Assignment 1 Case Study (Individual Assignment)Dynamic Lot SizingThe dynamic lot-size model in inventory theory, is a generalisation of the Economic Order Quantity (EOQ) model thattakes into account that demand for the product varies over time.Dynamic lot sizing sometimes refers to as Time-Varying Demand as well. In contrast to EOQ model where demandis constant, in the time-varying deterministic demand model, demands of various periods are unlike. The variationscan depend on different reasons. For example, production on a contract, which requires that certain quantities aredelivered on specified dates. Note that we are still considering deterministic demand, i.e., all variations are known inadvance. In the basic models, lead-time is disregarded. When dealing with lot sizing for time-varying demand, it isgenerally assumed that there are a finite number of discrete time steps, or periods. A period may be, for example, 1day or a week. We know the demand in each period, and for simplicity, it is assumed that the period demand takesplace at the beginning of the period. There is no initial stock. When delivering a batch, the whole batch is delivered atthe same time. The holding cost and the ordering cost are constant over time. No backorders are allowed. We shall usethe following notation: Var T = di = Definitionnumber of periods,demand in period i, i = 1, 2, , T, OC = ordering cost,HC = holding cost per unit and time unit.ProblemCostco has received the following demands for a product in 2020:Month 1 2 3 4 5 6 7 8 9 10 11 12Demand 300 700 800 900 3300 200 600 900 200 300 1000 800Suppose ordering cost (OC) is $504 and holding cost (HC) of one unit of product in a year is $3.There is no shortage cost. Backordering is not allowed in this model.To achieve the minimum total cost (ordering cost + holding cost), how many times the company should place orders ina year? In each order, how many products should be ordered? What is the total cost in a year?WatchWatch these two videos: Video 1: Lot Sizing Video 2: Lot sizing heuristicsQuestionsQ1 (2 marks)Given that the total demand of the whole year is 10,000 products, suppose the company is going to use the EOQ modelfor the accumulated demand of one year (10,000). In other words, ignore the monthly demand. Compute:1 Optimal order quantity (Q*) Total cost Frequency of orders Time between ordersQ2 (5 marks)Use mixed integer linear programming to solve the problem regarding the monthly demand. Suppose that holding costis applied to the ending inventory. Develop the mathematical model in the Word document. Solve the problem in Excel Develop a plan in the Word document and explain when and how many products should be ordered in order tominimise the total cost. Recalculate the optimal value of objective function (total cost with the new assumption that the holding cost isapplied to the average inventory (not ending inventory).Q3 (1 mark)Use Lot for Lot heuristic method and compute the total cost.Q4 (3 marks)Use Part Period Balancing heuristic method, develop a schedule to show when and how many products should beordered, and compute the total cost.Q5 (4 marks)Use Silver_Meal heuristic method, develop a schedule to show when and how many products should be ordered, andcompute the total cost.Note: Silver Meal heuristic method was coined by Gorham (1968).Q6 (3 marks)Over the last five questions, you applied the methods which were explained in the videos. Now, it is your turn toresearch!In this section, students are required to use Dynamic Programming based on the Wagner-Whitin Algorithm to developa schedule to show when and how many products should be ordered, and compute the total cost.To understand how Wagner-Whitin Algorithm works: Refer to the section 4.6 (The Wagner-Whitin Algorithm works:) of Axsaters book (Axsater, 2006) which isavailable online via RMIT library. Check slides 14 to 18 of this reference in which a sample problem is solved using the Wagner-Whitin Algorithm.If you are interested to read the original article (Wagner and Whitin, 1958), you can click here.Summary (2 marks)Put the results of all methods in a summary table and discuss.RubricPlease refer to the end of this document.2Rubric of Assignment 13ReferencesAxsater, S. (2006) Inventory control. Second Edition. Boston, MA: Springer US (International series in operationsresearch & management science).Gorham, T. (1968) Dynamic order quantities, Production and Inventory Management, 9(1), pp. 7581.Wagner, H. M. and Whitin, T. M. (1958) Dynamic version of the economic lot size model, Management science.INFORMS, 5(1), pp. 8996.Axsater, S. (2006) Inventory control. Second Edition. Boston, MA: Springer US (International series in operationsresearch & management science).Gorham, T. (1968) Dynamic order quantities, Production and Inventory Management, 9(1), pp. 7581.Wagner, H. M. and Whitin, T. M. (1958) Dynamic version of the economic lot size model, Management science.INFORMS, 5(1), pp. 8996.4
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