Decision-Making Game: Inventory Applications

"He Shoots, He Scores" At a recent trade show, a Canadian company unveiled its radical new product for the sports equipment industry - a graphite hockey stick! The company, known as "He Shoots, He Scores" has enthusiastic plans for the stick. As owner of a medium-sized retail sporting goods store, you are aware of the various costs involved in ordering and holding inventory. Taking into account the respective costs, you are to develop an appropriate ordering policy for this brand-new item. Since this is a new product, you have no historical data on which to base your forecast of demand. However, you have data on the number of sticks sold for other new, state-of-the-art sticks from prior years: Demand Jul Aug Sep Oct Nov Dec Jan Feb Mar Apr May Jun 2 years ago 20 35 59 79 42 83 34 41 38 19 27 25 Last year 24 44 49 100 51 81 68 62 33 26 26 21 As in any business, sales for any given month could be extremely volatile (or not). In this game, the demand for the next year is generated from a Normal distribution (which ranges from negative infinity to infinity). It is not necessary to know the parameters of the Normal distribution for this game, but they are given at the end of these instructions. "He Shoots, He Scores" will allow you to purchase hockey sticks for $20. Market research results given at the recent trade show indicated that potential customers would pay up to $30 for the item. Thus, you plan to use $30 as your selling price. Note that the amount you sell in a given month is always the lowest of either monthly demand, or beginning inventory + quantity ordered. Placing an order costs you $60 (note that the manufacturer allows at most one replenishment per month). Any unsatisfied demand (a stockout, or should we call it a "stick"out?) costs you $7 per unit short. Backorders are not allowed (since customers will most likely purchase the hockey stick from a competitor if you don't have enough on-hand). Inventory remaining at the end of a month costs you $1 per unit. plan replenishments (when to order, how much to order) on a month-by-month basis for the next 12 months. Assume that the first month in the planning horizon is July, and that there is no inventory on-hand. After you make your replenishment decision, the instructor will announce the demand for that month. Then, you may make the decision for next month. Use the attached table to indicate your monthly replenishments, and to tabulate the results of your respective strategy. If a stockout occurs, write "0" for the ending inventory, and put a "0" for the beginning inventory of the subsequent month. Part1: Read the Game Description and Answer the questions concerning cost structure (*) Provide the General function of cost or revenue components. For example, the inventory level = Inventory at the beginning +Order Quantity (3) =(1)+(2) Month i (1) Inventory at the beginning of the month I items (2) Order Quantity (before demand realization) Q items (can take zero, if you decide to not to order) (3) Inventory Level = (1)+(2) (4) Observed Demand D items/month (5) Inventory Leftover (inventory at the end of the month) = (6) Revenue = List all the cost components and their corresponding formulas ( ) Total Cost = ( ) Monthly Net profit = Part 2 : For now assume that the demand is deterministic (known in advance) and given as follows for the next 12 month. July Aug. Sept. Oct. Nov. Dec. Jan. Feb. March April May June Demand 26 56 33 84 49 79 43 55 35 22 27 23 We would like to find some replenishment strategies (a lot sizing model) given the above set-up (no stock outs allowed) 1-Find the performance associated with the below replenishment strategy and compare between them. (1) Lot For LOT policy (2) Single Lot Policy (order only one time) (3) Economic Order Quantity (EOQ) (4) Periodic Order Quantity (5) Silver-Meal Policy 2-Find the optimal replenishment policy (using any method leading to optimality) 3-Compare and comment on the various results (*) show the steps of your calculation, you may use the below appendix to summarize each of the strategy. Replenishment Strategy (Heuristic): July Aug. Sept. Oct. Nov. Dec. Jan. Feb. March April May June 1 Beg. Inventory 0 2 Order quantity 3 Number available = (1) + (2) 4 Demand 26 56 33 84 49 79 43 55 35 22 27 23 5 End. Inventory = max[(3)-(4), 0] Revenue: 6 Sales = $30 * min [(3), (4)] Costs: 7 Ordering If (2)>0, = $60 + ($20* (2)), If (2)=0, = 0 8 Shortage = - $7 * min[0, (3)-(4)] 9 Holding = $1 * (5) 10 Total Costs = (7) + (8) + (9) 11 Monthly Profit = (6) - (10) 12 Annual Profit