Stochastic Models in Operations Research Case Study: Optimal Replenishment Policy for MML Step Sheets LEARNING OBJECTIVES Inventory management deals with determining the level of a commodity that a business must maintain to ensure smooth operation of its activities. The complexity of an inventory problem does not allow the development of a general model that covers all possible situations. The inventory problem involves placing and receiving orders of given sizes periodically. From this prospective, an inventory policy answers two questions: how much to order? and when to order? The basis for making these decisions is the minimization of an inventory cost function which contains some of the following components: 1. Purchasing cost is the price per unit of an item. At times, the item is offered at a discount if the order size exceeds a certain amount, which is a factor in deciding how much to order. 2. Setup cost represents the fixed charge incurred when an order is placed regardless of its size. Increasing the order quantity reduces the setup cost associated with a given demand. 3. Holding cost represents the cost of maintaining inventory in stock. It includes the interest on capital, and the cost of storage, maintenance, and handling. 4. Shortage cost is the penalty incurred when we run out of stock due to possible variability in the demand. It includes potential loss of income and the more subjective cost of loss in customer's goodwill. 5. Salvage value of obsolete inventory. Inventories of perishable goods or products with outdated designs need to be disposed or sold for a loss to create space for newly purchased or manufactured items. An inventory system may be based on periodic review (for example, ordering every week or every month), in which new orders are placed at the start of each period. Alternatively, the system may be based on continuous review, where a new order is placed when the inventory level drops to certain level, called the reorder point. An example of a periodic review can occur in a gas station where new deliveries arrive at the start of each week. Continuous review occurs in retail stores where items (such as cosmetics) are replenished only when their inventory level on the self drops to a certain level. The objective of this case study is to determine the economic order quantity (EOQ) for the step sheets inserted in the brochures of a Master of Manufacturing Logistics (MML) Program offered at a well-known university in Pennsylvania that minimizes the average annual purchasing cost. The analysis of the problem requires the development of a specific cost model that takes into account the quantity discounts offered by the document services company that produces the brochures and the annual probability that the step sheets may have to be updated. DESCRIPTION OF CASE STUDY The MML Program is an integrated two-semester academic program offered by both the College of Engineering and the College of Business at a prestigious university in Pennsylvania. Students enrolled in the program have baccalaureate degrees in engineering, business, or science, and average three years of work experience. Although enrollment is limited to fifty students, the MML marketing team has implemented a number of advertising initiatives to attract highly motivated students with outstanding academic 2 credentials to the program. Some of the most successful strategies to improve the visibility of the program include introduction of the program to junior and senior students in information sessions at the main campus and other university campuses, participation of the program in local and national (engineering and business) job fairs, and development and maintenance of a competitive website. The program also offers academic scholarships based on merit to top applicants, which are funded by the MML Industrial Advisory Board and the Graduate School. About two years ago the MML Program developed new program brochures for distribution to prospective students and also to companies visited during the two-day field trip that is organized each semester as part of the MML curriculum. A brochure consists of a folder and five step sheets. The folder contains the MML logo and some general information about the program. The five step sheets inserted in the folder provide detailed information about the program including (i) curriculum, (ii) partnership with industry, (iii) admission guidelines, (iv) placement statistics, and (v) financial assistance. Two years ago, 5,000 folders and 2,000 sets of step sheets were ordered to Advanced Color Graphics (ACG), a document services company. Large order quantities were placed due to the high fixed ordering cost set by ACG. The order for step sheets was smaller because the marketing team believed that step sheets would have to be updated in two years. Currently, the inventory level of steps sheets is close to zero and revisions need to be prepared due to updates in the curriculum before a new order of can be submitted. ACG has prepared a cost quotation for the present and future orders under the following two conditions and the requirement that order quantities must a multiple of 500 sets of step sheets: 1. Exact Reprint (no changes in the step sheets) a. Initial 500 sets of 5 step sheets: $1,157 total. b. Additional 500 sets of 5 step sheets: $174 per 500 sets. 2. Reprint with changes (step sheets can be revised) 3 a. Initial 500 sets of 5 step sheets: $1,532 total. b. Additional 500 sets of 5 step sheets: $174 per 500 sets. The current consumption of step sheets is approximately 1,000 sets per year and the marketing team does not anticipate any changes in future demand. The main concern, based on past curriculum revisions, and changes in corporate relations and admission requirements, is that the probability that step sheets require updates by the end of any given academic year is estimated to be 0.30. Based on the current demand, cost structure and annual redesign probability (0.30), and assuming that the holding cost and the additional administrative cost for submitting an order are negligible, and that shortages are not allowed, the marketing team needs your assistance in determining the EOQ value that minimizes the average annual cost. * Please note that, do NOT use the 0.30 probability provided in the case study description on your case study, or you are at risk of getting zero point in the case study. Each team must use the probability assigned to them in the final list of teams that will be posted on ANGEL on Wednesday, June 21, 2017. 4 CASE STUDY OPTIMAL REPLENISHMENT POLICY FOR MML STEP SHEETS Case Study Description and Analysis Overview Master of Manufacturing Logistics (MML) Program MML Step Sheets Problem Description Discussion Illustration of Solution Procedure Master of Manufacturing Logistics (MML) Program The MML Program is an integrated two-semester academic program offered by both the College of Engineering and the College of Business at a prestigious PA university. MML marketing team has implemented a number of advertising initiatives to attract highly motivated students with outstanding academic credentials to the program: - Introduction of the program to junior and senior students in information sessions at the main campus and other university campuses. - Participation of the program in local and national (engineering and business) job fairs. - Development and maintenance of a competitive website. The program also offers academic scholarships based on merit to top applicants, which are funded by the MML Industrial Advisory Board and the Graduate School. MML Step Sheets About two years ago the MML Program developed new program brochures for distribution to prospective students and corporate sponsors. A brochure consists of a folder and five step sheets. The five step sheets inserted in the folder provide detailed information about the program including - - - - - curriculum, partnership with industry, admission guidelines, placement statistics, and financial assistance. Two years ago, 5,000 folders and 2,000 sets of step sheets were ordered to Advanced Color Graphics (ACG), a document services company. Large order quantities were placed due to the high fixed ordering cost set by ACG. The order for step sheets was smaller because the marketing team believed that step sheets would have to be updated in two years. Problem Description Currently, the inventory level of steps sheets is close to zero and revisions need to be prepared due to updates in the curriculum before a new order of can be submitted. ACG has prepared a cost quotation for the present and future orders under the following two conditions and the requirement that order quantities must a multiple of 500 sets of step sheets: - Exact Reprint (no changes in the step sheets) Initial 500 sets of 5 step sheets: $1,157 total. Additional 500 sets of 5 step sheets: $174 per 500 sets. - Reprint with changes (step sheets can be revised) Initial 500 sets of 5 step sheets: $1,532 total. Additional 500 sets of 5 step sheets: $174 per 500 sets. The current consumption of step sheets is approximately 1,000 sets per year and the marketing team does not anticipate any changes in future demand. Problem Description (cont.) The main concern, based on past curriculum revisions and changes in corporate relations and admission requirements, is that the probability that step sheets require updates by the end of any given academic year is estimated to be 0.30. It can be assumed that the holding cost and the additional administrative cost for submitting an order are negligible. Shortages are not allowed. The marketing team needs your assistance in determining the economic order quantity (EOQ) that minimizes the average annual cost. Discussion This problem can be solved under the assumptions that orders can only be submitted at the beginning of an academic year, the annual demand rate is 1,000 sets of step sheets, and the cost structure and probability of design changes (0.30) will remain constant. Since the demand rate is 1,000 and shortages are not allowed, the EOQ value must be a multiple of 1,000. The annual average cost for a specific order size can be determined by solving a Markov chain. Illustration of Solution Procedure Illustration of Solution Procedure (cont.) * Please note that, do NOT use the 0.30 probability provided in the case study description on your case study, or you are at risk of getting zero point in the case study. Each team must use the probability assigned to them in the final list of teams that will be posted on ANGEL on Wednesday, June 21, 2017. Illustration of Solution Procedure (cont.)