Assignment:
Part I: Formulating linear programming models for Kangaroo.
In order to analyze the Kangaroo Oil case, we begin by formulating linear programming models which describe Kangaroo's operations. To this end, you need to brainstorm with your group to specify the three elements of the LPs: the decision variables, the objective function, and the constraints. You also need to make a set of assumptions for the coefficients and parameters used in the model.
1. Decision variables
To determine the decision variables, you may want to think about exactly which actions are under Kangaroo's control. Kangaroo will want to know how much to buy from each crude oil source, how much to send to each refinery, and how much output of each type is available at each refinery (i.e., actions related to sourcing and production). Kangaroo will also want to know how much gas or distillate to send to each market (i.e., actions related to distributing outputs). Thus, a set of variables representing or describing these quantities could be your decision variables.
2. Objective function
Due to the fact that all of Kangaroo's sales are through long-term contracts with locked-in prices, the revenue that Kangaroo will realize is fixed. Therefore, you can formulate this problem as a cost minimization problem. Think about the various elements of this cost function, arising from sourcing, transportation, refining, and distribution to the final markets.
3. Constraints There are some basic constraints (there might be more) which are de-scribed below:
(a) Kangaroo cannot buy more than its maximum capacity from each crude oil source.
(b) Each refinery cannot process more than its operating capacity.
(c) Demand in each market must be met: There is no possibility of allowing unmet demand.
(d) Routes between Australia and Japan are not eligible due to Kangaroo's internal policy. You may model these either in your constraints or by appropriately modifying the coefficient of the objective function.
(e) You may enter the values in thousands of barrels to eliminate the convergence issues in Excel, but make sure to be consistent while entering the values. Now you are ready to proceed to your analysis. Please refer to the Project submission guidelines posted on Learn before writing your report.
Question 1: Formulate the integrated sourcing, production and distribution problem as a linear program. In particular, specify your decision variables, objective function, and constraints. Briefly discuss any key assumptions used to finalize your LP formulation.
Next, encode your LP model in Excel. To help you with your analysis, I will post an Excel template, but you can also initially choose to build your own model from scratch. You will use Excel Solver to compute the optimal solution, and then conduct further analysis using the Sensitivity Report and by modifying the base model or building a new model.
Question 2: Based on the optimal solution of this model, what is the annual sourcing and production cost? What is the total annual distribution cost?
Hint: If Excel reports "no solution," change the demand constraints to inequalities. That is, instead of specifying that the amount supplied to each market must exactly equal demand, you now specify that the amount supplied to each market must be at least as much as the demand.
Question 3: Instead of the integrated approach, where you minimize the total costs for production, sourcing and distribution, how would your results change if you adopted a hierarchical approach, in which you first optimize the production and sourcing costs (ignoring the distribution costs) and then, optimize the distribution costs (based on the optimal sourcing and production decisions you came up with)? Which approach is more advantageous? Briefly discuss the differences without actually solving for the hierarchical approach.
Part II: Applying linear programming to generate policy implications
After presenting your preliminary work, Cristina believes that your model can provide useful insights for Kangaroo's operations. In particular, she is interested in some operational and strategic issues, which Kangaroo is currently considering for the fiscal 2015 operations. These questions are discussed in this section. Some questions can be answered by examining the Excel output, while for others you may have to modify and re-solve the LP formulation.
3.1 Should Kangaroo buy additional crude oil from the Brunei fields?
Currently, suppliers in Iran and Brunei have crude oil capacities of 275,000 and 300,000 barrels per year respectively. However, Kangaroo has an option to buy an additional 25,000 barrels of crude oil from the Brunei fields. In order to exercise this option, Kangaroo has to pay a strike price of $250,000 to the local oil authority.
Question 4: Should Kangaroo exercise the option to buy the additional 25,000 barrels from the Brunei fields? If your answer is yes, how much savings can Kangaroo realize? Please use the sensitivity report, whenever possible.
3.2 Should Kangaroo enter Singapore market? For the following question, please use the original base model. In particular, ignore the
modifications in Section 3.1.
Due to the lack of long-term storage facilities, Kangaroo is always interested in adding new demand as long as its revenue exceeds the cost of doing so. Negotiations have begun with clients in Singapore who are interested in buying distillate from Kangaroo. If the negotiations are successfully completed, this will potentially add a distillate requirement of 20,000 barrels (with extra revenue of $4.5 million). It costs $10 and $5.5 to ship one barrel of distillate to Singapore from Australia and Japan, respectively.
Question 5: At optimum how much additional cost would Kangaroo incur by entering the Singapore market? Is it profitable to enter Singapore market?
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