Executive Summary
Therefore, with regards to this situation, the main objective BarCo management has is to implement a gas resource curtailment plan which minimises the impact of the natural gas shortage on overhead contributions and maximises the firm’s profits. As such, this business analysis report intends to discuss and offer solutions to these operating constraints by utilising resource planning techniques. By considering production variables, operating constraints and planning restrictions, a set of curtailment plans that minimises distribution costs and maximises profits attained from BarCo’s operations can be able to be put into action.
Current constraints discussed within this report include the distribution prices of natural gas between MaxEnergy’s supply locations to BarCo manufacturing facilities. To minimise distribution costs during curtailment, an analysis is undertaken to establish to lowest possible cost for distribution between these locations. Furthermore, to minimise total production costs, a product mix analysis is undertaken to assess how much of each product needs to be produced to maximise total profits from operations. Furthermore, by utilising a sensitivity analysis, an examination of the key variables within this situation can occur to see how the optimal solution changes if fixed operating constraints such as unit profit are allowed to change. Lastly, potential recommendations for future work to prevent supply problems in future are presented to BarCo to bring about change that would not as severely disrupt operations for the business.
1. Introduction
Due to the unprecedented heatwave and bushfires throughout Summer, 2019, several natural gas resources operated by MaxEnergy were severely depleted, and thus caused a shortage of natural gas. According to provisions established by a Federal Commission, in the event of natural gas depletion, the following priorities for the allocation of gas to consumers needs to occur as established in Table 1 below.
Table 1: Natural Gas resource allocation priorities for Max Energy
| Priority Number | Description of Priority |
| 1 | Natural gas needs to be available to residents and commercial properties for heating and cooling purposes. |
| 2 | Commercial and industrial firms that use natural gas as a source of raw material for the creation of products. |
| 3 | Industrial firms that use natural gas as a fuel to power a boiler |
As such, based on these allocation priorities, MaxEnergy has notified BarCo, that it can be subjected to rolling brownouts, which are temporary and periodic curtailments on the supply of a resource, in this case, natural gas. As BarCo heavily relies on natural gas to run its production operations, it has become vital during these circumstances that an analysis of resource allocation needs to be performed to determine where gas can be allocated to run the business efficiently as well as adequately meet the company’s organisational objectives.
To allocate resources effectively such that a minimum impact on profits is attained, management decisions regarding inventory, transportation, and network design to make the most effective use of limited resources needs to take place. Analysis methodologies that can be used to solve such problems include Linear Programming. This resource management technique can be utilised to efficiently distribute constrained resources. Previously, linear programming has been widely adopted as a modelling technique used in business areas such as supply chain management as part of planning and decision support systems.
This report utilises a Linear programming model in decision-making relative to resource allocation by understanding the business problem of BarCo Corporation from the perspective of supply chain and operations management lens. Strategic options and recommendations to minimise the impact on profits/overhead contribution are provided by evaluating the tangible and intangible benefits and the risks connected with the expected outcomes.
2. Description and Formulation of Problem
The operating situation which BarCo’s management finds itself in can be succinctly described as decision-making under uncertainty, since it affects the core input and output areas of the business, such as the supply, demand, and operating processes (Peidro, Mula, & Jimenez, 2010). Uncertainty in natural gas supply has resulted in MaxEnergy requiring customers to change utilisation strategies. The most negative consequences of this include the introduction of uncertainty and as such reduces BarCo’s ability to effectively forecast future production and distribution requirements.
Thus, BarCo must navigate its supply chain onto an alternative strategic course by implying new inputs or operating constraints to its’ distribution and production configuration. As a part of assessing the optimal distribution strategy, the following variables which need to be assessed are described in Table 2 below.
Table 2: Variables which will be assessed.
| Variable | Description of Variable |
| Manufacturing Plants | Manufacturing plants are the locations where the products for BarCo are manufactured. As there are three specific locations in which these products of manufactured, there are different distribution costs that dictate the price of shipping natural gas. |
| Supply Locations | The supply locations are the places from where MaxEnergy initially distributes natural gas to its customers. As there are three differing origins for the supply of natural gas, there are different distribution costs that dictate the price of shipping natural gas. |
| Production Capacity | The production capacity is a variable that stipulates how much of each product can be safely produced by BarCo per day. In this analysis, this will be measured as tons/day. |
| Production Rate | The production rate is a percentage factor for how much of the maximum production capacity is currently being produced. As BarCo does not necessarily operate at full capacity, the true daily production capacity is defined by the production rate. |
| Gas Consumption | Gas consumption is the operating variable that describes how much natural gas is required to produce a set amount of product. Within the context of this problem, gas consumption will be defined as 1000 cubic feet/ton. |
| Profit | Profit is defined as the amount of money made after all overheads have been paid for. Within the context of this problem, profit will be defined as $/ton of product. |
As such, by utilising these variables, this analysis will aim to analyse, assess and present a:
- Production plan for the products of BarCo with a curtailment of 20% and 40%
- Distribution plan for the supply of natural gas from Supply Locations to Manufacturing plants with a curtailment of 20% and 40%
Based on the results of these assessments, the production and distribution plan will highlight totals costs for this type of operation and will also specifically assess and present:
- A sensitivity analysis for production and distribution plans that will analyse how changes in some specific variables such as production capacity or profit will change the outcomes of the production and distribution plans
- A set of future recommendations that can be used by BarCo management to mitigate the risks presented by these operational problems
To successfully conduct this assessment, it is important to understand the current operations for BarCo. Table 3 below presents current production data for the products manufactured by BarCo. Table 4 identifies current distributions costs for natural gas from MaxEnergy’s supply locations to BarCo’s manufacturing plants, and Table 5 identifies the total supply and demand data between these facilities.
Table 3: Current Production and information of products produced by BarCo
| Product | Profit ($/Ton) | Maximum Production Capacity | Production Rate (% of Capacity) | Natural Gas Consumption (1000 cu.ft/ton) |
| Ammonia | 134 | 600 | 90 | 19 |
| Ammonium Phosphate | 80 | 1,600 | 80 | 13 |
| Ammonium Nitrate | 100 | 800 | 70 | 20 |
| Urea | 122 | 1,400 | 60 | 12 |
| Hydrofluoric Acid | 96 | 200 | 80 | 19 |
| Chlorine | 110 | 1,500 | 80 | 11 |
| Caustic Soda | 75 | 700 | 70 | 14 |
| Vinyl Chloride Monomer | 85 | 1,500 | 80 | 12 |
Table 4: Distribution Costs (These prices represent the cost to ship 1 unit of natural gas from a particular origin to a destination
| All Prices in $/1000 cu.ft of Natural Gas | Manufacturing Plants (Destination) | |||
| A | B | C | ||
| Supply Location (Origin) | I | 1.30 | 1.20 | 1.60 |
| J | 1.20 | 1.40 | 1.50 | |
| K | 1.80 | 1.60 | 1.40 |
Table 5: Supply and Demand of Gas
| Location of Supply | Supply (x 1000 cu.ft) | Locations of Demand | Demand (x 1000 cu.ft) |
| I | 20,000 | A | 20,000 |
| J | 40,000 | B | 50,000 |
| K | 25,680 | C | 15,680 |
| Total Demand | 85,680 | Total Supply | 85,680 |
3. Analysis
The production-distribution network for BarCo’s supply chain can be viewed as a model of an integrated system made up of different objectives, constraints, and assumptions (Fahimnia, Luong, & Marian, 2012) that all need to be united together to produce a successful outcome. As BarCo utilises a traditional approach to production, it can be optimised to determine the most efficient production combination. (Peidro, Mula, & Jimenez, 2010) proposes that linear programming can be used as a modelling methodology to optimise the production of BarCo products in the operating environment it is facing. As such, to utilise linear programming it is imperative to understand and define the operating objectives, input variables, constraints and assumptions that will be needed to develop the linear programming model (Peidro, Mula, & Jimenez, 2010). As such this specific information is defined below:
Objectives
The objective of this linear programming model is to:
- Determine the optimal quantities or amount of each product to be produced under a curtailment of 20 to 40% of natural gas supply that maximises the total profit generated.
- Determine the amount of natural gas to be supplied for specific supply locations to manufacturing plants under a curtailment of 20 to 40% of natural gas supply that minimises the total cost of natural gas distribution.
Decision Variables
The decision variables for this linear programming model are:
- The amount of each product to be produced.
- The amount of gas to be shipped from each supply location.
- The amount of gas to be received by each manufacturing plant.
Constraints
The constraints for this linear programming model are:
- The amount of natural gas shipped by a supply location needs to be less than or equal to the capacity available under a 20% to 40% curtailment.
- The amount of natural gas received by a manufacturing plant needs to be greater than or equal to the demand available under a 20% to 40% curtailment.
- The total amount of each product produced needs to be less than the maximum available production capacity (also considering the current production rate).
- The amount of gas used to manufacture the products cannot exceed the set amount available for consumption at the manufacturing plants after the implementation of the 20% and 40% curtailments.
Assumptions
To accurately undertake this assessment and produce valid linear programming models, a set of assumptions need to be made:
- The different products which BarCo manufactures can be produced at all three manufacturing plants (A, B and C).
- The production rate for each product is allowed to fall but cannot exceed its current stated production rate.
- Gas consumption for the production of products is constant with no production issues occurring which result in increases or decreases in consumption.
- Distribution costs between supply locations and manufacturing plants stay consistent regardless of the implementation of curtailment.
- Profit from the production of products stays consistent regardless of the implementation of curtailment.
- Curtailment of 20% or 40% respectively means that the supply and demand of gas also reduce by these amounts.
- The amount of gas available for supply and demand by Supply Locations and Manufacturing plants respectively, with the implementation of 20% and 40% curtailment is presented below in Table 6.
Table 6: Curtailment Supplies and Demands
| Supply from MaxEnergy Supply Location (x 1000 cu.ft) | Demand of BarCo Manufacturing Plants (x 1000 cu.ft) | ||||||
| Location | Normal Operation | Curtailment of 20% | Curtailment of 40% | Location | Normal Operation | Curtailment of 20% | Curtailment of 40% |
| I | 20,000 | 16,000 | 12,000 | A | 20,000 | 16,000 | 12,000 |
| J | 40,000 | 32,000 | 24,000 | B | 50,000 | 40,000 | 30,000 |
| K | 25,680 | 20,544 | 15,408 | C | 15,680 | 12,544 | 9,408 |
| Summation | 85,680 | 68,544 | 51,408 | Summation | 85,680 | 68,544 | 51,408 |
4. Results and Discussion
A set of linear programming models was established for the normal operating conditions, 20% curtailment and 40% curtailment. Implementing operational constraints that the amount shipped from a supply location cannot exceed its maximum capacity, and the amount of natural gas received needs to be greater than or equal to the amount demanded by the manufacturing plant, Tables 7, 8 and 9 present the total amount of natural gas that is shipped between respective supply locations and manufacturing plants. Based on these respective values, the objective of the linear program is to minimise the total cost of distribution.
Table 7: Normal Operation for distribution of natural gas at BarCo
| All values in (x 1000 cu.ft) | A | B | C | Total Supply from Supply Locations |
| I | 0 | 20,000 | 0 | 20,000 |
| J | 20,000 | 20,000 | 0 | 40,000 |
| K | 0 | 10,000 | 15,680 | 25,680 |
| Total Demand of Manufacturing Plant | 20,000 | 50,000 | 15,680 |
Based on this distribution plan, the minimum total distribution cost is:
Table 8: Operation for distribution of natural gas at Barco considering a 20% curtailment.
| All values in (x 1000 cu.ft) | A | B | C | Total Supply from Supply Locations |
| I | 0 | 16,000 | 0 | 16,000 |
| J | 16,000 | 16,000 | 0 | 32,000 |
| K | 0 | 8,000 | 12,544 | 20,544 |
| Total Demand of Manufacturing Plant | 16,000 | 40,000 | 12,544 |
Based on this distribution plan, the minimum total distribution cost is:
Table 9: Operation for distribution of natural gas at Barco considering a 40% curtailment.
| All values in (x 1000 cu.ft) | A | B | C | Total Supply from Supply Locations |
| I | 0 | 2,592 | 9,408 | 12,000 |
| J | 0 | 24,000 | 0 | 24,000 |
| K | 12,000 | 3,408 | 0 | 15,408 |
| Total Demand of Manufacturing Plant | 12,000 | 30,000 | 9,408 |
Based on this distribution plan, the minimum total distribution cost is:
A set of linear programming models was used to establish the normal operating conditions as well as the operating conditions for 20% and 40% curtailment. Implementing the constraints that the amount of each product produced cannot exceed the current production capacity for each product, Table 10 presents the production mix that should be implemented for all production models and Table 11 presents the total profits produced as a result of these production models.
Table 10: Optimal production mix that should be considered for normal operation, 20% curtailment and 40% curtailment.
| Product | Normal Operation (Tons) | 20% Curtailment (Tons) | 40% Curtailment (Tons) |
| Ammonia | 540 | 540 | 540 |
| Ammonium Phosphate | 1,280 | 1,280 | 266.77 |
| Ammonium Nitrate | 560 | 0 | 0 |
| Urea | 840 | 840 | 840 |
| Hydrofluoric Acid | 160 | 0 | 0 |
| Chlorine | 1,200 | 1,200 | 1,200 |
| Caustic Soda | 490 | 283.14 | 0 |
| Vinyl Chloride Monomer | 1,200 | 1,200 | 1200 |
| Summation of total amount of products produced | 6270 | 5,343.14 | 4,046.77 |
Table 11: Total Profit resulting from production mix that should be considered for normal operation, 20% curtailment and 40% curtailment.
| Product | Profit at Maximum Production | Profit at 20% Curtailment | Profit at 40% Curtailment |
| Ammonia | $72,360 | $72,360 | $72,360 |
| Ammonium Phosphate | $102,400 | $102,400 | $21,341.54 |
| Ammonium Nitrate | $56,000 | $0 | $0 |
| Urea | $102,480 | $102,480 | $102,480 |
| Hydrofluoric Acid | $15,360 | $0 | $0 |
| Chlorine | $132,000 | $132,000 | $132,000 |
| Caustic Soda | $36,750 | $21,235.71 | $0 |
| Vinyl Chloride Monomer | $102,000 | $102,000 | $102,000 |
| Total Profit produced by Production of Products | $619,350 | $532,475.71 | $430,181.54 |
Based on these linear programming analyses, the minimum distribution costs, and maximum production profits for 20% and 40% curtailment are established. To undertake these analyses, linear programming within Microsoft Excel was undertaken. To showcase this work, Appendix 1 display the linear program used to calculate the minimum production costs, whilst Appendix 2 will display the linear program used to determine the maximum profit that can be generated under the curtailment strategies.
Sensitivity Analysis
As part of this problem, it can be advantageous to assess how changes in variables such as decision variables and constraints change the outcome of the analysis as a whole. As part of this assessment, a sensitivity analysis will take place in which distribution costs and unit profits for the production of specific products are changed. In doing so, it should be possible to understand how changes in specific variables can impact final distribution costs and final production profits.
As can be shown, the highest cost of distributing gas happens to be between supply location K and manufacturing plant A. Table 12 below presents a sensitivity analysis in which the cost of supplying gas from supply location K to manufacturing plant A are reduced given 20% curtailment. Table 13 presents a sensitivity analysis in which the cost of supplying gas from supply location K to manufacturing plant A are reduced given 40% curtailment.
Table 12: Sensitivity Analysis for change in total cost for supplying natural gas from supply location K to manufacturing plant A with 20% curtailment.
| Capacity of Natural Gas (x 1000 cu.ft) | ||||||
| 0 | 5000 | 10000 | 15000 | 20000 | ||
| Cost of distributing natural gas ($) | $2.00 | $91,161.6 | $101,161.6 | $111,161.6 | $121,161.6 | $131,161.6 |
| $1.80 | $91,161.6 | $100,161.6 | $109,161.6 | $118,161.6 | $127,161.6 | |
| $1.60 | $91,161.6 | $99,161.6 | $107,161.6 | $115,161.6 | $123,161.6 | |
| $1.40 | $91,161.6 | $98,161.6 | $105,161.6 | $112,161.6 | $119,161.6 | |
| $1.20 | $91,161.6 | $97,161.6 | $103,161.6 | $109,161.6 | $115,161.6 | |
| $1.00 | $91,161.6 | $96,161.6 | $101,161.6 | $106,161.6 | $111,161.6 | |
| $0.80 | $91,161.6 | $95,161.6 | $99,161.6 | $103,161.6 | $107,161.6 | |
| $0.60 | $91,161.6 | $94,161.6 | $97,161.6 | $100,161.6 | $103,161.6 | |
| $0.40 | $91,161.6 | $93,161.6 | $95,161.6 | $97,161.6 | $99,161.6 | |
| $0.20 | $91,161.6 | $92,161.6 | $93,161.6 | $94,161.6 | $95,161.6 |
Table 13: Sensitivity Analysis for change in total cost for supplying natural gas from supply location K to manufacturing plant A with 40% curtailment.
| Capacity of Natural Gas (x 1000 cu.ft) | ||||||
| 0 | 5000 | 10000 | 15000 | 20000 | ||
| Cost of natural gas ($) | $2.00 | $68,371.2 | $78,371.2 | $88,371.2 | $98,371.2 | $108,371.2 |
| $1.80 | $68,371.2 | $77,371.2 | $86,371.2 | $95,371.2 | $104,371.2 | |
| $1.60 | $68,371.2 | $76,371.2 | $84,371.2 | $92,371.2 | $100,371.2 | |
| $1.40 | $68,371.2 | $75,371.2 | $82,371.2 | $89,371.2 | $96,371.2 | |
| $1.20 | $68,371.2 | $74,371.2 | $80,371.2 | $86,371.2 | $92,3,71.2 | |
| $1.00 | $68,371.2 | $73,371.2 | $78,371.2 | $83,371.2 | $88,371.2 | |
| $0.80 | $68,371.2 | $72,371.2 | $76,371.2 | $80,371.2 | $84,371.2 | |
| $0.60 | $68,371.2 | $71,371.2 | $74,371.2 | $77,371.2 | $80,371.2 | |
| $0.40 | $68,371.2 | $70,371.2 | $72,371.2 | $74,371.2 | $76,371.2 | |
| $0.20 | $68,371.2 | $69,371.2 | $70,371.2 | $71,371.2 | $72,371.2 |
As shown in Table 12, the lowest total cost obtained from distribution only occurs when no natural gas is shipped from supply location K to manufacturing plant A. However, an interesting trend appears whereby regardless of the capacity of natural gas shipped, if the cost of shipping is lowered, then overall distribution costs are lowered as well.
Furthermore, as can be shown, if either one of the curtailment plans takes places, the production of Ammonium Nitrate and Hydrofluoric Acid ceases. Table 14 will present a sensitivity analysis in which the profit generated by these products respectively is increased. This analysis will provide clarification on how much the profit for the products needs to be to make them worthwhile to produce during curtailment.
Table 14: Sensitivity Analysis for change in change in production profit through change in profit and amount of product products for all curtailment strategies and all products.
| Amount of Product to Produce (Tons) | |||||||
| 100 | 200 | 300 | 400 | 500 | 600 | ||
| Profit of Product Produced ($) | $100 | $10,000 | $20,000 | $30,000 | $40,000 | $50,000 | $60,000 |
| $120 | $12,000 | $24,000 | $36,000 | $48,000 | $60,000 | $72,000 | |
| $140 | $14,000 | $28,000 | $42,000 | $56,000 | $70,000 | $84,000 | |
| $160 | $16,000 | $32,000 | $48,000 | $64,000 | $80,000 | $96,000 | |
| $180 | $18,000 | $36,000 | $54,000 | $72,000 | $90,000 | $108,000 | |
| $200 | $20,000 | $40,000 | $60,000 | $80,000 | $100,000 | $120,000 |
Regardless of the products produced, a trend appears whereby if the unit profit generated by producing a product increases, the higher the profit will be. Similarly, as the amount of product produced increases, the total profit attained also increases in a similar fashion. For a more theoretical analysis of these trends, Appendix 3 below showcases actual sensitivity analysis reports generated by Microsoft Excel for each one of these linear programming models. As such, these sensitivity analyses assess the behaviour of independent variables to demonstrate how much they can change by under their current operating constraints.
Recommendations for BarCo Management to ease future concerns
Close facilities and concentrate on distributing gas to a singular location, with the lowest cost. Considering the localisation of the disaster, which has led to cutting natural gas supply it is advised for BarCo to consider an alternative source of the natural gas supplier. One such possible option is to import natural gas from other regions within the country or overseas. However, this type of option can lead to potentially higher cost and lead to increased cost of production and lower profitability. However, with a progressive approach to the estimation of the profit/loss model and finding alternative storages of natural gas; it is possible to find a profitable financial model with a lower contribution margin for the period of curtailment.
Another possible solution for BarCo is considering a substitute for natural gas, such as propane, butane, furnace oil and bunker oil. In this scenario, BarCo can employ an alternative source of fuel, especially for its’ secondary utilisation purposes, such as transportation and factory operations. It will enable to concentrate a natural gas utilisation only on producing those products that cannot be obtained in any other way.
As a strategic solution, BarCo should consider the environmental effects of the natural gas curtailment to convert new government policies into a competitive advantage. It is assumed that a shortage of the natural gas supply will lead to increased utilisation of “dirty” energy sources such as coal and oil. It will consequently increase pollution. Thus, it is highly likely, that government will introduce new environmental policies, such as increased taxes on dirty production, or vice versa – tax reduction for green products. In this possible scenario, it is advised to take advantage of the government initiatives to encourage green production by developing a set of procedures and equipment for reducing dirty emissions.
Finally, BarCo has the opportunity to take advantage of strategic procurement manoeuvre, such as a long-term partnership with MaxEnergy to become its largest customer. By sharing a strategic goals and securing long-term contracts to achieve a win-win partnership it becomes feasible for BarCo to get a special contract’s terms with extended purchase quotas for natural gas.
5. Conclusion
The BarCo Corporation currently needs to decide on the resource allocation used for its manufacturing process as it received a notification from MaxEnergy regarding the rapid depletion of natural gases. This issue has the potential to cause rolling brownouts or curtailments of natural gas supplies. As a result, BarCo Management must determine how it can minimise distribution costs and maximise profits during this situation.
By defining the decision variables, objective functions, constraints and necessary restrictions, a linear programming model is developed that provides the feasibility of a curtailment plan to minimize the fall in profits attained from BarCo’s current operations. The prime purpose of formulating a Linear programming model is to reduce the distribution costs and maximize profits through production.
By taking into consideration the relevant constraints and implementing appropriate assumptions, a set of linear programming models were formulated that led to the development of a production plan for 20 and 40% curtailment of natural gas resources and a distribution plan for 20% and 40% curtailment scenarios. Both these formulations provided clarity on how each curtailment plan bears an impact on the production BarCo’s products and this is further depicted by the curtailment’s influence on the profit occurrence.
Sensitivity analyses were also conducted to understand how changes in specific variables can impact final distribution costs and final production profits implied that overall distribution costs are directly proportional to the cost of shipping and the total profit attained changes with the increases in production of a product.
As the contribution to profit and overhead for products from BarCo has a lot of fluctuations, various considerations and careful discussions led to a few recommendations for management to ease future concerns. There is an option to distribute gas to a particular location with the lowest cost, consider an alternative source of the natural gas supplier by having a progressive approach towards finding a profitable financial model with a lower contribution margin for the period of curtailment and finding alternative storages of natural gas. Recognizing a substitute for natural gas is another possible solution to avoid the effects of natural gas depletion.
It is therefore advised that the management make a careful consideration of the recommendations and, suggestions to select a feasible contingency plan for allocation of natural gas among the firm’s products if curtailments are to become a reality.
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