Supply Chain Management

EG 3337 Supply Chain Management


  1. Type your answers using MS WORD and email me the file as an attachment. Please ensure that the email is submitted before the deadline. Please note that, no time extension or accommodation will be provided due to issues pertaining to connectivity. You may submit your answers in advance, if you are concerned about internet connectivity issues.
  2. While you are allowed to refer to resources such as books, notes and other research materials, you SHALL NOT discuss the problem with others (including other students or professionals). You should provide citation to the material you have referred.
  3. You are required to provide appropriate reference citation to the material you used as a reference, failing which you may not receive a test grade on the exam.
  4. You may use MS Excel or other software resources in solving the problem. However, you are required to organize all the materials within the MS WORD document (as tables or figures or charts) and send one single file as an email attachment. Do not cut and paste from Excel as it appears on Excel. Each number (or table of values) should be accompanied by a description (using a sentence or a paragraph explaining the number or table of values.
  5. By answering this assignment, you agree to the Student Code of Honor, and in particular, towards this assignment, you did not lie, cheat or steel, nor did you tolerate those who did so. Please note that academic dishonesty will result in a final letter grade of ‘F’ on the course.



Pompeii Italian Grill Restaurant serves an exquisite Italian cuisine in the heart of San Antonio, Texas. The restaurant’s high seller is an Italian pasta dish that uses two main ingredients, namely the Mariella Capellini Pasta and the Basil, Garlic & Black Olive Sauce. The Italian brand Mariella Capellini Pasta is purchased from the firm, which is an e-commerce website operated by a privately-owned importer and distributor headquartered in South Florida. The distributor operates via a 3PL, a warehouse to store the pasta product to be delivered to the restaurant. Whereas, the Basil, Garlic & Black Olive Sauce is purchased from a local manufacturer, namely the Shayne Foods.

The restaurant usually serves its customer demand for the pasta dish by using 25000 lbs of pasta per year and 25000 lbs of sauce per year, on a fairly uniform and constant basis. The restaurant expects the demand to be similar for a foreseeable future time period. Since both the ingredients are required in equal amounts at the point of use, the restaurant replenishes its inventory for both the ingredients at the same time. In particular, they utilize a truck to collect the ingredients for replenishment by paying $200 per shipment. Assume that the capacity of the truck is not an issue. As soon as the truck brings both the ingredients, the ingredients are stored in appropriate cold storage aisles for future use. However, due to the handling and wastage, approximately 4% of the pasta and 9% of the sauce are wasted, consistently. The pasta is purchased at $0.70 per lb and the sauce is purchased at $5 per lb. The inventory costs are computed at 67% per year of per unit costs.

The 3PL firm, which exclusively serves the restaurant, buys the pasta ingredient from the Italian manufacturer at $0.10 per lb and spends $1200 per order. The 3PL incurs approximately 5% per year of the per-unit cost in inventory holding and can hold inventory without any capacity limitations. The 3PL follows an inventory policy where it purchases an order quantity that is an integer multiple of the order quantity placed by the restaurant.

Whereas, Shayne Foods, which exclusively produces the sauce to serve the restaurant, buys the sauce ingredient from farmers and spends $2200 per production setup and procurement order of the ingredients. Shayne Foods incurs approximately 8% per year of the per-unit cost in inventory holding on both the raw ingredients and the finished product. Raw materials such as tomato, garlic, basil, and olives cost $0.4, $1, $3, $2, respectively. For each pound of the sauce, 0.94 pound of tomato, 0.02 pound of garlic, 0.03 pound of olives, and 0.01 pound of basil leaves are required. The production cost per pound of the final product is $1 per pound. Due to FDA and quality control requirements, Shayne Foods purchases the ingredients, exclusively for the restaurant and processes them as per its stringent quality standards on a lot-for-lot basis. That is, once the factory receives a purchase order from the restaurant (assuming a certain constant lead-time), the factory procures from the farmers an appropriate amount of the ingredients by factoring the wastage amount. The purchased ingredients are inventoried in a cold storage section of the facility. Production process starts as soon as the procured raw ingredients are received, and the inventoried ingredients are constantly and uniformly depleted as needed for production. The production rate is 125,000 million pounds per year. The processed final product is inventoried again in the cold storage. Once the finished inventory reaches the replenishment order size placed by the restaurant, the entire finished lot is shipped out to the restaurant and the production resources are assigned for processing orders from other customers. In the production process, the factory has experienced an average of 12% wastage of ingredients, which cannot be claimed back.

  1. Draw the inventory profile for each stage of the supply chain, define the decision variables and formulate the average annual cost functions for each supply chain partner.
  2. Analyze the supply chain assuming that the replenishment decisions are made in sequence, that is, the restaurant decides first, followed by the 3PL, and Shayne Foods. In particular, derive the average annual cost functions for each supply chain partner, and determine the individual costs, order quantities, and cycle times.
  3. Determine the supply chain optimal replenishment quantities, cycle times and the supply chain cost.
  4. Provide ideas on how to incentivize the restaurant, 3PL and Shayne Foods to shift their operations from the scenario specified in part (2) to the scenario specified in part (3).
    1. In particular, explain using the values obtained in the previous parts the incentives in dollar amounts per pound and who should provide incentives to whom and by what amount to break-even the cost increases, if any.
    2. In addition, explain using the values obtained in the previous parts the incentives in dollar amounts per pound and who should provide incentives to whom and by what amount to split the cost savings in the supply chain equally between the facilities.


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