MHC Ltd. Game. Roberto Cigolini Department of Management, Economics and Industrial Engineering Politecnico di Milano

Transcription

1 MHC Ltd. Game Roberto Cigolini Department of Management, Economics and Industrial Engineering Politecnico di Milano

2 ManHole Covers Ltd. Game 1. Introduction Ms. Morin is the general manager of MHC Ltd., a company that manufactures manhole covers for paving that moved its main plant from the neighbourhood of Chartres (France) to a new production site in Poland. Twice a month, during the summer, Ms. Morin has to define the number of units (and their size) to produce during the following fortnight. To do so, she takes into account the sales trend, the plant production capacity, the inventory on hand, the cost of overtime work and loss of lost sales. Even though the company s production range is much wider, the game is focused only on 18 inch and 36 inch (diameter) manhole covers and you are required to decide what, how many and when to produce every fortnight during the time horizon spanning from March to September, as described below. 2. Sales forecasts Company sales and broadly speaking the sales of the whole sector are affected by a remarkable seasonal factor: according to figure 1, the flow of orders is low in autumn and winter (from October to March), it increases in spring, and maximises in July. Figure 1. Qualitative shape of sales trend January April July October 1

3 Almost 33% of the overall annual sales take place in June and July, and 75% from April to September. However, sales can vary every 2 weeks by 25% as compared to the expected level. Last year, the maximum quantities of 18 inch and 36 inch manhole covers, sold in two weeks, have been 545 and 200 units respectively, whereas the overall sales amounted to 5,600 and 2,100 respectively. Foe the sake of simplicity, orders and deliveries can be assumed to take place every period (i.e. every two weeks). In other words, customers issue orders during the period in which they need the manhole covers and the order is filled within the same time bucket; otherwise, the corresponding sales are lost and no backlog is allowed. Ms. Morin (and you, in the game), do not know the demand in advance: she has to estimate it by following the general trend shown in figure 1 and the sales data of the last year. 3. Production capacity The plant production capacity of the depends on the production mix and it is constrained by the limited machinery flexibility: set up times and costs, and the past experienced suggested to use only four production mixes, with some modifications if overtime is activated, as depicted in table 1. For the sake of simplicity, you can suppose that overtime is activated immediately and it adds 50% production capacity without any loss in productivity. Table 1. Allowed production mixes Regular working hours + 50% overtime 18 inch 36 inch 18 inch 36 inch Costs Inventory holding cost. For each time bucket (a fortnight), the 18 inch manhole covers require 0.2 /piece, including the financial cost, handling and carrying charges and the insurance; 36 inch covers requires 0.6 /piece. Stock out cost. A stock out take place every time the sum of pieces manufactured and inventory on hand is unable to fulfil the demand: e.g. suppose that in a given period are 200 pieces are produced, while 10 are available at the beginning of the period, but demand equals to 220 units; then 220 ( ) = 10 pieces are out of stock cost of 10. So (besides the risk of losing the customer) stock out leads the margin linked to be lost, given that no backlog is allowed. Ms. Morin estimated, on average, a stock out cost for the 18 inch and 36 inch cover, 20 /piece and 60 /piece respective 2

4 ly. Notice that there is a ratio of 100 between stock out cost and inventory holding cost (per piece), which means that each piece lost is worth 100 pieces stocked for 1 time bucket. Overtime cost. The overtime involves a fixed charge of 200, corresponding to the maximum amount available (i.e. 50% of standard work hours). 5. Rules of the game The starting period of the game refers to the first two weeks of March (i.e. when sales are increasing) and the game finishes 7 months later, when sales are dropping in autumn and winter. Players are split into groups and by group at the beginning of each period, players have to define the number of pieces (for each one of the two products) to be manufactured during the same time bucket, according to table 1. Production mixes other than the ones reported in table 1 are not allowed. Each player could take into account the past sales and extrapolate trends, seasonality etc.; others could decide on the bases on their intuition, etc. Once the production mix is decided (for a given time bucket), it should be communicated to the game master. Once all the groups have communicated their decisions (for a given time bucket), the game master will announce the actual sales for that period. Then the players, will be able to calculate the final inventory level, stockout costs (if any), overtime costs, etc. The goal of the game lies in minimizing the overall cost for the entire horizon. To make the calculations easier, you should refer to the attached spreadsheet and follow the steps below. Decide the production mix for the considered period (time bucket), on the basis of table 1. Put these values in columns B (18 inch) and J (36 inch); then check the green light (column W). The initial inventory level has to be put in column C (18 inch) and K (36 inch). These values come from columns F (18 inch) and N (36 inch) of the previous period. Put the overall quantity available in the period (production and initial inventory) in column D (18 inch) and L (36 inch). Ask the game master the actual demands and put them in column E (18 inch) and M (36 inch). Calculate the final inventory level and enter this value in column F (18 inch) and N (36 inch), where: F = D E and N = L M; if the result is negative, put zero. Calculate stock holding costs and put them in column G and O, where G = 0.2 x F and O = 0.6 x N. Calculate the stock outs during the period and put these values in column H (18 inch) and P (36 inch), where H = E D and P = M L]; if H or P are negative, put zero. Calculate stock out costs and display the value in columns I and Q, where I = 20 x H and Q = 60 x P. Calculate the overall stock holding cost of the two products and put this value in column R, where R = G + O. 3

5 Calculate the overall stock out cost and put it in column S, where S = I + Q. In case of overtime, put 1 in column L; otherwise, put zero. Calculate the overall cost of the considered time bucket and put it in column U, where U = R + S x T. Calculate the cumulated overall cost per period and put it in column V. 6. Example Suppose that the initial inventory level on the 1 st March is 40 (18 inch) and 10 (36 inch) and Ms. Morin decides to produce inch manhole covers (column B) and inch manhole covers (column J), so that the overall quantities available correspond to 440 (18 inch) and 70 (36 inch) pieces. Consider now an actual demand of 330 pieces for 18 inch manhole covers and 80 for 36 inch ones: at the end of the period, the unsold products are inch pieces, so column H reports zero, which means that there has not been any out of stock (concerning 18 inch manhole covers) and column G reports 22 (i.e. 0.2 x 110) in. Column I confirms that there has not been any stock out cost for 18 inch manhole covers. However, since the actual demand for 36 inch manhole covers (80 pieces) has been greater than the maximum available quantity (70 pieces, see column L), 10 pieces are out of stock as far as this product is concerned (column P): for this reason, the final 36 inch manhole covers unsold are zero (column N), and the zero value is reported also in column O. Column P reports the 10 pieces out of stock and column Q its corresponding value (i.e. 60 x 10). Column R and S report the total inventory holding cost (G + O = ) and the total stock out cost (I + Q = ) respectively. The total cost of production for the first fortnight of March accounts for 622 (S + R = ). This value is put in column U and also in column V, given that the first time bucket of the horizon is considered. As a consequence, the initial inventory levels at the beginning of the second period (i.e. the second time bucket, corresponding to the second half of March) are 110 pieces (18 inch) and 0 (36 inch), taken from the columns F and N of the previous period. Now Ms. Morin decides to produce inch pieces and inch pieces for the second fortnight of March, without having to resort to overtime. The available quantities are 310 (18 inch) and 120 (36 inch). Consider the actual demand (provided by the game master) to be 140 (18 inch) and 50 (36 inch), so that there is no out of stock. The costs of holding inventory are respectively 34 (0.2 x 200) and 42 (0.6 x 70) and the overall cost of production is 76 (see column U), whereas column V reports 698 (i.e ). 4

6 18 inch 36 inch Sum Production orders (pieces) Initial inventory level (pieces) Initial availability (pieces) Actual sales (pieces) Final inventory level (pieces) Cost of holding stocks ( ) Stock out (quantity) Stock out cost ( ) Production orders (pieces) Initial inventory level (pieces) Initial availability (pieces) Actual sales (pieces) Final inventory level (pieces) Cost of holding stocks ( ) Stock out (quantity) Stock out cost ( ) Cost of holding stocks ( ) Stock out cost ( ) Overtime (boolean) Period (time bucket) Overall cost ( ) Cumulative overall cost ( ) Check March 1st half March 2nd half April 1st half April 2nd half May 1st half May 2nd half June 1st half June 2nd half July 1st half July 2nd half August 1st half August 2nd half September 1st half September 2nd half Total = To be decided by players = To be provided by the game master = Appropriate product mix = Incorrect product mix