February 13.80 13.53 12.60 11.59 
March 13.28 8.60 19.21 – 
April – – 11.47 – 
Total 44.79 41.26 67.60 34.90 
MonthWheatMustardGarlicCoriander
November 1.36 1.57 3.17 3.17 
December 5.59 6.34 10.34 9.46 
January 10.76 11.21 10.80 10.69 
February 13.80 13.53 12.60 11.59 
March 13.28 8.60 19.21 – 
April – – 11.47 – 
Total 44.79 41.26 67.60 34.90 
Figure 2

Box plot of average meteorological variables in the Jhalawar district.

Figure 2

Box plot of average meteorological variables in the Jhalawar district.

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Irrigation planning LP model development

LINGO Version 14.0 was used for LP model development. The LP model development was completed in two sections. The first section of the study is to develop LP models with multiple goals for different stages of water supply (i.e., 30, 24, and 21 days of CR in a month). In the second part of the analysis, the model is run over various time sections over 5 years to produce a long-term perspective on land allocations in the command area. The availability of food requirements for long-term scenarios in 2015, 2020, and 2025 was estimated based on the population growth rate data according to the 2011 population census. The actual number of days of canal run was observed during the rabi season 2013–14. In the LINGO 14.0 software environment, three objectives were framers to target net benefit, food production and labor maximization considering four constraints viz., water availability in terms of canal run days, food requirement for the command area population, crop area available, and upper and lower bounds. The input scenarios considered for the current study were canal run, long-term analysis, multi-objective and conjunctive use planning. The methodology flow chart describing these components and to develop optimal cropping area plans for RMC is displayed in Figure 3. The procedure developing the LP models for the three chosen minors on the RMC is as follows:
Figure 3

Methodology flowchart for development of OCPs.

Figure 3

Methodology flowchart for development of OCPs.

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Objective functions: Maximal output, net profit, and labor employment are the three goals in formulating an LP model.

Objective 1: Food production maximization

Food production must be maximized to protect the country's interests and achieve self-sufficiency in food production. Equation (1) shows the food production maximization.
(1)

Objective 2: Net benefit maximization

The net profit must be maximized for farmers and the region to develop economically. Equation (2) shows the net benefit maximization.
(2)

Objective 3: labor employment maximization

More employment opportunities must be created within the command area to prevent rural people from migrating to cities searching for work. The Equation (3) shows the labor employment maximization.
(3)

The coefficients in Equations (1)–(3) are the yield in quintals, the net benefit in rupees, and the labor requirement in man-days per hectare (ha), respectively. The average yield of wheat, mustard, garlic and coriander were 50, 18, 70, and 11 quintals per hectare, respectively, which are coefficients of in Equation (1). Similarly, the net benefit of wheat, mustard, garlic and coriander cultivation was rupees (Rs.) 51,161; 26,885; 15,643; and 43,320 per hectare, respectively, displayed as coefficient in Equation (2). In addition, the man-days required for cultivation of wheat, mustard, garlic, and coriander were 112, 86, 175, and 91 man-days per hectare, respectively, as displayed coefficients in Equation (3). The symbols X11, X12, X13, and X14 are areas in ha under wheat, mustard, garlic, and coriander, respectively.

Constraints: The constraints to the model developed are as follows:

Area constraints

The area under different crops during the rabi season in the command area should not exceed the total CCA in a hectare. The area constrains for different minors are given as follows:

Ratanpura minor: Chaplada minor: A2) X11 + X12 + X13 + X14Maraita II minor:

Water constraints

The existing water sources in the command area are sufficient to meet the crop's irrigation needs. As a result, the crop's monthly water demand does not exceed the total monthly water available from available sources. The monthly labor need should be within the framework of the labor force available locally in the command area in that particular month. Table 3 shows the monthly water requirements constraints for selected minors. Table 4 shows the labor availability constraints in the chosen minor's command area.

Table 3

Monthly water requirements constraints for selected minors

Ratanpura minor 
November (W1): 1.358X11 + 1.571X12 + 3.171X13 + 3.171X14 ≤ 4043.52 
December (W2): 5.585X11 + 6.343X12 + 10.343X13 + 9.457X14 ≤ 4043.52 
January (W3): 10.758X11 + 11.214X12 + 10.80X13 + 10.687X14 ≤ 4043.52 
February (W4): 13.80X11 + 13.529X12 + 12.60X13 + 11.585X14 ≤ 4043.52 
March (W5): 13.284X11 + 8.60X12 + 19.21X13 ≤ 4043.52 
April (W6): 11.47X13 ≤ 4043.52 
Chaplada minor 
November (W1): 1.358X11 + 1.571X12 + 3.171X13 + 3.171X14 ≤ 2747.52 
December (W2): 5.585X11 + 6.343X12 + 10.343X13 + 9.457X14 ≤ 2747.52 
January (W3): 10.758X11 + 11.214X12 + 10.80X13 + 10.687X14 ≤ 2747.52 
February (W4): 13.80X11 + 13.529X12 + 12.60X13 + 11.585X14 ≤ 2747.52 
March (W5): 13.284X11 + 8.60X12 + 19.21X13 + 0.0X14 ≤ 2747.52 
April (W6): 0.0X11 + 0.0X12 + 11.47X13 + 0.0X14 ≤ 2747.52 
Maraita minor 
November (W1): 1.358X11 + 1.571X12 + 3.171X13 + 3.171X14 ≤ 1762.56 
December (W2): 5.585X11 + 6.343X12 + 10.343X13 + 9.457X14 ≤ 1762.56 
January (W3): 10.758X11 + 11.214X12 + 10.80X13 + 10.687X14 ≤ 1762.56 
February (W4): 13.80X11 + 13.529X12 + 12.60X13 + 11.585X14 ≤ 1762.56 
March (W5): 13.284X11 + 8.60X12 + 19.21X13 + 0.0X14 ≤ 1762.56 
April (W6): 0.0X11 + 0.0X12 + 11.47X13 + 0.0X14 ≤ 1762.56 
Ratanpura minor 
November (W1): 1.358X11 + 1.571X12 + 3.171X13 + 3.171X14 ≤ 4043.52 
December (W2): 5.585X11 + 6.343X12 + 10.343X13 + 9.457X14 ≤ 4043.52 
January (W3): 10.758X11 + 11.214X12 + 10.80X13 + 10.687X14 ≤ 4043.52 
February (W4): 13.80X11 + 13.529X12 + 12.60X13 + 11.585X14 ≤ 4043.52 
March (W5): 13.284X11 + 8.60X12 + 19.21X13 ≤ 4043.52 
April (W6): 11.47X13 ≤ 4043.52 
Chaplada minor 
November (W1): 1.358X11 + 1.571X12 + 3.171X13 + 3.171X14 ≤ 2747.52 
December (W2): 5.585X11 + 6.343X12 + 10.343X13 + 9.457X14 ≤ 2747.52 
January (W3): 10.758X11 + 11.214X12 + 10.80X13 + 10.687X14 ≤ 2747.52 
February (W4): 13.80X11 + 13.529X12 + 12.60X13 + 11.585X14 ≤ 2747.52 
March (W5): 13.284X11 + 8.60X12 + 19.21X13 + 0.0X14 ≤ 2747.52 
April (W6): 0.0X11 + 0.0X12 + 11.47X13 + 0.0X14 ≤ 2747.52 
Maraita minor 
November (W1): 1.358X11 + 1.571X12 + 3.171X13 + 3.171X14 ≤ 1762.56 
December (W2): 5.585X11 + 6.343X12 + 10.343X13 + 9.457X14 ≤ 1762.56 
January (W3): 10.758X11 + 11.214X12 + 10.80X13 + 10.687X14 ≤ 1762.56 
February (W4): 13.80X11 + 13.529X12 + 12.60X13 + 11.585X14 ≤ 1762.56 
March (W5): 13.284X11 + 8.60X12 + 19.21X13 + 0.0X14 ≤ 1762.56 
April (W6): 0.0X11 + 0.0X12 + 11.47X13 + 0.0X14 ≤ 1762.56 
Table 4

Labor availability constraints in the selected minor's command area

Ratanpura minor 
October: 7X12 + 9X13 + 7X14 ≤ 20550 
November: 12X11 + 27X12 + 12X13 + 28X14 ≤ 20550 
December: 33X11 + 10X12 + 24X13 + 13X14 ≤ 20550 
January: 35X11 + 6X12 + 24X13 + 6X14 ≤ 20550 
February: 6X11 + 26X12 + 21X13 + 27X14 ≤ 20550 
March: 26X11 + 10X12 + 44X13 + 10X14 ≤ 20550 
April: 41X13 ≤ 20550 
Maraita II minor 
October: 7X12 + 9X13 + 7X14 ≤ 20010 
November: 12X11 + 27X12 + 12X13 + 28X14 ≤ 20010 
December: 33X11 + 10X12 + 24X13 + 13X14 ≤ 20010 
January: 35X11 + 6X12 + 24X13 + 6X14 ≤ 20010 
February: 6X11 + 26X12 + 21X13 + 27X14 ≤ 20010 
March: 26X11 + 10X12 + 44X13 + 10X14 ≤ 20010 
April: 41X13 ≤ 20010 
Ratanpura minor 
October: 7X12 + 9X13 + 7X14 ≤ 20550 
November: 12X11 + 27X12 + 12X13 + 28X14 ≤ 20550 
December: 33X11 + 10X12 + 24X13 + 13X14 ≤ 20550 
January: 35X11 + 6X12 + 24X13 + 6X14 ≤ 20550 
February: 6X11 + 26X12 + 21X13 + 27X14 ≤ 20550 
March: 26X11 + 10X12 + 44X13 + 10X14 ≤ 20550 
April: 41X13 ≤ 20550 
Maraita II minor 
October: 7X12 + 9X13 + 7X14 ≤ 20010 
November: 12X11 + 27X12 + 12X13 + 28X14 ≤ 20010 
December: 33X11 + 10X12 + 24X13 + 13X14 ≤ 20010 
January: 35X11 + 6X12 + 24X13 + 6X14 ≤ 20010 
February: 6X11 + 26X12 + 21X13 + 27X14 ≤ 20010 
March: 26X11 + 10X12 + 44X13 + 10X14 ≤ 20010 
April: 41X13 ≤ 20010 

Food requirement constraints (in quintals) in different minors are as follows:

Ratanpura minor: Mustard – F2) 18X12 ≥ 166.52

Chaplada minor: Wheat – F1) 50X11 ≥ 1,197.49 and Mustard – F2) 18X12 ≥ 99.79

Maraita II minor: Wheat – F1) 50X11 ≥ 1,945.60, and Mustard – F2) 18X12 ≥ 162.14

Upper and lower bounds

The upper and lower boundaries are put in to take care of the social fondness of the people living in the area. Thus, the primary diversification of the cropping pattern is confined to model analysis. The upper and lower bound constraints are shown in Table 5.

Table 5

The upper and lower bound constraints in the selected minor's command area

Ratanpura minorChaplada minorMaraita II minor
(F1) X11 ≥ 28.62 (F1) X11 ≥ 24.64 (F1) X11 ≥ 19.63 
(F2) X12 ≥ 28.62 (F2) X12 ≥ 24.64 (F2) X12 ≥ 19.63 
(F3) X13 ≥ 28.62 (F3) X13 ≥ 24.64 (F3) X13 ≥ 19.63 
(F4) X14 ≥ 28.62 (F4) X14 ≥ 24.64 (F4) X14 ≥ 19.63 
Ratanpura minorChaplada minorMaraita II minor
(F1) X11 ≥ 28.62 (F1) X11 ≥ 24.64 (F1) X11 ≥ 19.63 
(F2) X12 ≥ 28.62 (F2) X12 ≥ 24.64 (F2) X12 ≥ 19.63 
(F3) X13 ≥ 28.62 (F3) X13 ≥ 24.64 (F3) X13 ≥ 19.63 
(F4) X14 ≥ 28.62 (F4) X14 ≥ 24.64 (F4) X14 ≥ 19.63 

Net benefit, food production, and labor maximization for selected minors in 2013–2014

Ratanpura minor

The net benefits obtained were Rs. 31,510,150.38, Rs. 25,412,360.48, and Rs. 21,594,752 for investments of Rs.18,805,174.62, Rs.15,424,627.52 and Rs. 13,209,457 for 30, 24, and 21 days of CR in a month, respectively. The food productions achieved were 14,939.23 qt., 12,118.4 qt., and 10,512.79 qt., and labor employments achieved were 41,022.71, 34,698.98, and 29,922.32 man-days for 30, 24, and 21 days of CR in a month, respectively. The OCP derived cropped areas were 39.96, 28.62, 170.04, and 47.57 ha for wheat, mustard, garlic, and coriander, respectively, for 30 days of CR; 39.96, 28.62, 127.94, and 59.04 ha for wheat, mustard, garlic, and coriander, respectively, for 24 days of CR; 39.96, 28.62, 106.89 and 47.03 ha for wheat, mustard, garlic, and coriander, respectively, for 21 days of CR. Results showed that the land area allotted to different crops under varying CR was different for Ratanpura minor. The results of the LP modeling for various CR days during the rabi season 2013–2014 has been shown in Table 6.

Table 6

LP model results for various canal running days during the rabi season 2013–2014

Net benefit, food production, and labor employment in RMC
SeasonRatanpura minorChaplada minorMaraita II minor
No. of running days
No. of running days
No. of running days
30 days24 days21 days30 days24 days21 days30 days24 days21 days
Rabi Wheat 39.96 39.96 39.96 24.64 24.64 24.64 38.91 38.91 38.91 
Mustard 28.62 28.62 28.62 24.64 24.64 24.64 19.63 19.63 19.63 
Garlic 170.04 127.94 106.89 114.95 86.35 72.04 56.05 30.16 16.17 
Coriander 47.57 59.04 47.03 54 37.68 29.52 21.89 19.63 19.63 
Total (ha)  286.19 255.56 222.5 218.23 173.31 150.84 136.48 108.33 94.34 
Investment (Rs.)  18805174.62 15424627.52 13209457 13418488 10408732 8902970 7674817 5320403 4084289 
Achievement level 
Production in qt.  14939.23 12118.4 10512.79 10316.02 8134.5 7043.04 6463.13 4625.97 3646.67 
Labor in man-day  41022.71 34698.98 29922.32 29908.97 23418.85 20172.04 17846.84 13110.43 10662.18 
Net benefit (Rs.)  31510150.38 25412360.48 21594752 22268446 17081474 14486422 12246542 8093152 5901716 
Net benefit, food production, and labor employment in RMC
SeasonRatanpura minorChaplada minorMaraita II minor
No. of running days
No. of running days
No. of running days
30 days24 days21 days30 days24 days21 days30 days24 days21 days
Rabi Wheat 39.96 39.96 39.96 24.64 24.64 24.64 38.91 38.91 38.91 
Mustard 28.62 28.62 28.62 24.64 24.64 24.64 19.63 19.63 19.63 
Garlic 170.04 127.94 106.89 114.95 86.35 72.04 56.05 30.16 16.17 
Coriander 47.57 59.04 47.03 54 37.68 29.52 21.89 19.63 19.63 
Total (ha)  286.19 255.56 222.5 218.23 173.31 150.84 136.48 108.33 94.34 
Investment (Rs.)  18805174.62 15424627.52 13209457 13418488 10408732 8902970 7674817 5320403 4084289 
Achievement level 
Production in qt.  14939.23 12118.4 10512.79 10316.02 8134.5 7043.04 6463.13 4625.97 3646.67 
Labor in man-day  41022.71 34698.98 29922.32 29908.97 23418.85 20172.04 17846.84 13110.43 10662.18 
Net benefit (Rs.)  31510150.38 25412360.48 21594752 22268446 17081474 14486422 12246542 8093152 5901716 

Chaplada minor

Similar to the Ratanpura minor, the Chaplada minor attained the net benefits of Rs. 22,268,446.3, Rs. 17,081,474, and Rs. 14,486,422 for investments of Rs.13,418,487.7, Rs. 10,408,732, and Rs. 8,902,970 under 30, 24, and 21 days of CR in a month, respectively. The food productions in the Chaplada minor achieved were 10,316.02 qt., 8,134.5 qt. and 7,043.04 qt. and labor employments were 29,908.97, 23,418.85, and 20,172.04 man-days for 30, 24, and 21 days of CR in a month, respectively. The OCP derived were 24.64, 24.64, 114.95, and 54 ha for wheat, mustard, garlic, and coriander, respectively, for 30 days of CR; 24.64, 24.64, 86.35, and 37.68 ha for wheat, mustard, garlic, and coriander, respectively, for 24 days of CR; 24.64, 24.64, 72.04, and 29.52 ha for wheat, mustard, garlic, and coriander, respectively, for 21 days of CR. The variation in the OCP under different CR may be due to the water availability constraints in terms of the CR.

Maraita II minor

Maraita II minor obtained the net benefits of Rs.12,246,542, Rs. 8,093,152, and Rs. 5,901,716 for investments of Rs.7,674,817, Rs. 5,320,403, and Rs. 4,084,289 for 30, 24, and 21 days of CR in a month, respectively. The food productions achieved were 6,463.13 qt., 4,625.97 qt., and 3,646.67 qt., and the labor employment achieved were 17,846.84, 13,110.43, and 10,662.1 man-days for 30, 24, and 21 days of CR in a month, respectively. The OCP derived were 38.91, 19.63, 56.05, and 21.89 ha for wheat, mustard, garlic, and coriander, respectively, for 30 days of CR; 38.91, 19.63, 30.16, and 19.63 ha for wheat, mustard, garlic, and coriander, respectively, for 24 days of CR; 38.91, 19.63, 16.17, and 19.63 ha for wheat, mustard, garlic, and coriander, respectively, for 21 days of CR. Table 6 shows the decrease or increase in the OCP under 24 and 21 days of CR compared to 30 days of CR. Results revealed that the wheat and mustard crop area was unchanged under 24 and 21 days of CR. This could be primarily due to higher importance was given to wheat and mustard crops over other crops to meet the food and cooking oil demands of the population in the command area. Also, the wheat is the staple food in the study region and thus higher importance is given to it. However, the garlic and coriander crop area changed under 24 days of CR and 21 days of CR scenario.

Change in the OCP and objective functions under various water availability scenarios

Under a limited water availability scenario, shifting the canal rotation period from 30 days of CR to 24 and 21 days of CR resulted in 24.75 and 37.13% decrease in the garlic cropped area for Ratanpura minor. Similarly, for Chaplada minor, the garlic cropped area was reduced by 24.88 and 37.32%, respectively, under 24 and 21 days of CR. Maraita II minor had shown a maximum change in the garlic cropped area under limited water availability with values of 46.13 and 71.15% under 24 and 21 days of CR compared to the 30 days of CR. This maximum decrease in the garlic cropped area under the limited water availability scenario for Maraita II minor suggests replacing high water-requiring crops to less water-demanding crops for sustainable agriculture production. Interestingly, coriander crop area increased under 24 days of CR scenario for Ratanpura minor compared to 30 days of CR scenario. This could be due to the higher selling price of the spice crop than cereals like wheat.

Nevertheless, the coriander area decreased by 1.13% under 21 days CR scenario. For the Chaplada and Maraita II minor, the coriander-cropped area has significantly reduced under 24 and 21 days of CR. No change was observed for wheat and mustard crop areas under limited water availability. This is due to fact that these are the most important crops for meeting the food need as well as cooking oil demand and other uses. The total area under the minors was decreased under 24 and 21 days of CR with a reducing trend from head minor (Ratanpura) to tail minor (Maraita II) except for Chaplada and Maraita II minor under 21 days of CR scenario. The change in the garlic area, coriander area, total cropped area, net benefit, food production, labor employment, and investment under 24 and 21 days of CR compared to 30 days of CR for Ratanpura, Chaplada, and Maraita II minor under OCP is shown in Table 7.

Table 7

Percentage change in the optimal cropping area under 24- and 21-day CR scenarios

ParticularRatanpura minor
Chaplada minor
Maraita II minor
Average
24 days21 days24 days21 days24 days21 days
Garlic area −24.75 −37.13 −24.88 −37.32 −46.19 −71.15 −40.23 
Coriander area +24.11 −1.13 −30.22 −45.33 −10.32 −10.32 −12.20 
Total area −10.70 −22.25 −20.58 −30.88 −20.62 −30.87 −22.65 
Net benefit −19.35 −31.46 −23.29 −34.94 −33.91 −51.8 −32.45 
Food production −18.88 −29.62 −21.14 −31.72 −28.42 −43.57 −28.89 
Labor employment −15.41 −27.05 −21.69 −32.55 −26.53 −40.25 −27.24 
Investment −17.97 −29.75 −22.42 −33.65 −30.67 −46.78 −30.20 
ParticularRatanpura minor
Chaplada minor
Maraita II minor
Average
24 days21 days24 days21 days24 days21 days
Garlic area −24.75 −37.13 −24.88 −37.32 −46.19 −71.15 −40.23 
Coriander area +24.11 −1.13 −30.22 −45.33 −10.32 −10.32 −12.20 
Total area −10.70 −22.25 −20.58 −30.88 −20.62 −30.87 −22.65 
Net benefit −19.35 −31.46 −23.29 −34.94 −33.91 −51.8 −32.45 
Food production −18.88 −29.62 −21.14 −31.72 −28.42 −43.57 −28.89 
Labor employment −15.41 −27.05 −21.69 −32.55 −26.53 −40.25 −27.24 
Investment −17.97 −29.75 −22.42 −33.65 −30.67 −46.78 −30.20 

− indicates decrease, + indicates increase.

Application of LP model to generate long-term land allocation with net benefit, food production, and labor employment maximization

Land allocation with net benefit, food production, and labor employment maximization in 2015

The net benefits obtained were Rs 31,510,150.4, Rs. 22,268,446.3, and Rs. 12,246,542 for the investment of Rs. 18,805,174.6, Rs. 13,418,487.7, and Rs. 7,674,816.99 for 30 days of CR in a month for Ratanpura, Chaplada, and Maraita II minor for 2015, respectively. The food production achieved were 14,939.23 qt., 10,316.02 qt., and 6,463.13qt for Ratanpura, Chaplada, and Maraita II minor, respectively. The labor employment maximization achieved were 41,022.71, 29,908.97, and 17,846.84 man-days for 30 days of CR in a month for Ratanpura, Chaplada, and Maraita II minor. The OCP derived for 2015 were 39.96, 28.62, 170.04, and 47.57 ha for wheat, mustard, garlic, and coriander, respectively, for Ratanpura minor. Net benefits of Rs. 25,412,360.5 and 21,594,752.1 was achieved for the investments of Rs.15,424,627.5 and 13,209,456.9, respectively, for Ratanpura minor under 24 and 21 days of CR in 2015. The food productions and man-days achieved in 2015 under 24 and 21 days of CR scenarios were 12,118.4 qt and 10,512.79 qt and 34,698.98 and 29,922.32, respectively, Ratanpura minor. For Chaplada minor, the net benefits obtained was Rs. 17,081,474.1and Rs.1,448,621.6 for the investments of Rs. 10,408,731.9 and 8,902,970.49, respectively, for 24 and 21 days of CR. At the same time, food production and man-days achieved were 8,134.5 qt. and 7,043.04 qt, and 23,418.85 and 20,172.04, respectively, for 24 and 21 days of CR in 2015. Maraita II minor had shown net benefits of Rs. 8,093,151.5 and 5,901,716.2 for investments of 5,320,403.5 and 4,084,289.2, respectively, under 24 and 21 days of CR in 2015. The food production and man-days achieved were 4,625.97 qt. and 3,646.67 qt and 13,110.43 and 10,662.18, respectively, for 24 and 21 days of CR in 2015. The optimal cropped area for various levels of water availability in 2015 has shown in Figure 4.
Figure 4

OCPs for various levels of water availability in 2015.

Figure 4

OCPs for various levels of water availability in 2015.

Close modal
The influence of limited canal water availability scenario in terms of CR on change in the garlic, coriander, total cropped area, net benefit, food production, labor employment, and investment under 24 and 21 days of CR compared to 30 days of CR for Ratanpura, Chaplada, and Maraita II minor were assessed and displayed in the radar chart (Figure 5). The area under coriander has increased under 24 days of CR compared to 30 days of CR. In the radar chart, the Ratanpura minor under 24 and 21 days of CR showed as RTCR 24 and RTCR 21, respectively. Similarly, Chaplada and Maraita II minors under 24 and 21 days of CR have been shown as CPCR 24, MTCR 24, CRCR 21, and MTCR 21, respectively.
Figure 5

Change in the OCP and the objective function values (%) under 24- and 21-day CR in 2015.

Figure 5

Change in the OCP and the objective function values (%) under 24- and 21-day CR in 2015.

Close modal

Land allocation with net benefit, food production, and labor employment maximization in 2020

The net benefits of Rs 31,215,422.3, Rs. 22,131,564.4, and Rs. 11,936,979.2 were obtained for investments of Rs. 18,674,011.7, Rs. 13,355,078.6, and Rs. 7,531,567.6 for 30 days of CR in a month for Ratanpura, Chaplada, and Maraita II minors. The food productions achieved were 14,931.74 qt., 10,310.0 qt., and 6,449.85 qt. for 30 days of CR for Ratanpura, Chaplada, and Maraita II minor. The labor employment achieved is 40,867.73, 29,820.56, and 17,647.83 man-days for 30 days of CR in a month for Ratanpura, Chaplada, and Maraita II minors. The OCP derived for 30 days of CR were 44.14, 28.62, 167.15, and 46.28 ha for wheat, mustard, garlic, and coriander, respectively, for Ratanpura minor. Net benefits of Rs. 25,094,239.6 and Rs. 21,276,631.2 were achieved for investments of Rs.15,277,491.4 and 13,062,320.8, respectively, for Ratanpura minor under 24 and 21 days of CR. The food production and man-days under the 24 and 21 days of CR scenario were 12,104.97 qt and 10,499 qt. and 34,494.86 and 29,718.2, respectively, for Ratanpura minor. For Chaplada minor, the net benefit obtained was Rs. 16,944,592.2, Rs. 14,349,972.8 for an investment of Rs. 10,345,322.8 and 8,839,857.17, respectively, for 24 and 21 days of CR. At the same time, food production and man-days achieved were 8,128.51 qt. and 7,037.16 qt. and 23,330.44 and 20,084.54, respectively, for 24 and 21 days of CR. Maraita II minor had shown net benefits of Rs. 7,603,803.9 and Rs. 5,412,368.3 for investments of Rs. 5,084,901.2 and 3,848,786.7, respectively, under 24 and 21 days of CR. The food production and man-days achieved were 4,517.47 qt. and 3,538.17 qt. and 12,786.4 and 10,338.15, respectively, for 24 and 21 days of CR. The land area allocated to different crop activities under OCP is found for various levels of water availability in 2020 for Ratanpura, Chaplada, and Maraita II minor, as shown in Figure 6.
Figure 6

OCP for various levels of water availability in 2020.

Figure 6

OCP for various levels of water availability in 2020.

Close modal
Likewise, under limited water availability of CR, change in the garlic area, coriander area, total cropped area, net benefit, food production, labor employment, and investment under 24 and 21 days of CR compared to 30 days of CR for Ratanpura, Chaplada, and Maraita II minor was observed and displayed in the radar chart (Figure 7). The coriander showed an increase in the area under 24 days of CR compared to 30 days of CR.
Figure 7

Change in the OCP and the values of the objective function (%) under 24- and 21-day CR in 2020.

Figure 7

Change in the OCP and the values of the objective function (%) under 24- and 21-day CR in 2020.

Close modal

Land allocation with net benefit, food production, and labor employment maximization in 2025

The net benefits obtained were 30,835,068.9 Rs. 21,920,108.6, and Rs. 11,448,325.6 for investments of Rs. 18,504,772.1, Rs. 13,257,225.4, and Rs. 7,298,179.43 for 30 days of CR for Ratanpura, Chaplada, and Maraita II minors. The food productions achieved were 14,922.27 qt., 10,300.82 qt., and 6,357.07 qt. for 30 days of CR for Ratanpura, Chaplada, and Maraita II minor. The labor employments maximization achieved were 40,667.81, 29,684.69, and 17,327.16 man-days for 30 days of CR for Ratanpura, Chaplada, and Maraita II minor. The OCP derived were 49.54, 28.62, 1,673.42, and 44.61 ha for wheat, mustard, garlic, and coriander, respectively, for Ratanpura minor for 30 days of CR. Net benefits of Rs. 20,881,117.3 and 21,920,108.6 were achieved for investments of Rs.12,879,343.7 and Rs. 13,257,225.4, respectively, for Ratanpura minor under 24 and 21 days of CR. The food production and man-days achieved were 10,482.87 qt, 10,300.82 qt, 29,463.96, 29,684.69 under 24- and 21-days CR scenarios, respectively, for Ratanpura minor. For Chaplada minor, the net benefits obtained were Rs. 16,733,136.4 and Rs.14,139,650.3 for the investment of Rs. 10,247,469.6 and 8,742,591.7, respectively, for 24 and 21 days of CR. At the same time, food production and man-days achieved were 7,028.54 qt. and 6,133.07 qt. and 23,194.57 and 19,949.51, respectively, for 24 and 21 days of CR. Maraita II minor had shown net benefits of Rs. 7,066,509.3 and Rs. 4,875,073.7 for investments of Rs. 4,826,445.8 and Rs. 3,590,331.3, respectively, under 24 and 21 days of CR. The food production and man-days achieved were 4,398.67 qt and 3,419.37 qt. and 12,431.29 and 9,983.04 for 24 and 21 days of CR. The area allocated to different crop activities under OCP is found for various levels of water availability in 2025 for Ratanpura, Chaplada, and Maraita II minor, as shown in Figure 8.
Figure 8

Optimal cropping area for various levels of water availability in 2025.

Figure 8

Optimal cropping area for various levels of water availability in 2025.

Close modal
Additionally, under limited water availability of CR scenarios, change in the garlic area, coriander area, total cropped area, net benefit, food production, labor employment, and investment under 24 and 21 days of CR compared to 30 days of CR for Ratanpura, Chaplada, and Maraita II minor was observed and displayed in the radar chart (Figure 9) in 2025. The study highlights the significant impact of different cropping rotation (CR) durations on agricultural outcomes, including net benefits, food production, and labor employment, across Ratanpura, Chaplada, and Maraita II minors. By adjusting the cropping patterns and utilizing both surface and groundwater resources, the optimal configurations resulted in notable increases in net benefits and food production, especially for Ratanpura. The analysis also demonstrated that varying the CR duration – whether 30, 24, or 21 days – affects both the investment required and the returns in terms of crop yields and labor employment. The findings emphasize the importance of optimizing irrigation and cropping strategies to enhance productivity, resource efficiency, and livelihood opportunities, even in areas with limited water availability.
Figure 9

Change in the OCP and the values of the objective function (%) under 24- and 21-day CR in 2025.

Figure 9

Change in the OCP and the values of the objective function (%) under 24- and 21-day CR in 2025.

Close modal

Comparisons between existing and OCP

Equating the current command area cropping patterns with the OCP aids in proposing optimal water management strategies in the command area. The comparison is made between the existing cropping pattern and OCP to use surface water (30 days of CR) and groundwater combined for Maraita II, while the conjunctive use of groundwater is not considered for selected head and middle minors of RMC because no well was found in their command area for irrigation purpose in rabi season during canal running period. The distinction is made in terms of net benefit maximization, food maximization, and labor employment maximization. In the case of net benefit maximization for Ratanpura minor, the cropped area had increased by 10.94% over the existing cropping area (2013–2014). The net benefit, food production, and labor employment were increased by 122, 22.39, and 40.92%, respectively, under OCP over the existing cropping pattern for Ratanpura minor.

Similarly, for Chaplada minor, the net benefit, food production, and labor employment were increased by 93.4, 33.8, and 33.8%, respectively. Likewise, Maraita II minor had shown an increase in the net benefit, food production, and labor employment by 95.5, 25.9, and 33.1%, respectively. Figure 10 shows the current and OCPs for the objective of net benefit maximization (RMC minors). To attain net benefit maximization in Chaplada minor, the optimal cropped area was increased by 10.88 over the existing cropping pattern. In contrast, the net benefit, food production, and labor employment increased by 122, 22.39, and 40.92%, respectively, for Chaplada minor. Compared to Ratanpura and Chaplada minor, Maraita II reported a 7.5% increase in area over the existing cropping pattern. This is comparatively lesser than the head and middle reach minors due to the lack of assured water availability in the tail minor during rabi season. Figure 10 shows the existing and OCP for the RMC minors. The results of this study highlight the significant benefits of optimizing irrigation management, including substantial increases in net benefits, food production, and labor employment. By adjusting cropping patterns, farmers can enhance productivity and profitability, contributing to improved food security and economic resilience in rural communities. The findings also emphasize the importance of reliable water supply and tailored approaches for different regions, as water availability can significantly impact crop yields. These results suggest that efficient water use and localized irrigation strategies can promote sustainable agricultural practices, support job creation, and serve as a model for other regions facing similar challenges in optimizing water resources and agricultural output.
Figure 10

Comparison of existing and OCPs for RMC minors.

Figure 10

Comparison of existing and OCPs for RMC minors.

Close modal

Conjunctive use analysis of surface water and groundwater for Maraita II minor

The OCP results obtained for a 30-days CR for Maraita II minor shown a decrease in the crop area compared to the existing cropped area. This decrease in the crop area could be attributed to the utilization of both surface and canal water sources as there was no assured water canal water availability in the Maraita minor. The allocation of area to various crops for 30-days of CR, incorporating both surface and groundwater availability, was done with the goal of maximizing net profits. Maraita II monor achieved net benefit of Rs. 19,732,097.95, with an investment of Rs. 11,982,875.05 under the OCP. The food production maximization amounted to 9,668.99 quintals, contributing to local food demand. Moreover, the labor employment maximization was estimated to be 26,919.4 man-days, contributing to increased livelihood opportunities. Considering the combined utilization of surface and groundwater resources, the optimal cropped area for conjunctive use was determined to be 196.32 ha. The study demonstrates the potential for optimizing irrigation and cropping patterns to enhance agricultural productivity and resource efficiency. By integrating both surface and groundwater resources, it is possible to maximize net benefits, food production, and labor employment, even in areas with limited and unreliable water availability. The results highlight the importance of tailoring cropping strategies to local conditions, optimizing water use, and ensuring sustainable agricultural practices. This approach not only boosts economic returns but also contributes to food security and rural livelihoods, making it a valuable model for other regions facing similar water constraints. The resulting OCP for different crops were 38.91 ha for wheat, 19.63 ha for mustard, 99.23 ha for garlic, and 38.55 ha for coriander, as depicted in Figure 11.
Figure 11

Optimum cropping pattern in the Maraita II command area under conjunctive use planning.

Figure 11

Optimum cropping pattern in the Maraita II command area under conjunctive use planning.

Close modal

LP is an extensively utilized optimization technique for allocating limited resources due to the proportionate nature of the allocation problem (Haouari & Azaiez 2001; Hacısüleyman & Özger 2024). A common use of this method in the literature on water resources is to determine the OCP under limited resources available (Haouari & Azaiez 2001). The OCP is critical information for farmers because it serves as the initial recommendation for cultivation. Also, the OCP information may be on hand information for the policy making agencies and agriculture departments to promote the best cropping patterns for deriving the optimum benefits. The findings of the present investigation showed that more net benefits, food production, and labor employment could be achieved by employing an OCP over the existing cropping pattern followed in the study area. Also, water availability in the canal directly affects crop production, labor employment, and crop yield. Therefore, in this investigation, OCPs were developed for 30 days of canal run (CR), 24 and 21 days of CR under limited water availability scenarios. Kilic & Özçakal (2024) optimized irrigation programming for different water allocation strategies at network level for maximizing crop yields and benefits but also for ensuring the sustainable use of limited resources. The model was tested using five distinct water allocation strategies. It was implemented on the Sarıkız Irrigation Association's command area within the Ahmetli Regulator Right Bank Irrigation System in the Gediz Basin. The results demonstrated that the model successfully identified the optimal system rotation period, the boundaries and sizes of the most effective water allocation zones, and the best irrigation schedules under current conditions. We also found that the optimized cropping patterns aids in achieving the sustainability.

The obtained OCP results for Ratanpura, Chaplada, and Maraita minors indicate that the area under wheat was reduced, while the area under mustard, garlic, and coriander increased for 30 days CR, aiming to maximize net benefit, food production, and labor employment. Shifting to the OCP from the existing cropping pattern could result in a 122% increase in net benefits, a 22.39% increase in food production, and a 40.92% increase in labor employment in the Ratanpura minor. The OCP analysis for the long-term scenarios (2015, 2020, and 2025) suggested a decrease in the cropped area under wheat and increase in the area under garlic to achieve maximizum net benefits, food production, and labor employment. Kumar et al. (2023) applied non-linear optimization model to kharif and rabi crops in the Ghonga Jalashay command area of Bilaspur, Chhattisgarh, to maximize net returns. The model, developed using Lingo 19.0 optimization software, incorporates inputs such as cultivation costs for different crops and soil types, irrigation requirements, and crop sale prices to determine the optimal solution. The results indicated a net return of Rs. 59,52,64,300 from kharif rice cultivated on 7,311 ha, and a net seasonal return of Rs. 3,80,84,680 from summer rice. The model also provided optimal solutions for five selected rabi crops – sunflower, wheat, mustard, safflower, and gram – based on the available irrigation water. The total net return for these crops was Rs. 19,38,47,900, with the optimal areas allocated as 2,151.81 ha for sunflower, 1,537 ha for wheat, 819 ha for mustard, 204.98 ha for safflower, and 409.86 ha for gram. Compared to the area and net return from summer rice, the area for rabi crops increased eightfold, and the net return was six times higher. Our study also found that the net benefits were maximized under OCP than the existing cropping pattern.

The long-term scenario helps to identify the overlying constraints and suggests feasible measures to optimize food production. This study has also demonstrated that the application of conjunctive use in the tail-end reaches to meet the crop water need by combining surface and groundwater sources for sustainable agriculture development. The analysis of conjunctive water utilization for Maraita II minor indicated that the garlic crop should receive the maximum allocation of area, while the mustard crop should be allocated the minimum area. The results motivate to employee optimization techniques in the command area for developing feasible and sustainable OCPs. Net benefit maximization under OCP for 30 days of CR was observed highest for head minor, i.e., Ratanpura minor compared to the Chaplada and Maraita II minors.

Under the OCP, the cropped area under the principal rabi crop, i.e., wheat, was reduced in the command areas of Ratanpura, Chaplada, and Maraita II minors. In contrast, the area under mustard, garlic, and coriander was increased for both Ratanpura and Chaplada minors. In Maraita II minor command, mustard cropped area decreased under OCP compared to the existing cropping pattern. This could be because garlic and coriander crops assure better net returns than mustard crop; therefore, the area under garlic and coriander was increased under OCP. The findings of the present investigation are in line with studies reported by Barati et al. (2020), where they have reported decreasing in the area under the wheat crop and an increase in the cropped area for high-value crops such as saffron, rose, etc.Li et al. (2023) established spatial–temporal optimal allocation regulation method for irrigation water resources in Helan County, Qingtongxia Irrigation District, Ningxia. The study concluded that the balanced and optimal allocation method for irrigation water resources, encompassing both total water use and groundwater depth control, not only enhances the efficient and rational utilization of limited water resources but also effectively regulates groundwater depth to ensure regional ecological health and sustainable development. Wei et al. (2023) introduced an innovative approach to optimizing water and land resources allocation in the ‘reservoir and pumping station’ irrigation system through crop rotation. They utilized two hybrid algorithms, namely the Decomposition Aggregation Dynamic Programming (DADP) method combined with the LP successive approximation algorithm [(DADP–LP) SA], as well as the Orthogonal Design (OD) method-based DADP algorithm (OD–DADP). The solution outcomes demonstrated enhanced annual output values for water-deficient irrigation area and efficient allocation of limited water and land resources. Zhang et al. (2023) utilized the Hybrid Strategy Whale Optimization Algorithm (HSWOA) to optimize economic, social, and ecological benefits in Handan, China. Their study aimed to achieve optimal allocation of water resources. The researchers concluded that the proposed water resource allocation strategy was indeed optimal, emphasizing its effectiveness in enhancing economic, social, and ecological outcomes. OCPs increase net benefits. Our results also indicated that the under OCP better net benefits, food maximization and labor employment maximization can be achieved. Hacısüleyman & Özger (2024) applied LP approach to develop OCP based on food–energy–water nexus and developed different scenarios. They concluded that the all the scenarios analyzed led to lower water consumption, reduced energy demands, and decreased carbon dioxide emissions. Among them, Scenario 6, which allows a 5% variation in cultivation areas without a total area cap, consistently proved to be the most effective. It achieved an average reduction of 3.94% in water usage, 2.95% in energy requirements, and 1.62% in carbon dioxide emissions compared to the baseline scenario. Scenario 11, which permits a 5% variation in cultivation areas while maintaining a total area limit, was the second most effective in terms of water conservation. It resulted in a 3.45% reduction in water use, a 1.85% decrease in energy needs, and a slight 0.11% reduction in carbon dioxide emissions across all time periods.

Conjunctive water use analysis for the tail-end minor showed a decrease in the cropped area under wheat and mustard crops and an increase in the cropped area under garlic and coriander crops to derive maximum benefits and utilize water sustainably. Several authors (Majeke et al. 2013; Bamiro et al. 2015) employed the LP approach in the command areas to derive information on OCPs for maximum benefits under limited input resources availability and endorsed the technique for better land, water, and human resources management. The present investigation illustrated the capability of LP approach in deriving OCPs under various scenarios.

Understanding the optimal crops area combination is vital in assessing irrigation needs for a diversified cropping pattern for efficient operation of reservoirs. LP techniques hold excellent potential in water resource management to optimize water availability for different uses. Under the present investigation, LP models were developed to derive information on OCPs under varying input scenarios and develop strategies to achieve higher water use efficacy. The OCP were developed for three objectives viz., net benefit, food production and labor maximization. Results revealed that net benefit was raised by 122, 93, and 95% for Ratanpura, Chaplada, and Maraita minor, respectively, OCP estimated for 30-days CR in 2013–2014. Similarly, food production increased by 22.39, 16.74, and 25.70%, while labor employment increased by 40.92, 33.78, and 33.01% for Ratanpura, Chaplada, and Maraita II minors, respectively, compared to the existing cropping pattern for 30 days of CR. Similar findings were observed for the 24 and 21 days CR scenarios. The conjunctive water use evaluation for Maraita II minor resulted in OCP of 38.91 ha for wheat, 19.63 ha for mustard, 99.23 ha for garlic, and 38.55 ha for coriander. These areas were 7.50% more than the area under existing cropping pattern.

Long-term scenario analysis may assist in long-term planning in selecting the appropriate cropping pattern to bring sustainability. The OCP derived for 30 days of CR for 2020 is 44.14, 28.62, 167.15, and 46.28 ha for wheat, mustard, garlic and coriander, respectively, for Ratanpura minor. Similarly, the OCP derived for 30 days of for the year 2025 was 49.54, 28.62, 163.42, and 44.61 ha for wheat, mustard, garlic and coriander, respectively, for Ratanpura minor. Similar results were obtained for Chaplada and Maraita II minors. The findings of the present investigation would indeed be valuable in the long-term optimization of water resources in meeting the desired objectives like net benefit, food, and labor employment maximization in the study area under consideration. The present study considered the formulation of LP models encompassing three objectives. However, the current study did not account for the effects of climate change on crop production and water availability. Rising temperatures could potentially impact crop water demand. Therefore, it is important to incorporate elevated crop water demand by analyzing climatic variables spatially and temporally when determining water availability and crop demands.

J.R., R.C., and M.K prepared and wrote the original draft; R.C, J.R., and K.M. wrote, reviewed, and edited; J.R. helped in discussion. All authors have read and agreed to the published version of the manuscript.

This research received no external funding.

The authors are greatly indebted to the Head of the Soil and Water Engineering Department and the teaching and supporting staff, College of Technology and Engineering, Maharana Pratap University of Agriculture and Technology, Udaipur, for facilitating the conduction of the experiment.

All relevant data are included in the paper or its Supplementary Information.

The authors declare there is no conflict.

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